Sub-aperture Processing Based Adaptive Beamforming for Photoacoustic Imaging

Abstract

Delay-and-sum (DAS) beamformers when applied to photoacoustic (PA) image reconstruction produces strong sidelobes due to the absence of transmit focusing. Consequently, DAS PA images are often severely degraded by strong off-axis clutter. For pre-clinical in vivo cardiac PA imaging, the presence of these noise artifacts hampers the detectability and interpretation of PA signals from the myocardial wall, crucial for studying blood-dominated cardiac pathological information and to complement functional information derived from ultrasound imaging. In this paper, we present photoacoustic sub-aperture processing (PSAP), an adaptive beamforming method, to mitigate these image degrading effects. In PSAP, a pair of DAS reconstructed images is formed by splitting the received channel data into two complementary non-overlapping sub-apertures. Then, a weighting matrix is derived by analyzing the correlation between sub-aperture beamformed images and multiplied with the full-aperture DAS PA image to reduce sidelobes and incoherent clutter. We validated PSAP using numerical simulation studies using point target, diffuse inclusion and microvasculature imaging and in vivo feasibility studies on five healthy murine models. Qualitative and quantitative analysis demonstrate improvements in PAI image quality with PSAP when compared to DAS and coherence factor weighted DAS (DAS_CF). PSAP demonstrated improved target detectability with higher generalized contrast-to-noise (gCNR) in vasculature simulations where PSAP produces 19.61 % and 19.53 % higher gCNR than DAS and DAS_CF, respectively. Furthermore, PSAP provided higher image contrast quantified using contrast ratio (e.g., PSAP produces 89.26 % and 11.90 % higher contrast ratio than DAS and DAS_CF in vasculature simulations) and improved clutter suppression.

I. Introduction

Photoacoustic imaging (PAI) is an evolving non-invasive medical imaging modality which generates optically induced ultrasound (US) images to characterize tissue optical absorption [1]. PAI has shown the potential to complement US imaging by adding molecular sensitivity to US anatomical information [1]. Due to its sensitivity to endogenous chromophores such as oxygenated (HbO₂) and deoxygenated hemoglobin (Hb), PAI measures oxygen saturation (%sO₂) in blood vessels to characterize physiological status (e.g. ischemia, hypoxia or hypoxemia) [2, 3]. PAI has been utilized extensively for both clinical [1, 2] and pre-clinical applications [4–8].

For typical photoacoustic (PA) integrated US imaging systems, acoustic waves generated by rapid thermal expansion of tissue induced through pulsed optical irradiation are detected by US array transducers [9]. Image reconstruction or beamforming algorithms use received channel data to form PA images. For its simplicity and speed, delay-and-sum (DAS) is the most common beamforming algorithm utilized. However, DAS has some undesirable characteristics such as wider main lobes, higher sidelobe levels and incoherent clutter that reduce image quality [10–12]. DAS is particularly unsuitable for PA due to absence of transmit (Tx) focus which increases sidelobe induced off-axis clutter.

Adaptive beamforming methods have been reported in the peer-reviewed literature for the reduction of these artifacts [12–15]. State-of-the-art adaptive beamforming approaches include, use of machine learning (ML), data driven adaptive beamforming (e.g., minimum variance (MV), iterative reconstruction and coherence based beamformers (e.g., short-lag spatial coherence). MV beamforming uses aperture apodization weights that are adaptively calculated to reduce off-axis contributions [12]. We have previously shown that MV beamforming does not improve in vivo cardiac PAI quality [16]. Park et al. [17] proposed a delay-multiply-and-sum (DMAS) algorithm [18] where time delayed PA signals in aperture domain are combinatorically coupled and multiplied before summation to enhance signal coherence non-linearly thus gaining higher image contrast. Mozaffarzadeh et al. [19] introduced a double stage DMAS algorithm where DAS terms in signal coherence estimation were replaced with DMAS terms. This approach showed improvement in terms of signal-to-noise ratio (SNR) and image contrast when compared to conventional approaches. Kirchner et al. demonstrated the applicability of DMAS for multi-spectral PAI by proposing a signed DMAS method where sign of DAS beamformer is preserved to ensure linearity of the reconstructed results [20].

Several variations of MV and DMAS have also been reported in literature [13–15, 21–24]. Ma et al. proposed Multiple DAS with Enveloping algorithm where they suppressed sidelobe artifacts by calculating the whole N-shaped PA signal for each pixel [25]. Use of iterative reconstruction methods employing signal sparsity and low-rankness have also been reported [26–30]. All these methods improve image quality by adopting sophisticated data statistics and models with a high computational burden [31]. Recently, ML based algorithms that achieve image quality improvement while maintaining low computational burden have gained momentum [31]. ML models have been used to address PAI issues such as limited view [31–35], adaptive beamforming [36, 37], reflection artifact removal [38, 39] and expanding penetration depth [40]. However, most reported ML models were trained on synthetic data tuned for these specific problems thus generalizability of these methods when applied to in vivo imaging requires further investigation.

Another class of beamforming algorithm utilized to improve PAI quality employ coherence analysis of received channel data termed as coherence factor (CF). Park et al. [12] calculated CF weighting as a ratio of the coherent to incoherent sum of received channel data and weighted MV beamforming to obtain better performance than DAS for point target and inclusion phantoms. Zemp et al. [41] used CF for PAI of microvasculature with a high-frequency array. Robustness of CF calculations was improved by Wang et al. by incorporating local channel SNR [42]. Several variations in CF calculation such as sign coherence factor for high frequency annular-array PAI [43], eigen-space MV beamforming [22][44][45], CF weighting using DMAS and MV respectively for coherence calculation have also been reported. Another popular coherence-based beamformer is the Short-lag spatial coherence (SLSC) beamformer where spatial correlation of channel data at short lag values are utilized to generate PA images [46–49]. SLSC has shown remarkable image quality improvement when applied to PA-based surgical guidance [4, 50–52]. However, SLSC image contrast stems from spatial correlation of channel data rather than optical absorption of imaged tissue which is detrimental when multi-wavelength PAI is used for spectral unmixing to estimate blood oxygenation. Recently, we have extended CF calculations into the spatiotemporal domain and showed improved image quality over DAS and MV for in vivo cardiac PAI [16, 53]. However, further in vivo investigation revealed that CF weighting may also lead to undesirable signal suppression from the myocardial wall during sidelobe suppression. Furthermore, most of the reported adaptive methods [12, 16, 21, 22, 43, 44, 53] have shown performance improvement for coherent targets than DAS but for diffuse scattering arising from constructive or destructive interference of spatially distributed optical absorbers [54], they tend to suppress the signal of interest.

