Incoherent Clutter Suppression Using Lag-One Coherence

Abstract

The lag-one coherence (LOC), derived from the correlation between the nearest-neighbor channel signals, provides a reliable measure of clutter which, under certain assumptions, can be directly related to the signal-to-noise ratio of individual channel signals. This offers a direct means to decompose the beamsum output power into contributions from speckle and spatially incoherent noise originating from acoustic clutter and thermal noise. In this study, we applied a novel method called lag-one spatial coherence adaptive normalization (LoSCAN) to locally estimate and compensate for the contribution of spatially incoherent clutter from conventional delay-and-sum (DAS) images. Suppression of incoherent clutter by LoSCAN resulted in improved image quality without introducing many of the artifacts common to other adaptive imaging methods. In simulations with known targets and added channel noise, LoSCAN was shown to restore native contrast and increase DAS dynamic range by as much as 10–15 dB. These improvements were accompanied by DAS-like speckle texture along with reduced focal dependence and artifact compared with other adaptive methods. Under in vivo liver and fetal imaging conditions, LoSCAN resulted in increased generalized contrast-to-noise ratio (gCNR) in nearly all matched image pairs (N = 366) with average increases of 0.01, 0.03, and 0.05 in good-, fair-, and poor-quality DAS images, respectively, and overall changes in gCNR from −0.01 to 0.20, contrast-to-noise ratio (CNR) from −0.05 to 0.34, contrast from −9.5 to −0.1 dB, and texture μ/σ from −0.37 to −0.001 relative to DAS.

I. Introduction

ACOUSTIC clutter is widely considered one of the primary sources of image degradation in medical ultrasound. Clutter is commonly described as a temporally stationary haze that reduces the contrast and visibility of underlying structures. Clinically, this translates to the loss or misinterpretation of diagnostic information, limiting the ability of practitioners to perform important clinical tasks. Image degradation by clutter is ubiquitous across medical ultrasound and has negatively impacted its diagnostic efficacy in virtually all applications ranging from echocardiography to fetal sonography [1–4].

Clutter is typically attributed to three primary mechanisms: reverberations among tissue layers, scattering from off-axis structures, and aberrations from heterogeneities in sound speed and attenuation [5]. All three phenomena give rise to perturbations in the backscattered echo wave fronts, which affect the correlations measured between pairs of channel signals received along an ultrasound array, collectively referred to as the spatial coherence. Spatial coherence is sensitive to all major forms of acoustic clutter as well as random thermal noise, making it particularly useful for characterizing and discriminating between backscattered signal and noise [6–10].

Several adaptive imaging methods have been proposed to mitigate the effects of clutter by leveraging the properties of spatial coherence. Minimum variance beamforming methods use measurements of coherence to adaptively suppress backscattered energy from off-axis interference through a constrained optimization of receive apodizations [11], [12]. Methods such as coherence factor (CF) [13], generalized coherence factor (GCF) [14], and phase coherence factor (PCF) [15] use coherence-derived factors to directly weight beamsummed image data and reduce artifacts from weakly coherent off-axis scatter and grating lobes. More recently, groups have explored the use of filtered delay-multiply-and-sum (F-DMAS) methods that incorporate element-wise multiplications of echo signals prior to channel summation as a way to increase beamformer sensitivity to spatial coherence [16], [17]. The application of coherence as a direct source of image contrast has also been explored in methods such as short-lag spatial coherence (SLSC) imaging, which maps the measurements of integrated spatial coherence to pixel brightness as opposed to the envelope detected magnitude displayed in conventional delay-and-sum (DAS) imaging [18–20].

Though effective in reducing the appearance of clutter and improving contrast, existing coherence-based methods face limitations that have impeded their clinical adoption. Many introduce dynamic range alterations that skew intrinsic contrast and, in some cases, increase texture variance [17], [21], [22]. These methods are similarly limited by a tendency to remove signals of interest in regions dominated by clutter. An example of this is the dark region artifact, common to many adaptive imaging methods, which appears when mainlobe energy is removed as a result of aggressive sidelobe suppression [23], [24].

In an attempt to address such limitations, model-based approaches to ultrasound image formation have been proposed to more accurately and more rigorously account for the constituent components of the beamsummed signal. Byram et al. [25] have proposed a method for aperture domain model image reconstruction (ADMIRE), which forms images by decomposing the aperture domain into a series of spatially encoded frequency and amplitude modulated signals and utilizing a subset of these signals for image reconstruction. More recently, Morgan et al. [26] have introduced a technique, termed multicovariate imaging of subresolution targets (MIST), which poses a least-squares problem to estimate and image the contribution of mainlobe echoes to the measured spatial covariance based on the assumed models for speckle and clutter covariance.

Both ADMIRE and MIST have demonstrated promise in reducing clutter without significantly altering native echogenicity of the desired echo signals. However, given their added complexity, i.e., MIST performs a multiparameter regression of spatial covariance and ADMIRE decomposes aperture domain signals into a model-space composed of several hundred to over a million predictors, these methods can require significant computational overhead, limiting their ability to perform in high frame rate, real-time applications [25], [26].

We recently introduced an analytical framework for estimating the contribution of additive spatially incoherent noise in channel echo data from measurements of spatial coherence [10]. In the context of medical ultrasound, spatially incoherent noise has been linked to clutter from sources, such as reverberation, rapidly varying aberrations, and thermal noise [6–10]. In abdominal imaging, incoherent clutter levels have been reported in the range of −13–14 dB relative to backscattered echoes in channel signals [10] and −30–0 dB relative to echoes in beamsummed pixels [4].

Drawing from the principles outlined in our previous article [10], this study presents a novel method, which we term lag-one spatial coherence adaptive normalization (LoSCAN), to estimate the local contributions of speckle and additive incoherent clutter to the DAS output and form images of the speckle-only component. By leveraging simple analytic models for signal-to-noise ratio (SNR) and spatial coherence, this technique aims to provide a computationally efficient means for restoring contrast loss due to incoherent clutter while preserving the grayscale or texture properties of conventional DAS imaging.

This article is organized as follows. In Section II, we introduce the theory that relates speckle and incoherent clutter magnitude to the DAS magnitude. Section III describes the simulation and clinical studies used to evaluate the proposed method. We present the results of this work in Section IV, followed by a discussion of these findings and practical implications in Section V.

II. Theory

A. Beamsum Speckle and Incoherent Clutter Power

In conventional DAS, we can model the beamsum signal as the sum of M channels, each consisting of zero-mean complex Gaussian speckle signal S and additive white noise N. Under these assumptions, the total beamsum power (${\Psi }_{S+N}$) can be defined as

$${\Psi }_{S+N}=\langle {\left|\sum _{i=1}^M\left(S_i+N_i\right)\right|}^2\rangle$$ (1)

where $\langle \cdot \rangle$ denotes the expected value.

