Debiasing-based Noise Suppression for Ultrafast Ultrasound Microvessel Imaging

Abstract

Ultrasound microvessel imaging (UMI) based on the combination of singular value decomposition (SVD) clutter filtering and ultrafast plane wave imaging has recently demonstrated significantly improved Doppler sensitivity, especially to small vessels that are invisible to conventional Doppler imaging. Practical implementation of UMI is hindered by high computational cost associated with SVD, and low blood signal-to-noise-ratio (SNR) in deep regions of the tissue due to the lack of transmit focusing of plane waves. Concerning the high computational cost, an accelerated SVD clutter filtering method based on randomized SVD (rSVD) and randomized spatial downsampling (rSD) was recently proposed by our group, which showed the feasibility of real-time implementation of UMI. Concerning the low blood flow SNR in deep imaging regions, here we propose a noise suppression method based on noise debiasing that can be easily applied to the accelerated SVD method to bridge the gap between real-time implementation and high imaging quality. The proposed method experimentally measures the noise-induced bias by collecting noise signal using the identical imaging sequence as regular UMI, but with the ultrasound transmission turned off. The estimated bias can then be subtracted from the original power Doppler (PD) image to obtain effective noise suppression. The feasibility of the proposed method was validated under different ultrasound imaging parameters (including transmitting voltages and TGC settings) with a phantom experiment. The noise-debiased images showed an increase of up to 15.3 dB and 13.4 dB in SNR as compared to original PD images on the blood flow phantom and an in vivo human kidney data set, respectively. The proposed noise suppression method has negligible computational cost and can be conveniently combined with the previously proposed accelerated SVD clutter filtering technique to achieve high quality, real-time UMI imaging.

I. Introduction

The emergence of ultrafast ultrasound plane wave imaging has substantially promoted the development of ultrafast microvessel imaging (UMI) with high frame-rate and high Doppler sensitivity [1–6]. The large number of Doppler ensembles that can be acquired with UMI can significantly improve the detection and characterization of small vessels, which are otherwise invisible to conventional Doppler imaging [1–3, 7]. The rich spatial-temporal information offered by ultrafast plane wave imaging can also be beneficial for separation of blood signals and tissue clutters, which is essential for detection of slow blood flow signals in the microvessels. Recently, UMI based on combinations of ultrafast plane wave imaging and singular value decomposition (SVD)-based clutter filtering has demonstrated superior performance in tissue clutter rejection [7–9]. Unlike conventional high-pass clutter filters that are based only on the temporal information, SVD-based filters take advantages of both the spatial and temporal information to achieve more robust tissue and blood signal separation [7–10]. UMI with SVD-based clutter filters is now commonly used in applications such as functional ultrasound imaging [11, 12] and super-resolution ultrasound imaging [13, 14].

One drawback of the state-of-the-art UMI technique is the expensive computational cost associated with SVD calculations on a large number of Doppler ensembles, which makes real-time implementation of UMI challenging. To address this drawback, a fast SVD clutter filtering method was recently proposed based on random SVD (rSVD) and randomized spatial downsampling (rSD) [15]. rSVD accelerates SVD calculation by approximating the largest singular values corresponding to tissue clutters (e.g. the first k singular values). rSD can further speed up rSVD by dividing the large ultrasound data matrices into randomly patterned, non-overlapping subsets, which can be processed in parallel for enhanced computational performance. The real-time potential of this fast SVD clutter filter technique was demonstrated in the previous study [15], without significant compromise in tissue clutter rejection performance.

Another drawback of UMI is the weak penetration of the unfocused plane waves, which results in deteriorated ultrasound signal-to-noise ratio (SNR) in deeper regions of the image. The low ultrasound SNR is associated with a high level of noise in the deep regions that makes it challenging to discern microvessels. Among the different sources of noise in ultrasound imaging, electronic noise is directly associated with imaging settings such as time-gain compensation (TGC) and the beamforming processes like dynamic focusing. As a result, electronic noise is spatially varying: deep imaging regions typically have higher TGC settings and use more channel data for beamforming, which generate higher electronic noise than in shallow imaging regions. This spatially varying noise manifests in the form of a characteristic ramp-shaped background noise profile in UMI power Doppler (PD) images [16], which can be considered as a result of additive bias. Such bias can considerably compromise the visualization of microvasculature, especially for vessels that are deep in the tissue. This study focuses on methods that can suppress such noise bias for real-time UMI.