Optimal image reconstruction should recover both coherent and diffuse PA signals while suppressing clutter. To this end, in this paper, we propose an image formation method based on sub-aperture processing to preserve DAS amplitude levels for myocardial wall PA signals while achieving sidelobe and clutter suppression like CF based beamformers. Here, the received channel data are first split into two non-overlapping sub-apertures as in dual apodization with normalized cross-correlation (DAX) [55] and acoustic sub-aperture processing (ASAP) [56] developed for B-mode and contrast enhanced ultrasound (CEUS) imaging respectively. A pair of sub-aperture PA images were then reconstructed using the DAS algorithm. Amplitude and phase correlation of the sub-aperture PA images were derived to form a weighting matrix to suppress sidelobe and clutter signals. Finally, the full-aperture DAS image was weighted using the weighting matrix to generate a PA sub-aperture (PSAP) image. In [57] ASAP was coupled with spatiotemporal filtering and temporal correlation estimation to improve the contrast-enhanced PAI. A limited ex vivo study was performed using DAX on contrast-based PAI [58]. In PSAP, we utilize the spatial correlation function derived from sub-aperture beamformed images to enhance non-contrast PAI where optical contrast is attributed to endogenous chromophores in vivo.

Three main contributions are reported in this paper. First, PSAP is proposed and extensive hybrid simulation studies using point target, diffuse inclusion and microvascular imaging are presented for validation. Second, parametric studies for PSAP are carried out to provide guidance for optimal algorithmic parameter selection for in vivo PAI applications. Third, in vivo feasibility of PSAP is demonstrated for single wavelength pre-clinical murine cardiac PAI by comparing performance against DAS and DAS_CF in an objective manner.

II. Conventional Methods in PA Image Reconstruction

A. Delay and Sum (DAS)

Commercial clinical and pre-clinical PAI systems use DAS beamforming to perform real-time image formation. The DAS beamformer first delays received PA signals considering one-way signal propagation times between each transducer element and an observation point in an image and then sums the delayed signals across the entire array. Thus, the reconstructed image is dynamically focused in receive.

Let X(t) = [x₁(t — τ₁) ; …… ; x_M(t — τ_M)] represent the received time-delayed PA channel data from a M-element linear array with the time delay of element m denoted by τ_m. DAS beamformation is defined as:

$$DAS(t)=\mathbf{W}{(t)}^H\mathbf{X}(t)$$ (1)

where W(t) denotes an aperture weighting vector. Here, uniform aperture weighting was used, and W(t) is a vector of ones resulting in non-adaptive beamforming. Note that τ_m is also a function of time due its variation with depth during dynamic receive beamforming.

B. Coherence Factor Weighted DAS (DAS_CF)

Coherence factor [12, 59] weighted DAS calculates a pixel-by-pixel weighting matrix as a ratio of the coherent sum to incoherent sum of time-delayed PA channel data X(t):

$$CF(t)=\frac{\left|\underset{m=1}{\overset{M}{\Sigma }}{x}_m(t-{\tau }_m)\right|}{M\underset{m=1}{\overset{M}{\Sigma }}{|x_m(t-{\tau }_m)|}^2}$$ (2)

Equation (2) illustrates that CF evaluates spatial coherence of channel data operating in the aperture domain. The estimated weighting matrix is multiplied to the DAS beamformed image resulting in CF weighted DAS (DAS_CF) as presented below:

$$DA{S}_{CF}(t)=CF(t)\times DAS(t)$$ (3)

III. Photoacoustic Sub-aperture Processing (PSAP)

A. Beamforming with Sub-aperture

For PSAP, using the same received time-delayed PA channel data X(t), two set of images, S₁(t) and S₂(t) are reconstructed using two non-overlapping sub-apertures with no common elements denoted by the vectors W₁(t) and W₂(t) [55, 56, 60–66]. Sub-aperture reconstructed images are represented using the following equations.

$$\begin{gathered} {\mathbf{S}}_1(t)={\mathbf{W}}_1{(t)}^H\mathbf{X}(t) \\ {\mathbf{S}}_2(t)={\mathbf{W}}_2{(t)}^H\mathbf{X}(t) \end{gathered}$$ (4)

To construct W₁(t) and W₂(t) we follow an approach reported in [55]. W₁(t) is made of ones and zeros with an alternating pattern of N elements on and N elements off. W₂(t) is complementary to W₁(t) and uses the opposite alternating pattern of N elements on and N elements off. An example of sub-apertures W₁(t) and W₂(t) formed with 4-4 alternating element pattern is shown in Figure 1. Here, we assume that any signal from on-axis main lobe will be highly correlated between S₁(t) and S₂(t) while off-axis interfering signals such as sidelobe and incoherent clutter will be decorrelated [55, 60]. Therefore, quantifying the similarity between S₁(t) and S₂(t) will enable determination of a weighting matrix for DAS PA to suppress sidelobe and incoherent clutter. A schematic diagram for PSAP is presented in Fig. 2. Seo et al. [55] used a similar approach for ultrasound B-mode images and Stanziola et al. [56] later extended the approach for CEUS. Here, we demonstrate that this approach results in significant clutter reduction in PA.

Fig. 1.

Sub-aperture W₁(t) and W₂(t) formed with 4-4 alternating element pattern.

Fig. 2.

Schematic diagram presenting the PSAP method.

B. Weighting Matrix Generation

Two approaches have been investigated in this paper to generate the weighting matrix. The first approach is based on using 2-D normalized cross-correlation (NCC) termed as PSAP_NCC and second approach utilizes phase differences between sub-aperture beamformed images termed as PSAP_Phase.

1). PSAP_NCC Weighting Matrix:

Our first approach follows DAX weighting reported by Shin et al. [62] where the pixel-wise 2-D NCC coefficient, ρ(i, j) at zero lag was computed between S₁ and S₂ to quantify the degree of similarity:

$$\rho (i,j)=\frac{\underset{k=i-K}{\overset{i+K}{\Sigma }}\underset{h=j-H}{\overset{j+H}{\Sigma }}({\mathbf{S}}_1(k,h)-{\overline{s}}_1)({\mathbf{S}}_2(k,h)-{\overline{s}}_2)}{\sqrt{\underset{k=i-K}{\overset{i+K}{\Sigma }}\underset{j-H}{\overset{j+H}{\Sigma }}{({\mathbf{S}}_1(k,h)-{\overline{s}}_1)}^2\times \underset{k=i-K}{\overset{i+K}{\Sigma }}\underset{j-H}{\overset{j+H}{\Sigma }}{({\mathbf{S}}_2(k,h)-{\overline{s}}_2)}^2}}$$ (5)