For spatially incoherent clutter that is uncorrelated with speckle signal, this expression can be separated into components representing the beamsum speckle (${\Psi }_S$) and incoherent clutter (${\Psi }_N$) powers

$${\Psi }_{S+N}=\langle {\left|\sum _{i=1}^M{S}_i\right|}^2\rangle +\langle {\left|\sum _{i=1}^M{N}_i\right|}^2\rangle ={\Psi }_S+{\Psi }_N.$$ (2)

It follows that the beamsum SNR (SNR_b) is simply:

$${\mathrm{SNR}}_b=\frac{\langle {\left|{\sum }_{i=1}^M{S}_i\right|}^2\rangle }{\langle {\left|{\sum }_{i=1}^M{N}_i\right|}^2\rangle }=\frac{{\Psi }_S}{{\Psi }_N}.$$ (3)

Combining (2) and (3), we arrive at the following equations:

$${\Psi }_S={\Psi }_{S+N}\left(\frac{{\mathrm{SNR}}_b}{1+{\mathrm{SNR}}_b}\right)$$ (4)

$${\Psi }_N={\Psi }_{S+N}\left(\frac{1}{1+{\mathrm{SNR}}_b}\right)$$ (5)

which solve for the constituent speckle and incoherent clutter components of the DAS output power given some estimate of the beamsum SNR.

B. Beamsum SNR

1). Relationship to Channel SNR:

We can further simplify (3) to examine the relationship between the beamsum SNR and the SNR of individual channel signals

$${\mathrm{SNR}}_b=\frac{\langle {\left|{\sum }_{i=1}^M{S}_i\right|}^2\rangle }{\langle {\left|{\sum }_{i=1}^M{N}_i\right|}^2\rangle }=\frac{{\sum }_{i=1}^M{\sum }_{j=1}^M\langle S_i{S}_j^{\ast }\rangle }{{\sum }_{i=1}^M{\sum }_{j=1}^M\langle N_i{N}_j^{\ast }\rangle }$$ (6)

where * denotes the complex conjugate. Normalizing the covariances $\langle S_i{S}_j^{\ast }\rangle$ and $\langle N_i{N}_j^{\ast }\rangle$ by their respective channel signal powers ${\psi }_S$ and ${\psi }_N$

$${\psi }_S=\sqrt{\langle {\left|S_i\right|}^2\rangle \langle {\left|S_j\right|}^2\rangle }=\langle {\left|S\right|}^2\rangle$$ (7)

$${\psi }_N=\sqrt{\langle {\left|N_i\right|}^2\rangle \langle {\left|N_j\right|}^2\rangle }=\langle {\left|N\right|}^2\rangle$$ (8)

we can rewrite (6) in terms of spatial coherence matrices $R_S\left[i,j\right]$ and $R_N\left[i,j\right]$

$$\begin{array}{l}{\mathrm{SNR}}_b=\frac{{\psi }_S{\sum }_{i,j=1}^M{R}_S\left[i,j\right]}{{\psi }_N{\sum }_{i,j=1}^M{R}_N\left[i,j\right]}=\frac{{\psi }_S{\sum }_{i,j=1}^M{R}_S\left[i,j\right]}{{\psi }_N{\sum }_{i,j=1}^{M}I\left[i,j\right]}\\ =\frac{{\psi }_S}{{\psi }_N}\left(\frac{1}{M}\sum _{i,j=1}^M{R}_S\left[i,j\right]\right)\end{array}$$ (9)

where ${\psi }_S$ and ${\psi }_N$ are the channel signal speckle and incoherent clutter powers, respectively, R_S [i, j] is the M × M spatial coherence matrix describing the normalized correlation of speckle between all pairs of receive channels i and j, and R_N [i, j] is the corresponding matrix for incoherent clutter described by an M × M identity matrix under the assumption that N_i and N_j are uncorrelated for all i ≠ j, i.e., spatially incoherent.

Given the following definitions for channel SNR (SNR_c) and beamformer gain (G), which respectively represent the ratios of speckle to incoherent clutter power and speckle to incoherent clutter coherence:

$${\mathrm{SNR}}_c=\frac{{\psi }_S}{{\psi }_N}$$ (10)

$$G=\frac{1}{M}\sum _{i,j=1}^M{R}_S\left[i,j\right]$$ (11)

we arrive at the following expression:

$${\mathrm{SNR}}_b={\mathrm{SNR}}_c\cdot G$$ (12)

which relates the beamsum SNR to the channel SNR through a simple scalar defined by the beamformer gain. The following presents a framework for estimating SNR_c and G and, in turn, SNR_b using measurements of spatial coherence.

2). Spatial Coherence in Incoherent Clutter:

Keeping the same assumptions of zero-mean Gaussian speckle signal S and incoherent clutter N, the spatial coherence between channels i and j can be represented as the normalized correlation

$$R_{S+N}\left[i,j\right]=\frac{\langle \left(S_i+N_i\right){\left(S_j+N_j\right)}^{\ast }\rangle }{\sqrt{\langle {\left|S_i+N_i\right|}^2\rangle \langle {\left|S_j+N_j\right|}^2\rangle }}.$$ (13)

For uncorrelated noise N, this simplifies to

$$R_{S+N}\left[m\right]=\{\begin{array}{ll}1,& m=0\\ \frac{{\mathrm{SNR}}_c}{1+{\mathrm{SNR}}_c}{R}_S\left[m\right],& m\ne 0\end{array}$$ (14)

where m is the spatial separation or lag between channels defined as $m=\left|i-j\right|$, $R_{S+N}\left[m\right]$ is the spatial coherence of speckle signal with contributions from incoherent clutter, and R_S[m] is the speckle-only spatial coherence describing the correlation of speckle in the absence of incoherent clutter. As shown in (14), the effect of spatially incoherent clutter is to introduce a jump discontinuity between lags 0 and 1 whose relative contribution to the total coherence function is determined by a nonlinear scaling of the channel SNR.

3). Estimating Channel SNR:

Considering only the coherence between spatially adjacent channels or the lag-one coherence (LOC), we can solve for the channel SNR in (14)

$${\widehat{\mathrm{SNR}}}_c=\frac{{\widehat{R}}_{S+N}\left[1\right]}{R_S\left[1\right]-{\widehat{R}}_{S+N}\left[1\right]}$$ (15)

where ${\widehat{R}}_{S+N}\left[1\right]$ and R_S[1] represent the measured and theoretical speckle-only LOC, respectively. R_S[1] can be readily derived from the van Cittert–Zernike (VCZ) theorem, which relates the expected spatial coherence of speckle to the autocorrelation of the transmit aperture [27]. In the example of a rectangular aperture, the speckle-only LOC predicted by VCZ theory is 1 − 1 / M, which, for clinically relevant aperture sizes (M ≫ 1), is well-approximated by R_S[1] ≈ 1 [10]. This holds true even more so for compact or point-like targets, where R_S[m] ≈ 1 across all lags.