One method that can effectively suppress the noise bias is the block-wise adaptive SVD clutter filter, which suppresses noise by rejecting high-order singular values [7]. The effectiveness of the block-wise adaptive SVD clutter filtering has been demonstrated in vivo using kidney and liver data, showing substantially improvement of PD SNR [7]. However, the block-wise SVD is computationally expensive due to the large amount of SVD calculations needed for the spatially overlapping subsets of data. Another noise suppression method is based on noise equalization, where various approaches can be used to derive a noise field that can be used to equalize the PD images [16]. More specifically, the noise-equalized PD image is obtained by dividing the original PD image by the noise field. This can significantly improve the visual appearance of the microvessel images in a simple and effective way, but it does not actually improve the SNR of PD images [16]. In addition, the noise equalization method requires full SVD calculations for deriving the noise field, which is time-consuming and limits its real-time implementation. While rSVD can significantly improve the computational speed of SVD clutter filters, it does not calculate the higher-order singular values. Therefore, the noise equalization method based on rejection of high-order singular values is not possible with rSVD [15]. For SVD clutter filtering based UMI, therefore, methods that can simultaneously overcome the abovementioned two drawbacks and achieve both real-time implementation and noise suppression have not been reported.

Noise suppression methods based on the coherence of ultrasound signals have also been explored recently. A coherent flow PD method was proposed based on short-lag spatial coherence (SLSC) imaging, which takes advantage of the spatial coherence information to improve flow detection [17, 18]. One drawback of this method is the high computational cost associated with the coherence calculations at the channel data level. Another noise suppression method is based on splitting the ultrasound channel data into multiple subgroups, among which the noise is uncorrelated and thus can be suppressed via correlation [19]. While this method can effectively suppress the noise bias and improve the contrast of PD images, it requires multiple clutter filtering calculations on different subgroup data, which may not be suited for SVD-based UMI for the purpose of real-time implementations.

To bridge the gap between high-quality SVD-based UMI and its real-time implementation, this study proposes a fast and robust noise suppression method based on noise debiasing, which can be combined with the accelerated SVD methods to facilitate the realization of high quality and real-time UMI. This method measures the noise bias experimentally by turning off the ultrasound pulse transmission. Noise debiasing can be achieved by subtraction of the estimated noise bias from the power of the blood signal (i.e., power Doppler). The underlying principle is that PD signal can be expressed as a summation of the power of blood signal and the noise bias. Unlike the noise equalization method where the noise field is derived from the highest-order singular value, the proposed method here does not require a full SVD calculation, and thus can be conveniently combined with rSVD and rSD for real-time UMI [15].

The paper is structured as follows: the debiasing-based noise suppression method is first introduced in the context of full SVD filtering and compared with the previously proposed noise equalization method using an in vivo kidney data set. A blood flow phantom experiment was implemented to assess the reliability of the noise suppression method under different imaging settings (transmitting voltages and TGCs). The influence of the noise ensemble size (number of noise frames) on the noise bias estimation and the corresponding quantitative SNR of the PD image were evaluated to provide guidelines for noise frame acquisition in real-time application. The proposed debiasing method was then incorporated into the accelerated SVD techniques, demonstrating the improved performance of accelerated SVD-based UMI with noise suppression. We then discuss the results and conclude the paper.

II. Materials And Methods

A. Ultrasound imaging parameters

The method presented in this study directly measures the power of the electric noise from the ultrasound system to estimate noise bias, which can be directly subtracted from the PD image. A single set of in vivo kidney data was utilized throughout the study to help elaborate, and quantitatively evaluate the proposed method, as shown in Fig. 1. A blood flow phantom experiment was used to test the feasibility of the proposed method under different sNR by changing the transmitting voltage and TGC settings, and evaluate the effects of noise ensemble length. The ultrasound data were acquired with a Verasonics Vantage ultrasound system (Verasonics Inc., Kirkland, WA, USA) and a curved array transducer C1–6-D (GE Healthcare, Wauwatosa, WI). Plane wave transmission was used at a pulse-repetition-frequency (PRF) of 7143 Hz with a center frequency of 4.46 MHz. A 10-angle spatial coherent compounding (−9° to 9° with an increment step of 2°) was implemented. The post-compounding frame rate was set to be 500 Hz, which indicates a waiting time interval between acquisitions of consecutive compounded frames. An ensemble of 300 frames (the number of ultrasound frames used for clutter filtering and PD image generation) were acquired for each data set. Ultrasound post-beamformed inphase/quadrature (IQ) data were obtained with a size of 233×298×300 (N_z × N_x × N_t, where N_z and N_x correspond to IQ data size in axial and lateral dimensions, respectively, and N_t corresponds to data size in slow-time dimension, i.e., the ensemble size) and a spatial pixel resolution of 0.345 mm in both axial and lateral dimensions, hereafter referred to as S₀ (x, z, i) (before clutter filtering).

Fig. 1.

(a) B-mode image of an in vivo kidney. (b) Power Doppler image of the in vivo kidney based on global SVD clutter filtering. (c) Experimentally measured noise power image shown in dB scale. (d) Noise bias removed power Doppler image. Images (b)-(d) are under the same color scale.