where, i and j denote i^th sample of j^th A-line with a kernel dimension of 2K+1 samples by 2H+1 A-lines, ${\overline{s}}_1$ and ${\overline{s}}_2$ are the mean values over the 2-D kernel. Using ρ(i, j), the weighting matrix NCC_W (i,j) was computed as follows [55]:

$$NC{C}_W(i,j)=\max (\rho (i,j),\epsilon )$$ (6)

where, ε is a minimum NCC threshold value chosen to be 0.001 in this work. Here, signals with correlation values less than ε were considered as sidelobe and incoherent clutter and subsequently suppressed using the weighting matrix. In both sidelobe and incoherent clutter regions, typical NCC values are low ranging from −1 to −0.8. Thus, weighting DAS-beamformed RF data directly with the NCC matrix introduces a sign reversal rather than artifact suppression. Therefore, a max operator was used in equation (6) to ensure that the resultant weighting matrix has positive weights ranging from ε(0.001) to 1 resulting in 20log10(0.001) = 60 dB amplitude reduction applied to clutter signals [62]. Furthermore, NCC_W calculation was robust to noise due the use of 2D kernel and data up-sampling using linear interpolation, therefore no additional filtering (e.g., 2D median filter) was necessary [62]. Finally, the DAS beamformed data was multiplied by the weighting matrix to generate a PSAP_NCC image as shown:

$$PSA{P}_{NCC}(i,j)=NC{C}_W(i,j)\times DAS(i,j)$$ (7)

2). PSAP_Phase Weighting Matrix:

Since main lobe signals are highly correlated between sub-aperture beamformed images, they result in zero or small phase difference, whereas interfering signals will be out-of-phase resulting in increased phase difference. Therefore, in our second approach, we utilized phase information derived from the complex cross-correlation between the sub-aperture beamformed images to determine the weighting matrix [56, 60]. For S₁ and S₂, corresponding complex valued IQ signals s₁ and s₂ were derived using Hilbert transformation. The complex cross-correlation function, R was calculated as follows:

$$R(i,j)={\mathbf{s}}_1(i,j)\times {\mathbf{s}}_2^{*}(i,j)$$ (8)

The weighting matrix was determined using the phase angle of R to suppress any off-axis signals following an approach reported by Stanziola et al. [56] as shown below:

$$Phas{e}_W(i,j)=\exp \left(-\frac{k^2}{k_0^2}\right)$$ (9)

where k denotes the phase angle of R(i,j), and k₀ is an empirically determined phase factor to attenuate out-of-phase signals. Phase_W estimation is a point wise calculation (no kernel), thus the resultant weighting matrix was more sensitive to noise when compared to NCC_W. Therefore, 2-D median filtering was applied to the weighting matrix for reducing noise. Finally, the DAS beamformed data is multiplied by the weighting matrix to generate PSAP_Phase images as shown:

$$PSA{P}_{Phase}(i,j)=Phas{e}_W(i,j)\times DAS(i,j)$$ (10)

IV. Materials and Methods

A. Numerical Simulations

All simulations were performed using the k-Wave MATLAB toolbox [67]. To detect PA channel data, a 128-element linear array transducer with 72-μm element width, 18-μm kerf and 84-MHz sampling frequency operating at a center frequency of 21-MHz, and 100% fractional bandwidth was modelled in k-Wave. For all simulations, the imaging field-of-view (FOV) was divided into a 2-D k-Wave grid having a node spacing of 15-μm in both axial and lateral directions. The speed of sound and medium density was assumed to be 1540 m/s and 1000 kg/m³, respectively. For all quantitative evaluations, envelope detected PA beamformed data were used.

1). Point Target Simulation:

Four 100-μm diameter spherical absorbers were placed in a homogenous background with zero optical absorption to model a point target numerical phantom. They were positioned along the vertical axis with an inter-point target separation of 4 mm starting from a depth of 8 mm from the transducer surface. Imaging FOV was 22 × 11.5 mm². Each point target had an initial pressure value of 3 Pa. Optical and acoustic attenuation was not simulated. For quantitative evaluation, the main-lobe-to-sidelobe (MLSL) ratio was computed [19]:

$$MLSL=20\times {\log }_{10}\left(\frac{{\mu }_{\max }-{\mu }_{\min }}{{\sigma }_n}\right)$$ (11)

where, μ_max and μ_min denote the maximum and minimum signal amplitude within a 2 × 5 mm² rectangular region-of-interest (ROI) centered on each point target and σ_n represents the standard deviation of signal amplitudes from two 2 × 2 mm² ROIs within the signal ROI. The full-width-at-half-maximum (FWHM) at −6 dB was also calculated using 1-D lateral plots through the point targets, quantifying the distance in millimeters between points at the peak half maximum level.

2). Diffuse Inclusion Simulation:

To understand how well PSAP preserves signals from diffuse targets, we performed simulations with inclusions having randomly distributed optical absorbers. A hybrid simulation approach using MCMatlab [68] and k-Wave [67] software packages was used [16]. PAI requires simulation of the optical component which provides the initial pressure distribution to perform acoustic simulation and subsequent PA channel data synthesis. Here, MCMatlab [68] generates the initial pressure distribution required for the k-Wave [67] acoustic simulation. Two 3 mm-diameter circular targets were placed along the vertical axis of a 16 × 11.5 mm² phantom at a depth of 7 mm and 13 mm, respectively. Each circular target contained randomly distributed optical absorbers with a spatial density of 299 absorbers/mm² [69, 70]. Ten independent optical absorber realizations were generated for statistical analysis. First, spatially variant (r = optical absorber spatial location) and wavelength (λ) dependent absorbed optical energy density [A(λ, r)] was calculated using MCMatlab with the simulation parameters listed in Table I. Then, A(λ, r) was utilized to determine the initial pressure distribution (p₀) for the acoustic simulation as follows [71]:

$$p_0(\lambda ,r)=\mathrm{\Gamma }\times A(\lambda ,r)$$ (12)

where, Γ is the dimensionless Grueneisen parameter set to be 0.129 in this work [72]. To evaluate the performance of PSAP under varying level of channel noise, white noise was also added to the simulated channel data resulting in SNRs (SNR_c) ranging from −25 to 25 dB.

TABLE I.