4). Estimating Beamformer Gain:

Given that R_S is Hermitian symmetric, we can simplify (11) in terms of the 1-D spatial coherence function R_S[m], where

$$G=1+\frac{2}{M}\sum _{m=1}^{M-1}{R}_S\left[m\right]\left(M-m\right).$$ (16)

To evaluate the above-mentioned equation, R_S[m] can be obtained by measuring the coherence function ${\widehat{R}}_{S+N}\left[m\right]$ and rescaling it by a ratio of the theoretical and measured LOC values to remove the discontinuity introduced by incoherent noise

$$\widehat{G}=1+\frac{2}{M}\frac{R_S\left[1\right]}{{\widehat{R}}_{S+N}\left[1\right]}\sum _{m=1}^{M-1}{\widehat{R}}_{S+N}\left[m\right]\left(M-m\right).$$ (17)

To minimize the number of coherence calculations, further simplifications can be made by defining (17) in terms of the coherence factor (CF) [28]. For zero-mean Gaussian speckle signal S and incoherent clutter N,

$$\begin{array}{l}\mathrm{CF}=\frac{\langle {\left|{\sum }_{i=1}^M{S}_i+N_i\right|}^2\rangle }{M{\sum }_{i=1}^M\langle {\left|S_i+N_i\right|}^2\rangle }\\ =\frac{1}{M}+\frac{2}{M^2}\sum _{m=1}^{M-1}{R}_{S+N}\left[m\right]\left(M-m\right).\end{array}$$ (18)

Substituting (18) into (17), we find an equivalent expression for beamformer gain

$$\widehat{G}=1+\frac{R_S\left[1\right]}{{\widehat{R}}_{S+N}\left[1\right]}\left(\widehat{\mathrm{CF}}\cdot M-1\right).$$ (19)

5). Estimating Beamsum SNR:

Together, (15) and (19) provide the equations for estimating the component terms that define beamsum SNR. Plugging these values into (12) and assuming R_S[1] = 1, we arrive at an expression for estimating beamsum SNR using only measurements of $\widehat{\mathrm{CF}}$ and ${\widehat{R}}_{S+N}\left[1\right]$ given the total number of receive elements M

$${\widehat{\mathrm{SNR}}}_b=\frac{{\widehat{R}}_{S+N}\left[1\right]+\widehat{\mathrm{CF}}\cdot M-1}{1-{\widehat{R}}_{S+N}\left[1\right]}.$$ (20)

In practice, a number of steps can be taken to improve the tractability of this estimation problem. Given that (20) is derived from random variables and their expected values, averaging of ${\widehat{R}}_{S+N}\left[1\right]$ and $\widehat{\mathrm{CF}}$ over spatial ensembles can be performed to better approximate their ensemble statistics. We can, furthermore, impose lower bounds on ${\widehat{R}}_{S+N}\left[1\right]$ and $\widehat{\mathrm{CF}}$ to avoid negative estimates of SNR_c and SNR_b, which are physically unrealizable but arise due to noise in the measurement of coherence.

C. Image Formation

Equations (4), (5), and (20) provide a means to solve for and separate the speckle and incoherent clutter components of the DAS output. Among many applications, this analytic framework has promising application in adaptive imaging, where (4) can be used to isolate the backscattered energy of speckle-generating and point-like targets from that of incoherent clutter in order to restore imaging contrast.

Recasting (4) in terms of magnitude and substituting (20) in for SNR_b, we can model the speckle-only magnitude (${\widehat{V}}_S$) at each axial by lateral pixel [z, x] in a DAS image as

$${\widehat{V}}_S\left[z,x\right]=V_{\mathrm{DAS}}\left[z,x\right]\cdot w_S\left[z,x\right]$$ (21)

where V_DAS is the DAS output magnitude equivalent to $\sqrt{{\Psi }_{S+N}}$ and w_S is the weighting factor

$$w_S\left[z,x\right]=\sqrt{\frac{{\widehat{R}}_{S+N}\left[1;z,x\right]+\widehat{\mathrm{CF}}\left[z,x\right]\cdot M-1}{\widehat{\mathrm{CF}}\left[z,x\right]\cdot M}}.$$ (22)

Together, (21) and (22) describe the pipeline for LoSCAN, wherein the speckle signal component of the beamsummed magnitude can be estimated through a pixelwise multiplication of w_S and V_DAS. The result is an image that approximates the appearance of DAS in the absence of spatially incoherent clutter. As ${\widehat{V}}_S$ is an estimate of magnitude, the output of LoSCAN is log-compressed and displayed in the same manner as conventional DAS.

III. Methods

A. Coherence Measurement

LoSCAN was implemented by evaluating (21) and (22) from measurements of ${\widehat{R}}_{S+N}\left[1\right]$ and $\widehat{\mathrm{CF}}$ obtained via

$${\widehat{R}}_{S+N}\left[1;z,x\right]=\frac{1}{M-1}\sum _{i=1}^{M-1}\frac{u_i\left[z,x\right]u_{i+1}^{\ast }\left[z,x\right]}{\left|u_i\left[z,x\right]\right|\left|u_{i+1}\left[z,x\right]\right|}$$ (23)

$$\widehat{\mathrm{CF}}\left[z,x\right]=\frac{{\left|{\sum }_{i=1}^M{u}_i\left[z,x\right]\right|}^2}{M{\sum }_{i=1}^M{\left|u_i\left[z,x\right]\right|}^2}$$ (24)

where M is the total number of receive elements and u_i and u_i+1 are the time-delayed complex in-phase and quadrature (IQ) channel signals received by elements i and i + 1 at spatial location [z, x] [28], [29].

To ensure nonnegative estimates of SNR, ${\widehat{R}}_{S+N}\left[1\right]$ and $\widehat{\mathrm{CF}}$ were spatially averaged prior to calculating w_S. This was performed by way of a 5 × 5 wavelength (λ) rectangular moving average. In addition to spatial averaging, coherence measurements were bounded to maintain minimum values for ${\widehat{R}}_{S+N}\left[1\right]$ and $\widehat{\mathrm{CF}}$ corresponding to SNR_c ≥ −15 dB. Lower bounds were found by evaluating (14) and (18) given SNR_c,min, where

$${\widehat{R}}_{S+N}\left[1;z,x\right]\ge \frac{{\mathrm{SNR}}_{c,\min }}{1+{\mathrm{SNR}}_{c,\min }}$$ (25)

$$\widehat{\mathrm{CF}}\left[z,x\right]\ge \frac{1}{M}+\frac{2\left(M-1\right)}{M^2}\frac{{\mathrm{SNR}}_{c,\min }}{1+{\mathrm{SNR}}_{c,\min }}.$$ (26)

In this study, SNR_c ≥ −15 dB was selected based on previous studies showing significant increases in LOC variance around this range of channel noise levels [9], [10].

B. Field II Simulations

Field II [30], [31] was used to simulate RF channel data for a range of different imaging phantoms. Simulations were performed for a 128-element, 0.5-mm pitch linear array transmitting and receiving at 5 MHz with a 60-mm focus and F/2 focal geometry. For each phantom, simulations were repeated across ten unique speckle realizations, each populated with 15 scatterers per resolution cell. Spatially incoherent clutter was introduced by scaling and adding Gaussian white noise filtered by the transducer bandwidth to each channel.