Diffuse Inclusion Optical Simulation Parameters

Parameter	Value	Unit
Simulation cuboid	1.6×1.2×0.5	cm3
Water coupling layer	1	mm
Vessel absorption (μa at 7mm, 13 mm)	(4.43,5.60)	cm−1
Vessel scattering (μs at 7mm, 13 mm)	(58.82,58.82)	cm−1
Vessel oxygen saturation (7 mm, 13 mm)	(35.0,95.0)	%
Background absorption (μa)	0.01	cm−1
Background scattering (μs)	10	cm−1
Optical Wavelength	850	nm
Collimated top-hat beam radius	0.5	cm
Incident laser energy	30	mJ

Quantitative analysis was done using Contrast ratio (CR) and generalized contrast-to-ratio (gCNR) [69, 73], using:

$$CR=20\times {\log }_{10}\left(\frac{{\mu }_i}{{\mu }_o}\right)$$ (13)

$$gCNR=1-\sum _{j=0}^{N_{bin}-1}\min \{h_i(x_j),h_o(x_j)\}$$ (14)

where, μ_i and μ_o represent mean envelope detected PA signal amplitudes for target and background ROIs, respectively. Equation 14 is a histogram-based simpler implementation of gCNR [73] with h_i and h_o denoting the target and background histograms respectively. To calculate histograms, the entire range of PAI values were divided into 100 bins (N_bin) with bin centers denominated by j.

3). Microvasculature Simulation:

To understand how well PSAP preserves signals of interest in anatomically relevant heterogeneous media, we performed simulations mimicking typical in vivo microvasculature networks using 40 reference vascular images collected from the fundus oculi drive [31, 74]. Database contained binary images of blood vessels manually extracted from digital color images of the retina with white pixels denoting vessel segmentation. We use these binary images in our hybrid simulation framework to simulate raw channel data. First, optical absorbers were randomly distributed inside the blood vessels with a spatial density of 299 absorbers/mm². Then, MCMatlab [68] was used to derive the absorbed optical energy density [A(λ, r)] with parameters listed in Table II. Finally, equation 12 was used to generate the initial pressure distribution and acoustic simulation was done using k-Wave [67]. CR and gCNR were computed for quantitative comparison. Rectangular ROIs containing vessel signals were defined randomly using ground truth images as target Rois. The same Rois were shifted to adjacent background locations and denoted as background ROIs.

TABLE II.

Microvasculature Optical Simulation Parameters

Parameter	Value	Unit
Simulation cuboid	1.6×1.2×0.5	cm3
Water coupling layer	3	mm
Vessel absorption (μa)	5.6	cm−1
Vessel scattering (μs)	58.82	cm−1
Vessel oxygen saturation	75	%
Background absorption (μa)	0.01	cm−1
Background scattering (μs)	10	cm−1
Optical Wavelength	850	nm
Collimated top-hat beam radius	0.5	cm
Incident laser energy	30	mJ

B. In vivo Cardiac PAI Experiments

In vivo cardiac PAI data from five healthy murine models were collected using an experimental protocol approved by the Institutional Animal Care and Use Committee (IACUC) at the University of Wisconsin-Madison and described in detail in [16]. A Vevo 2100-LAZR imaging system (FUJIFILM VisualSonics, Inc., Toronto, Canada) was used for the collection of raw PA channel data in IQ format. Briefly, 1000 frames at the 850 nm wavelength of PA IQ channel data in parasternal long axis (PLAX) view were acquired using a LZ 250 transducer (256-element array, center frequency = 21 MHz) with simultaneous acquisition of physiological signals (ECG and respiratory signal). Physiological signal gating was performed offline using a custom MATLAB script (MathWorks, Inc., Natick, MA, USA) acquired from VisualSonics to reconstruct a PAI cardiac cycle. Data collection was done in PA RF mode to access raw channel data. Typical total acquisition time for in vivo data collection was 50 seconds. End-diastolic (ED) and end-systolic (ES) PAI frames were selected using reconstructed PAI M-mode images to perform quantitative analysis using CR and gCNR. Target ROIs were manually drawn on the epicardium and endocardium to locate myocardial wall PA signals. Then, the target ROIs were shifted to the left ventricular (LV) chamber and denoted as background ROIs. For DAS PAI images, we have consistently observed dominant PA signals concentrated in the endocardial and epicardial walls corroborating findings from literature [75]. To ensure, that our quantitative analysis is not biased by PA signals that may appear as temporally varying noise between the endocardial and epicardial wall during cardiac motion, ROIs were limited only to the epicardial and endocardial walls. Therefore, the target ROI was the summation of these two ROIs. Furthermore, shifting the target ROIs in the LV chamber ensured that both target and background ROIs had equal area during CR and gCNR evaluation.

C. Algorithm Implementation and Data Processing

All beamforming algorithms were implemented to run on a GPU in MATLAB (Mathworks Inc., MA) for cross-platform acceleration. DAS and DAS_CF beamforming were performed using a 64-element, dynamic apodization having a constant f-number of 1 and uniform aperture weighting. With the 64-element aperture, apodization was constant after 5.76 mm. For both PSAP_NCC and PSAP_Phase, sub-aperture data were upsampled by a factor of 2 both axially and laterally using linear interpolation before calculating the weighting matrix [76, 77]. Upsampling was done to improve robustness of NCC and phase estimation. Default parameter settings for PSAP_NCC and PSAP_Phase are summarized in Table III and IV, respectively. Choice of these parameters are justified in the Results and Discussion sections.

TABLE III.

PSAP_NCC Parameters

Experiment	Parameter	Value
Point Target	Sub-aperture alternating elements (N) 2-D NCC Kernel (Wavelength, A-lines)	8-8 (4.5λ,3)
Diffuse Inclusion Microvasculature In vivo	Sub-aperture alternating elements (N) 2-D NCC Kernel (Wavelength, A-lines)	2-2 (1.5λ,3)

TABLE IV.

PSAP_Phase Parameters

Experiment	Parameter	Value
Point Target	Sub-aperture alternating elements (N)	8-8
	Phase factor (k0)	π/9
	Median filter kernel (pixels, pixels)	(11,11)
Diffuse Inclusion Microvasculature In vivo	Sub-aperture alternating elements (N)	2-2
	Phase factor (k0)	π/3.5
	Median filter kernel (pixels, pixels)	(5,5)

One-way analysis of variance (ANOVA) with the Bonferroni multiple comparison test was used to determine statistical significance among DAS, DAS_CF, PSAP_NCC and PSAP_Phase. Statistical analysis was performed using SPSS Version 23 (IBM SPSS Statistics for Windows, Version 23.0, IBM Corp., Armonk, NY, USA).

V. Results

A. Numerical Simulations

1). Point Target Simulation:

Figures 3 (a)–(d) show beam-formed images obtained using DAS, DAS_CF, PSAP_NCC and PSAP_Phase, respectively. Significant sidelobes are apparent in the DAS image, that are suppressed by both CF weighting and PSAP. Qualitatively, DAS_CF provided the best reconstructed image.

Fig. 3.