1). Spatial Averaging:

To characterize the dependence of image quality on spatial averaging of $\widehat{\mathrm{CF}}$ and ${\widehat{R}}_{S+N}\left[1\right]$, simulations were performed for a phantom composed of two vertically oriented layers with −20-dB native contrast. For channel SNRs ranging from −40 to 40 dB, a series of LoSCAN images were formed using coherence values averaged over kernel sizes ranging from a single sample to 65 × 65 λ (1 cm²).

Texture statistics were measured across a 1 cm² region of uniform speckle centered about the focal depth to characterize the dependence of speckle texture on kernel size. For each spatial averaging condition, lateral profiles of the layer phantom within 1 mm of the transmit focus were axially averaged, and average profiles were compared to assess changes in the lateral resolution with different kernel sizes at −10-dB channel SNR.

To summarize these effects on a more clinically relevant target, a matched study was performed for a compact 5-mm cylindrical lesion with −20-dB native contrast. Image quality metrics were obtained at −10-dB channel SNR to examine the tradeoff between lesion contrast and texture with kernel size.

2). Lesion Targets:

To evaluate the performance of LoSCAN under calibrated levels of channel noise, simulations were performed for a series of 5-mm cylindrical lesions with varying native contrast ranging from −30 to 20 dB as well as an anechoic cyst. For channel SNRs ranging from −40 to 40 dB, LoSCAN images were formed using the default 5 × 5 λ kernel size. Image quality metrics were obtained from each lesion to examine the effect of LoSCAN on targets with varying grayscale contrast. For the −20-dB lesion, these metrics were compared with corresponding measurements obtained from matched images for 3-parameter MIST (1λ) [26], F-DMAS [16], GCF (M₀ = 1) [14], and SLSC (Q = 10%, 1λ) [18].

3). Dynamic Range:

To generalize the results from the lesion targets and characterize the dynamic range of LoSCAN, simulations were performed for a lateral grayscale strip similar in design to the one presented in [22]. This phantom consisted of a 10-mm-tall block of scatterers centered about the transmit focus with laterally decreasing echogenicity from 0 to −70 dB at −1 dB per lateral resolution cell. For DAS, LoSCAN, MIST, F-DMAS, GCF, and SLSC, lateral profiles of the grayscale phantom within 5 mm of the transmit focus were averaged. Average profiles were compared to assess differences in the dynamic range of each imaging method at 20-dB channel SNR.

4). Focal Dependence:

To evaluate the focal dependence of LoSCAN images, simulations were performed for a series of tall phantoms embedded with 5-mm cylindrical lesions with −12-, −20-, and −30-dB native contrasts. Under noise-free conditions, matched images for DAS, LoSCAN, MIST, F-DMAS, GCF, and SLSC were generated to compare the performance of each method away from the transmit focus.

5). Dark Region Artifact:

To assess the presence of dark region artifact in LoSCAN images, channel data were simulated for a 60-dB point target embedded in uniform speckle. Under noise-free conditions, matched images for DAS, LoSCAN, MIST, F-DMAS, GCF, and SLSC were generated to compare the performance of each method in the presence of off-axis interference.

C. In Vivo Liver and Fetal Imaging

The clinical feasibility of LoSCAN was evaluated using matched DAS and LoSCAN images generated from channel data acquired from a collection of in vivo liver and fetal targets. All data were collected using a C5-2v curvilinear array on the Verasonics Vantage 256 research scanner (Verasonics, Inc., Kirkland, WA, USA) under Investigational Review Board (IRB) protocols approved by the Duke University Medical Center. Acquisitions were performed with a pulse-inversion imaging sequence using a 2.4-MHz transmit frequency, 60-mm focus, and F/2 focal geometry. Fundamental and harmonic images were formed by taking either the difference or sum of interleaved noninverted and inverted channel data and filtering across the appropriate bandwidth. LoSCAN was performed using coherence estimates averaged over the default 5 × 5 λ kernel size. Details of the in vivo data set used in this study are outlined in Table I.

TABLE I.

Liver and Fetal Data Sets

	# Subjects	# Acquisitions	# Images (fund. & harm.)
Liver	16	93	186
Fetal	9	90	180

Using adjacent regions of uniform speckle as reference, image quality metrics were measured from large vessels in the liver and hypoechoic organs inside and amniotic fluid around the fetus. For each set of matched images, comprising of fundamental and harmonic DAS and LoSCAN images, metrics were calculated using the same regions of interest (ROIs) selected based on the harmonic DAS image.

D. Image Quality Metrics

Image quality was quantified using metrics for contrast (C), texture μ/σ, and contrast-to-noise ratio (CNR) calculated using the following definitions:

$$\text{C}=\frac{{\mu }_{\text{T}}}{{\mu }_{\text{B}}}$$ (27)

$$\mathrm{Texture}\mu /\sigma =\frac{{\mu }_{\text{B}}}{{\sigma }_{\text{B}}}$$ (28)

$$\mathrm{CNR}=\frac{\left|{\mu }_{\text{B}}-{\mu }_{\text{T}}\right|}{\sqrt{{\sigma }_{\text{B}}^2+{\sigma }_{\text{T}}^2}}$$ (29)

where μ is the mean and σ² is the variance of the image magnitude before compression within target (T) and background (B) ROIs of equal shape and area. Note that ROI sizes varied among different in vivo acquisitions based on the available targets within the imaging field of view.

For the same ROIs, measurements of generalized CNR (gCNR) were also obtained using the following formulation:

$$\mathrm{gCNR}=1-\int \min \left\{p_T\left(x\right),p_B\left(x\right)\right\}dx$$ (30)

where p_T(x) and p_B(x) are probability density functions for pixels inside the target (T) and background (B) regions, respectively, approximated using 100 bins across the full dynamic range of the image [32]. gCNR quantifies the separation between p_T(x) and p_B(x) to provide a metric of lesion detectability that is robust to dynamic range alterations. This value has physical meaning and describes the percentage of resolvable pixels given an optimal binary classification threshold, where gCNR = 1 indicates the ability to resolve 100% of pixels within target and background regions and complete separation of p_T(x) and p_B(x).

IV. Results

A. Field II Simulations

1). Spatial Averaging:

Fig. 1 shows plots of the texture statistics of LoSCAN images as a function of channel SNR for ${\widehat{R}}_{S+N}\left[1\right]$ and $\widehat{\mathrm{CF}}$ measurements averaged over kernels ranging from a single sample to 65 × 65 λ in size. At low channel SNRs, variance in the coherence weights w_s degrades texture μ/σ across nearly all kernel conditions. This variance is reduced with increasing channel SNR and kernel size, resulting in texture μ/σ which begins to approach that of DAS.

Fig. 1.

Measured texture μ/σ as a function of channel SNR for DAS and LoSCAN images formed with coherence measurements averaged over kernel sizes ranging from a single sample to 65 × 65 λ (1 cm²). Shaded regions represent the standard error over ten speckle realizations. LoSCAN preserves DAS speckle texture at high channel SNRs and with increased spatial averaging.

LoSCAN images and weights for varying degrees of spatial averaging are shown in Fig. 2(a) for a −20-dB layer at −10-dB channel SNR, with corresponding average lateral profiles plotted in Fig. 2(b). This particular combination of target and noise level was selected based on contrast measurements in Fig. 4(b) to represent conditions where image quality is significantly affected by LoSCAN and, therefore, more sensitive to kernel size. Outside these conditions, differences between DAS and LoSCAN are small, resulting in correspondingly less variation in image quality with differences in spatial averaging.