Beamformed images of simulated point targets (a) DAS, (b) DAS_CF, (c) PSAP_NCC (8-8) and (d) PSAP_Phase (8-8). Display dynamic range is 55 dB. Green and blue rectangles denote signal and noise ROIs, respectively. For PSAP_NCC and PSAP_Phase, axial kernel length and phase factor (k₀) were 4.5λ and π/9 respectively.

Figures 4 (a)–(b) show the lateral profiles of the point spread function (PSF) at depths of 8 and 20 mm respectively. Both CF and PSAP significantly reduced sidelobe levels when compared to DAS but DAS_CF had better lateral resolution. Table V summarizes MLSL and FWHM at −6 dB. The best and worst values of MLSL and FWHM were denoted with blue and red colors respectively in Table V. Results show that both CF and PSAP provide better image quality than DAS. They also have the lowest MLSL and highest FWHM values at all depths coorborating our qualitiave observations from Figures 3–4.

Fig. 4.

Lateral profiles of PSF of at depth of (a) 8 mm and (b) 20 mm for all methods. Both CF and PSAP significantly reduced sidelobe level of DAS.

TABLE V.

Comparison Of SNR and FWHM at −6 dB Values ^*

	MLSL (dB)				FWHM at −6 dB (mm)
Depth (mm)	DAS	DASCF	PSAPNCC	PSAPPhase	DAS	DASCF	PSAPNCC	PSAPPhase
8	41.15	75.7	70.5	80.3	0.21	0.17	0.21	0.20
12	38.16	70.4	71.2	57.8	0.32	0.24	0.30	0.29
16	35.91	66.0	60.4	59.1	0.41	0.33	0.40	0.36
20	33.81	61.8	46.5	80.7	0.53	0.41	0.50	0.38

^*The best and worst values with blue and red colors respectively

The variation in MLSL and FWHM as a function of alternating element numbers is shown in Fig. 5. Note the trade-off between MLSL [Figs. 5 (a)–(b)] and resolution [Figs. 5 (c)–(d)] when selecting the alternating element numbers. We observed reduction in MLSL for all point targets (red, blue and green curves) except at 20 mm depth with the 16-16 alternating pattern when compared to 8-8 for PSAP_NCC. For PSAP_Phase, a MLSL peak was achieved for all targets using the 8-8 alternating pattern except the one at 8 mm which shows a slight reduction from its peak. These observations suggest that selecting alternating element numbers with an 8-8 pattern achieves a balance for both PSAP_NCC and PSAP_Phase. The results also suggest that lower N is preferred for shallower depth [red curves in Figs. 5 (a)–(b)] and vice versa [black curves in Figs. 5 (a)–(b)].

Fig. 5.

Variation of MLSL with alternating element number for (a) PSAP_NCC and (b) PSAP_Phase respectively. Variation of FWHM at −6 dB with alternating element number for (a) PSAP_NCC and (b) PSAP_Phase respectively. For PSAP_NCC and PSAP_Phase, axial kernel length and phase factor (k₀) were 2.5λ and π/3 respectively.

The performance of PSAP_NCC as a function of axial kernel length are shown in Fig. 6. With higher axial kernel lengths, a steady improvement in MLSL was seen for shallower targets when compared to deeper targets with no signifcant variation at 20 mm as shown in Figs. 6 (a)–(e). Higher axial kernel lengths did not impact FWHM except for the 20 mm target [Fig. 6 (f)]. A 8-8 alternating pattern was used.

Fig. 6.

Variation of PSAP_NCC performance with axial kernel length. Point target at 8 mm depth beamformed using an axial kernel length of (a) 0.5λ, (b) 2.5λ, (c) 3.5λ and (d) 4.5λ respectively. Variation of MLSL and FWHM at −6 dB are shown in (e) and (f) respectively.

Figure 7 shows PSAP_Phase performance as a function of phase factor (k₀). Better sidelobe suppression was achieved with lower phase factors resulting in higher MLSL values as seen in Figs. 7 (a)–(e). Furthermore, reduction of FWHM values at depth was observed with lower k₀[Fig. 7 (f)]. A 8-8 alternating pattern was used. These results indicate that the phase factor can be adjusted to adatively control the level of sidelobe suppression of coherent targets.

Fig. 7.

Variation in PSAP_Phase performance with phase factor. Point target at 8 mm depth beamformed using a phase factor of (a) π, (b) π/3, (c) π/5 and (d) π/9 respectively. Variation of MLSL and FWHM at −6 dB are shown in (e) and (f) respectively.

2). Diffuse Inclusion Simulation:

Representative qualitative results with diffuse inclusions are shown in Figure 8. Figs. 8 (a)–(e) show the ground truth initial pressure disribution, along with the reconstrcuted images using DAS, DAS_CF, PSAP_NCC and PSAP_Phase, respectively. Strong sidelobes are seen in the DAS image [Fig. 8 (b)]. CF reduced sidelobes seen with DAS along with the undesirable supression of PA signals inside the inclusion [Fig. 8 (c)]. On the other hand, PSAP_NCC and PASP_Phase produced higher quality images with reduced sidelobe and better PA signal preservation inside the inclusion that more closely resembled ground truth image [Figs. 8 (d) — (e)]. However, strong sidelobes near the border of the shallow target in Figure 8 (b) causes positive correlation between sub-aperture images with the chosen parameters. This resulted in additional noise in the border regions of the PSAP images [Figs. 8 (d)–(e)].

Fig. 8.

Beamformed images of simulated 3-mm diameter diffuse targets. (a) ground truth initial pressure distribution, (b) DAS, (c) DAS_CF, (d) PSAP_NCC (2-2) and (e) PSAP_Phase. (2-2). Display dynamic range is 55 dB. Green and white ROIs denote signal and noise ROIs, respectively.

Figures 9 (a)–(c) present the CF, NCC_W and Phase_W weighting matrices used to obtain the corresponding DAS_CF, PSAP_NCC and PSAP_Phase images shown in Fig. 8. A linear scale ranging from 0 to 1 was used to display the results. Observe that the CF weighting matrix had unusable lower weight values inside both lesions. However, NCC_W and Phase_W both robustly estimated higher weighting values insde the lesions and lower weighting values inside sidelobe and clutter regions, thus hindering the undesirable signal suppression observed in the DAS_CF result (Fig. 8 (c)).

Fig. 9.

Weighting matrix comparison between CF and PSAP processing in diffuse inclusion simulation. (a) – (c) show CF, NCC_W and Phase_W weighting matrix respectively in a linear scale from 0 to 1.

Figure 10 summarizes statistical analysis, where both CF and PSAP show statistically significant differences in CR when compared to DAS with PSAP methods achieving the highest values [Figs. 10 (a)–(b)]. PSAP significantly improved inclusion detectability when compared to both DAS and DAS_CF as shown in Figs. 10 (c)–(d) where PSAP_NCC and PSAP_Phase had higher gCNR values (p<0.001) with no significant differences between each other.