Fig. 2.

(a) LoSCAN images and corresponding w_S maps formed with varying kernel size for a simulated −20-dB layer at −10-dB channel SNR. DAS and LoSCAN images are displayed with 50-dB dynamic range, while weights are shown on 0–1 scale. LoSCAN is performed by multiplying DAS images with spatially averaged estimates of w_S. (b) Lateral profiles of LoSCAN images for each kernel size averaged across ten speckle realizations, showing no loss in resolution with LoSCAN relative to DAS even with large kernels. Magnitudes are displayed relative to the average of the speckle region at lateral locations x < 0 cm. The lateral extents of each kernel are indicated by colored bars on the x-axis.

Fig. 4.

(a) Matched DAS (top) and LoSCAN (bottom) images of a simulated 5-mm lesion with −20-dB contrast for varying channel noise levels. Images are shown on a 50-dB dynamic range. (b) Measured contrast in DAS and LoSCAN images as a function of channel SNR for 5-mm lesions of varying native contrast. Shaded regions represent the standard error across ten speckle realizations. Native contrast values are given on the right. LoSCAN images recover native contrast at lower channel SNRs relative to DAS.

As shown in Fig. 2(b), lateral profiles at the layer boundary significantly overlap, demonstrating that resolution is maintained with spatially averaged w_S. With single-sample estimation, LoSCAN preserves the lateral profile of DAS with slight improvements in edge definition resulting from incoherent clutter suppression at the boundary. As the spatial averaging kernel is increased, lateral profiles show reduced texture variance without any apparent loss in edge definition or contrast for kernels as large as 10 × 10 λ. In the extreme case of a 65 × 65 λ kernel, both estimation noise as well as the local target dependence of w_s are suppressed. This produces LoSCAN images that locally approach the resolution, texture, and contrast of the uncompensated DAS image, which results in minimal clutter suppression at the layer boundary from 0 to 0.5 cm, consistent with the 1-cm² size of the 65 × 65 λ kernel.

As shown in Figs. 1 and 2, the primary tradeoff introduced by spatial averaging is between clutter suppression and texture statistics. This interaction is well-captured by measurements of contrast, texture μ/σ, CNR, and gCNR for varying kernel size. These metrics are plotted in Fig. 3(a)–(c) for a simulated 5-mm lesion with −20-dB contrast at −10-dB channel SNR when image quality differences before and after LoSCAN are large. Slight decreases in contrast performance are observed for kernel sizes smaller than 5 × 5 λ as a result of high texture variance and decreased model accuracy. Nonetheless, clutter suppression coupled with DAS-like texture statistics yields significant increases in CNR over DAS for all kernels below roughly 30 × 30 λ. The default 5 × 5 λ kernel size used in this study is denoted by circles shown in Fig. 3. At −10-dB channel SNR, this kernel maximizes incoherent clutter suppression in the −20-dB cyst, resulting in a roughly 44% increase in CNR and 0.23 increase in gCNR over DAS. This difference in gCNR suggests a 23% increase in the number of separable pixels between the regions inside and outside the lesion with LoSCAN. Image quality improvements become less obvious as texture statistics degrade with smaller kernels or as target dependence is suppressed by larger kernels.

Fig. 3.

Measured (a) contrast, (b) texture μ/σ, (c) CNR, and (d) gCNR as a function of kernel size for LoSCAN images of a simulated 5-mm lesion with −20-dB native contrast at −10-dB channel SNR. Shaded regions represent the standard error across ten speckle realizations. Increased spatial averaging decreases contrast improvements and improves texture, resulting in an optimal CNR and gCNR around the default 5 × 5 λ kernel size used in this study (circle).

2). Contrast and Texture Statistics:

Matched DAS and LoSCAN images are shown in Fig. 4(a) for the simulated −20-dB lesion under varying levels of channel noise. Results are shown for coherence measurements averaged over 5 × 5 λ kernels. Qualitatively, LoSCAN appears to restore lesion contrast that is lost under noisy imaging conditions. In addition to the improved contrast, images appear to largely retain DAS texture. At 15-dB channel SNR, images before and after LoSCAN appear virtually identical as the magnitude of speckle signal increases above the noise floor.

Fig. 4(b) shows plots of the corresponding measurements of contrast as a function of channel SNR for simulations of an anechoic cyst as well as lesions with native contrasts ranging from −30 to 20 dB. Across all targets, LoSCAN images are able to preserve contrast over a wider range of noise levels compared with DAS. For −20- to 20-dB targets, this results in the recovery of native contrast at significantly lower channel SNRs, while for −30-dB and anechoic targets, similar recovery of the asymptotic DAS contrast is observed. It should be noted that at high SNRs, the performance of LoSCAN is roughly identical to that of DAS, even for −30-dB and anechoic targets, where native contrast is only partially recovered by DAS. This suggests the presence of residual clutter that is not mitigated with LoSCAN.

Fig. 5(a) compares the measured contrast of LoSCAN and other adaptive imaging methods for the −20-dB lesion. LoSCAN effectively matches the performance of MIST, showing similar clutter suppression with changes in SNR and recovery of the expected lesion contrast. F-DMAS, GCF, and SLSC improve contrast at low SNRs but reveal alterations in the dynamic range. This is evidenced by the −25-, −27-, and −7-dB measured contrasts in F-DMAS, GCF, and SLSC images at high SNRs, none of which accurately reflects the −20-dB native contrast of the lesion.

Fig. 5.

Measured (a) contrast and (b) texture μ/σ from a simulated 5-mm lesion with −20-dB contrast for LoSCAN and other methods as a function of channel SNR. Shaded regions represent the standard error across ten speckle realizations. For moderate-to-high channel SNRs, LoSCAN is able to recover the texture and grayscale contrast of the noise-free DAS image. (c) Corresponding matched images at −10-and 10-dB channel SNRs formed with LoSCAN and other adaptive imaging methods. DAS in the noise-free condition (∞ dB) is included for comparison. All images are shown on a 50-dB dynamic range, except for SLSC that is displayed on a 0–1 scale after normalization.

Fig. 5(b) compares the texture statistics between LoSCAN and other adaptive imaging methods. At moderate-to-high channel SNRs, the texture of all methods but LoSCAN deviate from that of DAS, with MIST and SLSC showing higher and F-DMAS and GCF showing lower texture μ/σ relative to that of DAS. Of the adaptive methods, LoSCAN best preserves DAS speckle with μ/σ values that most closely follow the DAS μ/σ over the range of SNRs examined.

Matched images for the different adaptive imaging methods are shown in Fig. 5(c) and illustrate differences in the apparent contrast of the same target under −10- and 10-dB channel SNRs. Visually, LoSCAN appears to best recover the noise-free DAS image with regard to both grayscale contrast and speckle texture.