Fig. 10. Statistical analysis for performance comparison among DAS, DAS-CF and PSAP (n = 10).

Comparison of CR for lesions located at a depth of (a) 7 mm and (b) 13 mm respectively. Comparison of gCNR for lesions located at a depth of (a) 7 mm and (b) 13 mm respectively. Here, *** is p<0.001.

The choice of sub-aperture patterns was also investigated for diffuse inclusions. Figures 11 (a) and (b) show that peak CRs for inclusions located at shallower and deeper depth were achieved with 2-2 and 4-4 alternating patterns respectively for both PSAP_NCC and PSAP_Phase. But gCNR results [Figs. 11 (c)–(d)] show peaks with 2-2 alternating pattern indicating an ideal choice for diffuse inclusion detection. Thus, the 2-2 alternating pattern was chosen for subsequent analysis of microvasculature simulations and in vivo data.

Fig. 11. Impact of sub-aperture size on lesion contrast and detectability.

CR variation with the choice of sub-aperture for (a) PSAP_NCC and (b) PSAP_Phase respectively. gCNR variation with the choice of sub-aperture for (c) PSAP_NCC and (d) PSAP_Phase respectively.

Variations in CR and gCNR as a function of channel SNR (SNR_c) is presented in Fig. 12. Figures 12 (a)–(b) show CR variations at depths of 7 and 13 mm, respectively. For the 7 mm deep inclusion, DAS_CF, PSAP_NCC and PSAP_Phase present with higher CR than DAS for all SNR_c levels. PSAP_NCC showed higher CR values than DAS_CF and PSAP_Phase for SNR_c < 0 dB (Fig. 12 (a)). At the deeper depth (13 mm), DAS_CF, PSAP_NCC and PSAP_Phase had higher CR than DAS for SNR_c < −15 dB after which the inclusion is not visualized due to high noise levels. Figures 12 (c)–(d) show gCNR variation at depths of 7 and 13 mm, respectively. Fig. 12 (c) shows that PSAP results had higher gCNR than DAS and DAS_CF for the shallow target at all SNR_c levels. For the deeper target, PSAP results had higher gCNR for low levels of noise (SNR_c > 5 dB) after which the results converge to the results obtained with DAS_CF. DAS_CF, PSAP_NCC and PSAP_Phase had higher gCNR than DAS for SNR_c < −15 dB after which the inclusion was not distinguished from the background.

Fig. 12. Diffuse inclusion simulation CR and gCNR analysis as function of channel SNR.

(a) – (b) CR variation at a depth of 7 and 13 mm, respectively. (c) – (d) gCNR variation at a depth of 7 and 13 mm, respectively.

Table VI provides computational times computed over ten simulation instances of the diffuse inclusion simulation. Note that, PSAP requires more computational time due to additional sub-aperture beamforming and weighting matrix calculation.

TABLE VI.

Summary of Computational Time (Seconds)

Experiment	DAS & DASCF	PSAPNCC	PSAPPhase
Diffuse Inclusion*	0.14	0.33	1.85

^*Average time over 10 simulation realizations

3). Microvasculature Simulation:

A representative result from the microvasculature simulation is shown in Figs. 13 (a)–(e) with ground truth initial pressure disribution, reconstructed images with DAS_CF, PSAP_NCC and PSAP_Phase, respectively. Representative target and background ROI definitions for quantitative analysis are shown in Fig. 13. DAS image show severe clutter artifacts due to high sidelobe levels. With CF, clutter was reduced but the PA signal amplitude inside blood vessels were also undesirably suppressed thus negatively impacting deeper vessel detectability. PSAP_NCC and PSAP_Phase produced significantly better images when compared to DAS and DAS_CF achieving both clutter supression and blood vessel PA signal preservation. Fig. 13 (f) shows the axial profiles across the blue line ROI shown in Fig. 13 (a). Note that PSAP preserves DAS amplitude levels in the blood vessels and at the same time reduces clutter compared to DAS_CF.

Fig. 13.

Beamformed images of simulated microvasculature. (a) ground truth initial pressure distribution, (b) DAS, (c) DAS_CF, (d) PSAP_NCC (2-2) and (e) PSAP_Phase. (2-2). Signal variation across an axial line ROI shown in (f). Display dynamic range is 55 dB. Green and red rectangles in (a) denote signal and clutter ROIs, respectively. Blue line in (a) denotes axial profile ROI.

Figure 14 demonstrates that statistically significant improvements in CR and gCNR were achieved with PSAP when compared to DAS and DAS_CF. Fig. 14 also demonstrate that CF weighting stretches the dynamic range resulting in higher CR without improving the target detectability (no significant difference between DAS and DAS_CF gCNR values). With PSAP, improvements both in contrast and target detectability was achieved. The choice of sub-aperture was also investigated for microvasculature simulations as shown in Fig. 15. Peak CR and gCNR values were obtained with the 2-2 alternating pattern for both PSAP_NCC and PSAP_Phase. Fig. 15 also shows that performance can be severely impacted if larger number of alternating elements are chosen.

Fig. 14. Statistical analysis for performance comparison among DAS, DAS_CF and PSAP (n = 40).

Comparison of (a) CR and (b) gCNR for microvasculature simulation data. Here, *** is p <0.001.

Fig. 15. Impact of sub-aperture size on microvasculature contrast and detectability.

CR variation with the choice of subaperture for (a) PSAP_NCC and (b) PSAP_Phase respectively. gCNR variation with the choice of subaperture for (c) PSAP_NCC and (d) PSAP_Phase respectively.

B. In vivo Cardiac PAI

Figure 16 (b)–(e) shows in vivo cardiac PA images at ED reconstructed using DAS, DAS_CF, PSAP_NCC and PSAP_Phase, respectively. Corresponding US B-mode image with PAI aquisition ROI and relevant anatomical locations is shown in Fig. 16 (a). Myocardial wall PA signals and background clutter signals are shown in blue and white ROIs in the DAS image. Note that DAS_CF reduced clutter signals with simualtanous supression of myocardial wall PA signals. On the other hand, PSAP_NCC and PSAP_Phase showed improved myocardial wall signal specificity and reduced clutter in the LV chamber and thus provided higher quality image when compared to DAS and DAS_CF. In vivo cardiac PA images at ES are shown in Fig. 17, we observe similar findings as in ED images. Improvements achieved with PSAP can be further appreciated on the movie file provided as supplemental material. To reduce temporal noise, a moving average filter with three temporal samples were applied to all results shown in the movie. Figure 18 shows that PSAP_NCC and PSAP_Phase had higher CR and gCNR values compared to DAS and DAS_CF.

Fig. 16.

In vivo cardiac photoacoustic images at ED. (a) US B-mode, (b) (b) DAS, (c) DAS_CF, (d) PSAP_NCC (2-2) and (e) PSAP_Phase. (2-2). Green rectangle denotes PAI ROI. Blue and white ROIs indicate myocardial wall and clutter signals respectively.

Fig. 17.

In vivo cardiac photoacoustic images at ES. (a) US B-mode, (b) (b) DAS, (c) DAS_CF, (d) PSAP_NCC (2-2) and (e) PSAP_Phase. Green rectangle denotes PAI ROI. Blue and white ROIs indicate myocardial wall and clutter signals respectively.

Fig. 18. In vivo statistical analysis for performance comparison among DAS, DAS-CF and PSAP (n = 5).

(a) and (b) show CR and gCNR. n = 5 corresponds to the number of animal models.

VI. Discussion

In this paper, we presented our PSAP algorithms, validated using numerical simulations and in vivo animal studies both qualitatively and quantitatively. The key findings from these studies can be summarized as follows.

1. PSAP reduces PA clutter seen in DAS PA images utilizing similarity information between sub-aperture beamformed images.

2. PSAP improves PA target detectability at all depths by preserving DAS signal amplitude inside the target while achieving CF like clutter suppression in the background.

3. Optimal PSAP performance is parameter dependent and varies with application.

The variation in DAS image quality with f-number was evaluated using both point target and diffuse inclusion simulations. A f-number of 1 was chosen as it provided higher MLSL for point targets and higher CR and gCNR for inclusions. For coherent targets, PSAP reduces DAS sidelobe levels when compared to DAS_CF while maintaining DAS resolution [Figs. 3 and 4]. But DAS_CF provided the best quality images in terms of MLSL and FWHM with comparable performance with PSAP [Table V]. For PSAP_NCC and PSAP_Phase, choice of the alternating sub-aperture element number (N) showed a depth-dependent variation in MLSL [Fig. 5]. Varying the alternating pattern affects the PSF shape generated by each sub-aperture which in turn changes the correlation of sidelobe signals [56]. Furthermore, from the DAS image [Fig. 3 (a)], we observe depth-dependent variation of full aperture PSF due to variation in scattering intensity over depth [56]. Thus, larger number of alternating elements provide better MLSL deeper in tissue with 8-8 achieving a balance.

Two key algorithmic parameters – axial kernel length for PSAP-NCC and phase factor for PSAP-Phase were also investigated. Figures 6 (a)–(d) and 7 (a)–(d) show that lower axial kernel length and higher phase factor introduces positive correlation between sub-aperture beamformed images in sidelobe regions resulting in point-like artifacts in the images. These artifacts were seen in point target simulations due to the strong sidelobes in the original DAS image. Increasing axial kernel length steadily improved MLSL for shallower targets [8 and 12 mm shown by red and blue curves in Fig. 6 (e)] as they had wider sidelobes when compared to deeper targets [16 and 20 mm shown by green and black curves in Fig. 6 (e)]. On the other hand, we observed steady improvement in performance (MLSL and FWHM) when lower phase factor values were chosen for PSAP_Phase [Fig. 7]. Therefore, Figures 6 and 7 suggest that both axial kernel length and phase factor values should be adjusted based on the application to achieve desired sidelobe suppression. Overall, the results from point target simulations suggest that larger alternating element number (8-8), higher axial kernel length and lower phase factor is preferred when using PSAP for coherent target PAI [56].

Several groups including ours have reported on CF weighting for sidelobe lobe suppression [16, 43–45, 78]. However, analysis in this paper shows that although CF weighting suppresses clutter signals, it also leads to undesirable target PA signal suppression specifically at depths where the target signal is weaker due to optical attenuation [Figs. 8 and 13]. CF was originally developed for US imaging to tackle phase aberration [59] and utilizes very strict measures of coherence. This causes weak PA signals at depth to have lower coherence values thus suppressing them at the level of clutter signals. On the other hand, our PSAP approaches separate target PA signals from clutter using correlation (amplitude and phase) between sub-aperture beamformed images. Here, target PA signals were highly correlated both at shallower and deeper depths when compared to clutter signals due to the use of non-overlapping sub-apertures [55, 56, 60, 62]. Therefore, weaker PA signals at depth were better preserved with PSAP when compared to CF [Figs. 8 and 13]. Quantitative results show that DAS_CF, PSAP_NCC and PSAP_Phase provide higher CR values than DAS. However, we are also interested in improving signal detectability which is better quantified using gCNR [73]. Adaptive methods often nonlinearly alter the image dynamic range and histogram to which gCNR is invariant [69, 73]. gCNR analysis reveals that significant improvement is achieved using PSAP when compared to DAS_CF [Figs. 10 and 13]. Figures 11 and 15 also indicate that lower N is preferred for maintaining a balance between main lobe signal preservation and clutter signal suppression. With higher N, target PA signals start to get negatively correlated and suppressed through the PSAP weighting matrix. This results in lower CR and PA signal detectability (gCNR). Furthermore, lower axial kernel length and higher phase factor values were chosen to inhibit any undesirable suppression of target PA signal [Table III and IV]. Overall, the results for diffuse and microvasculature simulations suggest that lower alternating element number (2-2), lower axial kernel length and higher phase factor is preferred when using PSAP for diffuse target PAI.

PSAP and CF also showed similar CR trends as a function of SNR_c with better performance than DAS [Figs. 12 (a)–(b)]. However, PSAP processing provides improved target detectability (gCNR values) when compared to DAS and DAS_CF under low noise levels for both target depths. Additionally, PSAP processing had larger SNR_c operating regions for shallower versus deeper targets, observed by the left shift of the gCNR curve indicated by an arrow in Figure 12 (d). For lower SNR_c channel data with simulated optical attenuation, main lobe strength in the sub-aperture beamformed images degrades severely for deeper targets resulting in decorrelation during NCC and phase estimation. These results indicate that for PA imaging targets severely corrupted by incoherent clutter noise, PSAP processing is unable to distinguish between signal and noise providing similar performance as DAS_CF.