3). Dynamic Range:

The output dynamic range at 20-dB channel SNR is plotted in Fig. 6 for each adaptive imaging method. The + symbols highlight results specifically for a −20-dB input magnitude for comparison with contrast measurements shown in Fig. 5(a). Consistent with results shown in Fig. 5(a), F-DMAS, GCF, and SLSC show stretching and compression of the dynamic range, which results in output magnitudes that either overshoot (SLSC) or undershoot (F-DMAS and GCF) the expected linear intensity gradient of the simulated phantom. Meanwhile, MIST and LoSCAN not only preserve this gradient but also do so over a wider range of echogenicities compared with DAS. In this example, LoSCAN is observed to yield an effective 10–15-dB increase in dynamic range over DAS.

Fig. 6.

Measured dynamic range at 20-dB channel SNR for LoSCAN and other adaptive imaging methods averaged across ten speckle realizations. The true intensity gradient of the simulated grayscale phantom is indicated by the black line. MIST and LoSCAN show output magnitudes that more closely follow the ground truth compared with DAS and other adaptive methods.

4). Focal Dependence:

Fig. 7 highlights the differences in the depth-of-field between LoSCAN and other adaptive imaging methods. Under conditions with no added clutter, adaptive methods generate artifact away from the 60-mm transmit focus in the form of dropouts, increased texture variance, and loss of signal. Of the adaptive methods, focal degradation appears to be least severe in LoSCAN, which shares the same appearance as DAS everywhere but above roughly 30-mm depth where focusing errors begin to affect LOC. Image quality measurements at 25-mm depth shown in Fig. 7(b) reveal that LoSCAN closely maintains DAS texture and does not significantly skew the target contrast when imaging away from the transmit focus.

Fig. 7.

(a) Matched images of simulated −20-dB lesions above the 60-mm transmit focal depth formed with LoSCAN and other adaptive imaging methods. All images are shown on a 70-dB dynamic range, except for SLSC that is displayed on a 0–1 scale after normalization. (b) Contrast and texture μ/σ measured at 25-mm depth (dotted white) for −12-, −20-, and −30-dB lesions. Error bars represent the standard error over ten speckle realizations. Away from the focus, adaptive methods show distorted contrast and degraded texture statistics. These artifacts appear less severe in LoSCAN.

5). Dark Region Artifact:

Fig. 8 shows matched images of a 60-dB point target in uniform speckle formed with each adaptive imaging method. MIST, F-DMAS, GCF, and SLSC, which are more sensitive to off-axis interference, produce artifactual dropouts in regions containing high levels of sidelobe energy. This artifact is not observed with LoSCAN, which appears identical to DAS under the conditions examined in this example.

Fig. 8.

Matched images of a simulated 60-dB point target in uniform speckle formed with LoSCAN and other adaptive imaging methods. All images are shown on a 80-dB dynamic range, except for SLSC that is displayed on a 0–1 scale after normalization. Dark region artifacts appear in all images but DAS and LoSCAN.

B. In Vivo Imaging

Fig. 9 compares image quality metrics before and after LoSCAN for fundamental and harmonic in vivo images of liver vessels [see Fig. 9(a)–(d)] and fetal structures [see Fig. 9(e)–(h)]. LoSCAN images demonstrate consistent image quality improvements over DAS with 98.4% of liver and 93.9% of fetal images showing increased CNR and 91.9% of liver and 95% of fetal images showing increased gCNR.

Fig. 9.

Comparison of image quality metrics measured from hypoechoic structures in matched pairs of (a)–(d) liver and (e)–(h) fetal images before and after application of LoSCAN. Results are shown for fundamental and harmonic images obtained from 93 liver and 90 fetal acquisitions. Points above (blue) and below (gray) the diagonal indicate increased versus decreased performance of LoSCAN relative to DAS with the percentage of points above the diagonal given in the top-left corner. Dashed gray lines in (d) and (h) denote the boundaries defining good, fair, and poor DAS image qualities. Contrast improvements and moderate decreases in texture μ/σ with LoSCAN yield consistent increases in CNR and gCNR across in vivo liver and fetal images.

In Table II, changes in gCNR with LoSCAN are broken down based on DAS image quality. Images were classified into distinct categories based on the measured gCNR in DAS with gCNR > 0.85 representing good, 0.7 ≤ gCNR ≤ 0.85 representing fair, and gCNR < 0.7 representing poor image quality. Table II shows average overall increases in gCNR of 0.01, 0.03, and 0.05 in good-, fair-, and poor-quality DAS images, respectively. As expected, image quality improvements with LoSCAN are observed to be greater in poor-quality DAS images where the margin for improvement is greater.

TABLE II.

gCNR Improvements With LoSCAN for DAS Images of Varying Quality

		Liver	Fetal	Overall
Good	Mean	0.01	0.01	0.01
	Range	[−0.01, 0.06]	[−0.01, 0.06]	[−0.01, 0.06]
Fair	Mean	0.02	0.04	0.03
	Range	[−0.01, 0.08]	[−0.01, 0.14]	[−0.01, 0.14]
Poor	Mean	0.03	0.07	0.05
	Range	[−0.01, 0.16]	[0.01, 0.20]	[−0.01, 0.20]

Pairs of matched in vivo DAS and LoSCAN images for both fundamental and harmonic imaging are included in Figs. 10 and 11. Clutter suppression with LoSCAN is observed to improve the contrast of liver vessels in Fig. 10 and amniotic fluid in Fig. 11. Across all examples, the speckle texture, grayscale, and general appearance of coherent structure are well preserved with no observable losses in resolution with 5 × 5 λ spatial averaging of coherence measurements.

Fig. 10.

Example fundamental and harmonic in vivo liver images (top) before and (bottom) after LoSCAN with corresponding measurements of C, CNR, and gCNR calculated from ROIs outlined in dashed white. All images are shown on a 70-dB dynamic range.

Fig. 11.

Example fundamental and harmonic in vivo fetal images (top) before and (bottom) after LoSCAN with corresponding measurements of C, CNR, and gCNR calculated from ROIs outlined in dashed white. All images are shown on a 70-dB dynamic range.

V. Discussion

A. Reduced Artifact

The method for clutter suppression proposed in this study represents a conservative approach that compensates exclusively for channel noise captured by LOC. As LOC is tuned to measure the contribution of spatially incoherent clutter, this method is largely insensitive to coherent and partially coherent forms of clutter, which decorrelate more slowly across the array. These spatially correlated sources of clutter include tilted phase fronts generated by scatterers located slightly off-axis, slowly varying aberrations caused by bulk sound speed errors, and defocusing away from the transmit focus [33], [34].

In the context of image formation, restriction of the proposed estimation problem to lag one presents a number of advantages. Given that speckle signal itself is partially correlated, the task of discriminating between speckle and partially coherent clutter can be challenging. This is evidenced by the artifacts common to existing adaptive imaging methods, which are designed to suppress partially coherent off-axis interference. Such artifacts include the loss of speckle texture in F-DMAS and GCF [14], [17], depth-of-field limitations in MIST, F-DMAS, GCF, and SLSC [26], [34], [35], and dark region artifacts, as shown in Fig. 8. LoSCAN, which does not derive contrast from higher lags that are sensitive to correlated clutter, reduces the likelihood of such artifacts. This enables better preservation of DAS speckle [see Fig. 5(b)], a decreased focal dependence (see Fig. 7), and a reduced potential for dark region artifacts (see Fig. 8) compared with other coherence-based methods.