We also observed few erroneous vertical lines in DAS_CF images in Figs. 8 (a) and 13 (d) respectively, probably due to the Hilbert transformation of CF weighted beamformed PA RF data for envelope detection. CF weighting may have extended the signal bandwidth resulting in violation of the bandlimited signal assumption required with the Hilbert transform. This may happen in any weighting-based beamforming algorithm, however in DAS_CF results, we observed it within our imaging dynamic range. However, it did not impact the quantitative analysis, because the vertical line artifacts were outside our chosen ROI locations. Approaches to reduce the vertical line artifact include determining the envelope of beamformed PAI RF data first then weighting using the CF matrix or beamforming in the IQ domain by taking Hilbert transform of channel data or bandpass filtering of the RF data prior to Hilbert envelope detection. Additionally, we have investigated a filtered version of CF weighting by applying a spatial averaging filter with a kernel of size [1.5λ× 3 A-lines] on the CF map and observed that the filtered version of DAS_CF provides vertical line artifact reduction and minor improvements in the CR and gCNR when compared to the classical CF algorithm.

PSAP however does require additional computational time and memory for sub-aperture processing and weighting matrix generation. For real-time processing, parallel processing with GPUs can be harnessed by beamforming DAS and sub-aperture images in parallel from collected raw channel data.

A limitation of our simulations was that frequency dependent acoustic attenuation was not modelled. Typically, broadband PA signals are impacted by acoustic attenuation [79] especially when high frequency transducers are used for imaging resulting in depth dependent blurring of features and signal loss [80]. Future work will incorporate acoustic attenuation into the simulation model. Another limitation was the use of a planar phantom and performing simulations in 2D. In the future, simulations with 3D phantoms will be performed as the dimensions of the US beam is not negligible in the elevational direction. Finally, another limitation of the proposed technique is the use of the fixed alternating pattern number for sub-aperture generation. As the PSF with PAI varies over depth, we anticipate further performance improvement using depth-dependent dynamic sub-aperture generation by varying the alternating pattern number [61].

Benefits of PSAP are clear in the presented ED and ES images in Figs. 16 and 17. From the enclosed movie file, note that PA signals in the LV chamber appear as temporally varying random noise in the DAS cine loop. This makes interpretation of myocardial PA signals difficult especially during the systolic phase. This random variation can be attributed to higher blood flow velocities inside the LV chamber and strong optical absorption in the coronary artery [16, 81, 82]. This leads to a strong bias of PA signals towards the myocardial (endocardium and epicardium) walls and results in non-viable PA signals from the LV chamber [16, 75]. These random noise signals can be suppressed using CF as shown in Figs. 16–17 (c). However, CF also undesirably suppresses myocardial wall PA signals further corroborating our findings from simulation studies [Fig. 8, 13, 16, 17 and movie file]. One implication of undesirable myocardial wall PA signal suppression is that it can lead to inaccurate diagnosis of ischemia [16, 83, 84] as only healthy murine hearts were imaged in this paper. In contrast to CF, PSAP enables suppression of non-viable LV chamber PA signals while preserving DAS amplitude levels in the myocardial wall. This is a critical advantage over CF because DAS amplitude preservation is desired when multi-wavelength PAI is employed for oxygen saturation quantification [3]. Quantitative analysis shows that DAS_CF, provides higher CR values but reduced wall PA signal detectability as also indicated by the gCNR reduction when compared to DAS in Fig. 18. In contrast, PSAP_NCC and PSAP_Phase provided improvements in both CR and gCNR when compared to DAS demonstrating the in vivo feasibility of PSAP. Future in vivo validation studies will focus on application of PSAP for murine ischemia-reperfusion detection using single- and multi-wavelength cardiac PAI.

In this paper, we have focused on imaging the murine heart wall using linear array PAI. Researchers have also illustrated use of PAI to guide in vivo cardiac catheter interventions [85]. Furthermore, PAI has been used for imaging prostate brachytherapy seeds [38, 86], percutaneous radiofrequency ablation needle detection [87] and surgical guidance [4]. One recurring challenge in these applications is the PA image quality [4], and novel beamforming approaches have been proposed to tackle this challenge [12, 17, 49, 86]. Simulation and in vivo results presented in this paper suggest that PSAP can potentially improve image quality for the above mentioned applications by clutter reduction while maintaining target detectability thus contributing towards solving the image quality challenge. PSAP also be combined with adaptive beamforming methods such as minimum variance, DMAS beamforming [12, 14, 19, 22] for further image improvements.

VII. Conclusion

This paper presents photoacoustic image reconstruction based on correlation analysis between sub-aperture DAS beamformed images. Feasibility of our approach was validated using simulation and in vivo studies. Comparison with DAS and DAS_CF showed that PSAP improves PAI quality due to improved PA signal detectability and lower clutter levels.

Biographies

Rashid Al Mukaddim (Graduate Student Member, IEEE) received the B.S. degree in electrical and electronic engineering from the Islamic University of Technology (IUT), Board Bazar, Gazipur, Bangladesh, in 2014, and the M.S. degree in electrical and computer engineering from the University of Wisconsin-Madison, Madison, WI, USA, in 2018, where he is currently pursuing the Ph.D. degree in electrical and computer engineering. The focus of his research is to develop ultrasound strain and photoacoustic imaging algorithms for multi-modality assessment of myocardial health in murine models. He is interested in developing signal and image processing algorithms such as regularization, photoacoustic beamforming, achieve algorithm acceleration using GPU computing and successful translation of the developed methods into in vivo murine image assessment. Rashid is a student member of IEEE Ultrasonics, Ferroelectrics, and Frequency Control Society and IEEE Engineering in Medicine and Biology Society.

Rifat Ahmed (Member, IEEE) received B.Sc. degree in electrical and electronic engineering from the Islamic University of Technology, Gazipur, Bangladesh, in 2012, and M.S. and Ph.D. degrees in electrical engineering from the University of Rochester, Rochester, NY, USA, in 2017 and 2020.

He is currently a Research Scientist at the Biomedical Engineering Department, Duke University, Durham, NC, USA. His research interests are in ultrasound imaging, beamforming and elastography methods.

Tomy Varghese (S’92–M’95–SM’00) received the B.E. degree in instrumentation technology from the University of Mysore, Mysore, India, in 1988, and the M.S. and Ph.D. degrees in electrical engineering from the University of Kentucky, Lexington, KY, USA, in 1992 and 1995, respectively. From 1988 to 1990, he was an Engineer with Wipro Information Technology Ltd., Mysore. From 1995 to 2000, he was a Post-Doctoral Research Associate with the Ultrasonics Laboratory, Department of Radiology, University of Texas Medical School at Houston, Houston, TX, USA. He is currently a Professor with the Department of Medical Physics, University of Wisconsin—Madison, Madison, WI, USA. His current research interests include elastography, ultrasound imaging, quantitative ultrasound, detection and estimation theory, statistical pattern recognition, and signal and image processing applications in medical imaging.

Dr. Varghese is a fellow of the American Institute of Ultrasound in Medicine, and a member of the American Association of Physicists in Medicine and Eta Kappa Nu.