An obvious tradeoff, however, is the inability for LoSCAN to characterize and eliminate noise from partially coherent clutter. Under conditions where the spatial correlation length of clutter exceeds lag-one, minimal decreases in LOC are expected, resulting in high w_S values and poor suppression of the cluttered DAS output. This intuition is supported by contrast measurements of the −30-dB and anechoic lesions shown in Figs. 4(b) and 7(b). At high channel SNRs when off-axis scatter from nearby structures is the dominant source of clutter inside these lesions, LoSCAN yields almost no improvement in contrast over DAS, a trend consistent with the partial coherence of off-axis scatter and the decreased sensitivity of LOC to correlated clutter. This effect is expected to be most pronounced in weakly echogenic targets, where the relative contribution of off-axis clutter to the beamsum is greater. Although native contrast cannot be fully recovered in such targets, it should be noted that LoSCAN still demonstrates the same ability to suppress incoherent clutter and improve contrast at low channel SNRs.

B. Preserved Grayscale Contrast

Dynamic range alterations are a well-known drawback of many adaptive imaging methods [21], [22], [24]. The negative effects of such alterations are demonstrated in Fig. 5(a), which shows measured contrast values in F-DMAS, GCF, and SLSC that significantly deviate from the −20-dB native contrast of the simulated lesion. Measurements of the dynamic range shown in Fig. 6 help to generalize these findings to a broader range of targets, where deviations in the output magnitude for a given input echogenicity can be used to infer expected differences between the apparent and native contrasts of targets for a given imaging method [22]. In Fig. 6, this relationship is well-illustrated by the output magnitudes of F-DMAS, GCF, and SLSC at −20-dB input echogenicity (indicated by +), which show the same overshooting and undershooting behavior as corresponding measurements of contrast in Fig. 5(a). Although dynamic range measurements do not directly translate to lesion contrast, given differences in off-axis scattering and the target dependence of adaptive imaging methods, they nonetheless provide a means to more broadly characterize the relative contrast behavior of different methods across a wide range of target echogenicities.

Deviations from the ideal one-to-one mapping between true target echogenicity and beamformer output magnitudes suggest that the same distortions in contrast that are observed in F-DMAS, GCF, and SLSC images of the −20-dB lesion in Fig. 5(a) can be expected across a wide range of targets. For both F-DMAS and GCF, input–output curves show a negative bias starting at roughly −10 dB, suggesting that artifactual increases in contrast with F-DMAS and GCF are expected in other hypoechoic targets, particularly those with high native contrast. Dynamic range alterations are even more severe in the case of SLSC, which has an input–output curve that shows little to no overlap with the ideal, indicating loss of native contrast across virtually all targets. Such findings are consistent with those of previous studies [21], [22], which examine the influence of dynamic range alterations across several state-of-the-art adaptive imaging methods.

By employing an analytic model to relate clutter and speckle power, LoSCAN seeks to appropriately estimate and remove the contribution of incoherent clutter without altering the underlying speckle magnitude. Under simulated conditions that follow the assumptions of the model presented in (21), LoSCAN is able to restore contrast lost to incoherent clutter without distorting the intrinsic echogenicity of imaging targets. This is supported by contrast measurements shown in Fig. 4 and dynamic range curves shown in Fig. 6, which reveal significant overlap between the input–output responses of LoSCAN and the ideal. The extent of this overlap in Fig. 6, furthermore, demonstrates that LoSCAN is able to preserve grayscale contrast over a broader range of echogenicities than DAS, with performance comparable to that of the more computationally complex MIST method. Together, these results provide evidence that, unlike in many existing adaptive imaging methods, image quality improvements with LoSCAN are primarily attributed to an extended dynamic range and preservation of native contrast in the presence of incoherent clutter, rather than stretching or compression of the dynamic range.

C. Preserved Texture in Noise

The ability to perform model estimation by applying a series of scalar weights to DAS presents several advantages to LoSCAN, which are not shared by existing model-based methods. Under the assumption that clutter magnitudes are slowly varying in space, ${\widehat{R}}_{S+N}\left[1\right]$ and $\widehat{\mathrm{CF}}$ can be spatially averaged to improve model accuracy and reduce estimation variance. An expected consequence of such averaging is a loss of imaging resolution as the estimated weights are blurred across targets. However, by decoupling coherence weights from the DAS image in (21), the subsequent scaling of the DAS output by w_S in LoSCAN is shown to effectively preserve the original imaging resolution, as illustrated by lateral profiles in Fig. 2. This result is expected since the DAS magnitude V_DAS in (21) preserves the high spatial frequency information. In the case of the direct estimation task, in which all model estimates are derived from kernel averages, such aggressive averaging is impractical given the resultant loss in spatial resolution in the final image [26].

As shown in Fig. 1, spatial averaging provides an effective means to stabilize texture statistics under noisy imaging conditions. Among the methods examined in this study, LoSCAN most effectively maintains DAS texture in the presence of channel noise [Fig. 5(b)]. The ability to perform model estimation over large kernel sizes, furthermore, provides a means to more accurately estimate the ensemble statistics used to derive LoSCAN. This is demonstrated in Figs. 2 and 3(a) by contrast measurements, which show better recovery of the native contrast with LoSCAN as the kernel size is increased from a single sample to 5 × 5 λ.

While imaging resolution is preserved in LoSCAN with large kernels, it is important to note that there remains a tradeoff between spatial averaging and the contrast improvements achieved as weights are blurred across targets. Ultimately, this leads to a decreased ability for LoSCAN to recover contrast in targets on the order of or smaller than the kernel size [see Figs. 2(b) and 3(a)]. Additional work is needed to explore alternative approaches for improving the robustness of LoSCAN that better maintain the resolution of coherence weights. This may include the incorporation of higher lag coherences to improve the estimation of LOC or preprocessing steps, such as subaperture beamforming to reduce noise prior to coherence estimation [36]. The decoupling of model weights from the DAS output furthermore enables the use of higher order image processing techniques, such as median filtering [37], nonlocal means filtering [38], and region growing algorithms [39] to denoise coherence estimates without significant resolution loss. As LoSCAN is SNR dependent, SNR-adaptive w_S processing may also be used to dynamically optimize between coherence texture and resolution by increasing kernel size under low SNRs and decreasing kernel size under high SNRs when w_S values universally approach 1.

D. Clinical Feasibility

As evidenced by in vivo images shown in Figs. 10 and 11, the characteristics of LoSCAN translate well to realistic imaging conditions. Across the majority of image pairs, LoSCAN exhibits notable improvements over DAS that can be attributed to: 1) increased contrast in hypoechoic regions due to incoherent clutter suppression and 2) preservation of DAS-like speckle and grayscale contrast in the surrounding tissue. Figs. 10(h) and (j) and 11(h) and (j) include examples where these improvements are more subtle and serve to illustrate in vivo conditions that are consistent with simulations in which low levels of incoherent clutter result in minimal change in image quality with LoSCAN.

Quantitatively, these characteristics are well-captured by measurements of contrast, texture μ/σ, CNR, and gCNR shown in Fig. 9. Image quality metrics demonstrate that LoSCAN is able to recover contrast in the presence of clutter from both reverberation and aberration, revealing contrast improvements across all 186 liver and 180 fetal fundamental and harmonic images. Despite native tissue echogenicity being unknown in vivo, the observed increases in the measured contrast are expected given the selection of primarily hypoechoic imaging targets in this study. Based on the simulation results shown in Figs. 4 and 6, the apparent contrast of in vivo LoSCAN images is expected to more accurately reflect the native contrast of tissue.

In combination with small changes in texture μ/σ, improvements in contrast yield net increases in both CNR and gCNR across the majority of in vivo images with average increases of 0.04 and 0.07 in CNR and 0.02 and 0.03 in gCNR for liver and fetal targets, respectively. Although average improvements in CNR and gCNR are modest, this magnitude of change is consistent with the conservative processing of LoSCAN, which places heavy emphasis on the preservation of DAS texture and grayscale contrast. Combined with the fact that LoSCAN acts as an all-pass filter under high SNR conditions, image quality changes are expected to be less significant in LoSCAN compared with other adaptive methods, which more aggressively enhance contrast or smooth speckle texture, at the expense of generating images that vastly differ in appearance from those used clinically.

The conservative nature of LoSCAN is similarly conveyed by the ranges of CNR and gCNR improvement shown in Fig. 9. Across all targets and subjects examined in this study, differences in CNR and gCNR going from DAS to LoSCAN span from −0.05 to 0.34 and −0.01 to 0.2, respectively, both revealing lower bounds very close to zero. As quantified by gCNR, this range of image quality change suggests that LoSCAN at best yields significant gains in target detectability (up to a 20% increase in the number of separable pixels relative to DAS) and at worst produces images that are of similar or equal quality to DAS (1% decrease in the number of separable pixels relative to DAS). This is a promising result, one which supports the potential for LoSCAN as a method to improve DAS quality without introducing a substantial risk of image degradation.

With respect to clinical feasibility, in vivo results demonstrate promise in the application of LoSCAN for clinical imaging, where the ability to preserve DAS-like appearance and avoid severe artifact can often be of equal or even greater importance than any clutter suppression achieved with adaptive imaging methods. Given these preliminary findings, large-scale clinical and reader studies should be conducted to establish whether the unique properties of LoSCAN and the increases in quantitative metrics observed in this study translate to clinical utility.

E. Practical Implementation

Finally, it should be emphasized that LoSCAN represents a method to achieve similar image quality as more advanced model-based techniques but at a fraction of the computational cost. A comparison of computational throughput is included in Table III for LoSCAN and single-sample SLSC implemented using the same MATLAB script for calculating spatial coherence. Benchmarks are given as the total number of pixels computed per millisecond (pixels/ms) for a 128-element array and represent averages over 50 repeated runs on a 3.4-GHz Intel i7-3770 processor. Note that benchmarks in Table III were taken after the application of time delays and, therefore, reflect the throughput of any overhead that is required in addition to receive focusing. For reference, the factor of improvement compared with SLSC using a 20% short-lag value (Q) is provided below each benchmark.

TABLE III.

Computational Throughput of Spatial Coherence Methods

	LoSCAN (5×5 λ)	LOC	SLSC (Q = 10%)	SLSC (Q = 20%)	SLSC (Q = 30%)
pixels/ms	28.8	29.6	5.5	2.6	1.3
	11.1×	11.4×	2.1×	1×	0.5×

Consistent with the single-lag coherence estimate (i.e., LOC) used in LoSCAN and the multi-lag estimates required for SLSC, the computational speed of LoSCAN is observed to be as much as an order of magnitude higher than SLSC for common short-lag values. As previous studies have demonstrated pulse-inversion SLSC imaging with frame rates up to 32 Hz [40], [41], results in Table III suggest that similar, if not improved, real-time performance can be readily achieved with LoSCAN. The reduced complexity furthermore shows promising application of LoSCAN to 3-D imaging, where the overhead in processing high channel count matrix arrays using existing model-based methods would otherwise be prohibitive.

As LoSCAN uses the same coherence calculations as SLSC, efficient strategies that have been developed for SLSC can be similarly leveraged to reduce the complexity of LoSCAN. Besides code optimizations and implementation on parallel architectures, preprocessing steps, such as array sparsing or subaperture beamforming, can be applied to further reduce the number of correlation calculations [29]. Likewise, the principles of acoustic reciprocity may be leveraged to eliminate the need for channel data and enable the calculation of w_S from beamsummed image data [42]. Such modifications are expected to introduce tradeoffs in texture variance and model accuracy, which may be explored in future work.

VI. Conclusion

In this study, we introduced a novel model-based image compensation method termed LoSCAN that applies pixelwise measurements of spatial coherence to estimate and remove the contribution of spatially incoherent clutter from DAS. This method was evaluated across a wide range of simulated and in vivo conditions with comparison to existing adaptive imaging methods. LoSCAN was shown to recover contrast under cluttered conditions without introducing major artifacts or changes in dynamic range or texture. By retaining the appearance of conventional DAS, this method seeks to minimize the overhead required for its clinical adoption, including additional training on the part of clinicians and sonographers or the redesign of technologies that interface with clinical images, such as commercial postprocessing algorithms. In combination with its low computational cost, LoSCAN shows promise as a clinically viable technique to improve ultrasonic image quality in the presence of incoherent clutter.

Biographies

Will Long received the B.S. degree in biomedical engineering from the University of Rochester, Rochester, NY, USA, in 2013. He is currently pursuing the Ph.D. degree in biomedical engineering with Duke University, Durham, NC, USA.

His current research interests include adaptive imaging and image quality characterization.

Nick Bottenus received the B.S.E. degree in biomedical engineering and electrical and computer engineering and the Ph.D. degree in biomedical engineering from Duke University, Durham, NC, USA, in 2011 and 2017, respectively.

He worked as a Research Scientist of biomedical engineering at Duke University from 2017 to 2019. He is currently an Assistant Professor of mechanical engineering with the University of Colorado Boulder, Boulder, CO, USA, developing methods for performing large aperture ultrasound imaging and improving image quality through beamforming.

Gregg E. Trahey (Member, IEEE) received the B.G.S. and M.S. degrees from the University of Michigan, Ann Arbor, MI, USA, in 1975 and 1979, respectively, and the Ph.D. degree in biomedical engineering from Duke University, Durham, NC, USA, in 1985.

He served in the Peace Corps from 1975 to 1978 and was a Project Engineer at Emergency Care Research Institute in Plymouth Meeting, Pennsylvania, PA, USA, from 1980 to 1982. He is currently a Professor with the Department of Biomedical Engineering, Duke University and holds a secondary appointment with the Department of Radiology, Duke University Medical Center. His current research interests include adaptive beamforming and acoustic radiation force imaging methods.