B. Principles of debiasing-based noise suppression

Here we use the classic global SVD-based clutter filtering to explain the principles of debiasing-based noise suppression. The details of the global SVD-based clutter filter have been given in [8]. Briefly, the original ultrasound data set S₀ (x, z, i) is first reshaped into a 2D Casorati matrix with dimensions of N_z × N_x by N_t. Then an SVD is calculated for the reshaped 2D Casorati matrix. The lower-order singular values corresponding to tissue clutters are forced to zero, followed by an inverse SVD calculation to obtain the blood flow signal [7, 8]. The singular value thresholding (SVT) cutoff value is determined by the decay rate of the singular value curve [7]. After SVD-based clutter filtering, the remaining IQ data matrix S(x, z, i) consists of blood signal and additive electric noise, which can be represented by:

$$S(x,z,i)=S_B(x,z,i)+n(x,z,i)$$ (1)

where S_B is blood signal, n is assumed to be the addictive noise, x and z correspond to the lateral and axial dimension, respectively, and i corresponds to the temporal dimension. The PD signal is given by:

$$\begin{gathered} PD(x,z)=\sum _{i=1}^{N_t}S(x,z,i)S*(x,z,i) \\ =\sum _{i=1}^{N_t}{S}_B(x,z,i)S_B^{*}(x,z,i) \\ +\sum _{i=1}^{N_t}n(x,z,i)n*(x,z,i) \\ +\sum _{i=1}^{N_t}{S}_B(x,z,i)n*(x,z,i) \\ +\sum _{i=1}^{N_t}{S}_B^{*}(x,z,i)n(x,z,i) \end{gathered}$$ (2)

where * indicates the complex conjugate. Since electric noise and blood signal are uncorrelated, the cross-terms should each have a zero expectation, so that:

$$E\left[\sum _{i=1}^{N_t}{S}_B(x,z,i)n*(x,z,i)+\sum _{i=1}^{N_t}{S}_B^{*}(x,z,i)n(x,z,i)\right]=0$$ (3)

The expected PD(x, y) can then be expressed as:

$$\begin{gathered} E[PD(x,z)] \\ =E\left[\sum _{i=1}^{N_t}{S}_B(x,z,i)S_B^{*}(x,z,i)+\sum _{i=1}^{N_t}n(x,z,i)n*(x,z,i)\right] \\ =E\left[\sum _{i=1}^{N_t}{\left|S_B(x,z,i)\right|}^2\right]+E\left[\sum _{i=1}^{N_t}|n(x,z,i){|}^2\right] \end{gathered}$$ (4)

Figure 1(b) shows the PD image PD(x, z) of the in vivo kidney after the global SVD clutter filtering. In this study, all the PD images are displayed in a logarithmic scale (i.e., 10log₁₀(SNR)) for better visualization. The background ramp-shaped noise bias can be clearly observed. Therefore, based on equation 4, in order to estimate an unbiased blood flow signal, an estimation of the noise term $E\left[\sum _{i=1}^{N_t}|n(x,z,i){|}^2\right]$ is required. Here in PD, because the noise term is in the form of an additive bias, the noise suppression method introduced here is simply a debiasing process.

To acquire the noise field $(\tilde{n})$, the ultrasound transmit power was turned off by setting the transmit duty cycle and transmit apodization to zero. In this case no actual ultrasound signal is transmitted, while the probe is still attached and an identical system configuration and imaging sequence as used in the actual blood flow signal acquisition was used to collect electric noise. The noise power term $E\left[\sum _{i=1}^{N_t}|n(x,z,i){|}^2\right]$ in equation 4 can then be estimated as:

$$E\left[P{D}_n(x,z)\right]=\frac{N_t}{M}E\left[\sum _{i=1}^M|\tilde{n}(x,z,i){|}^2\right]$$ (5)

where $\tilde{n}$ is the measured noise with ultrasound transmission turned off, and M is the number of noise ensembles acquired. The noise ensemble M does not need to be equal to the blood ensemble N_t. A scaling factor $\frac{N_t}{M}$ is used to adjust for the possible difference between noise ensemble and blood ensemble. A smaller M can reduce the acquisition time for noise, which is beneficial for real-time UMI imaging. An example of the acquired noise field (M = 300) is depicted in Fig. 1(c). By subtracting PD_n (x, z) from PD(x, z), an improved PD image can be obtained, as an example shown in Fig. 1(d).

Equation (4) assumes that the global SVD clutter filtering process does not remove noise, and therefore the noise term $E\left[\sum _{i=1}^{N_t}|n(x,z,i){|}^2\right]$ is equal to the equivalent term for the collected noise $\tilde{n}$. However, in SVD calculation, noise will be distributed throughout the singular value curve, and thus the tissue clutter rejection process (i.e., removal of low-order singular values) would remove a small amount of noise, possibly making $E\left[\sum _{i=1}^{N_t}|n(x,z,i){|}^2\right]$ smaller than E[PD_n(x, z)]. It should also be noted that the electronic noise level might be slightly different with transmission turned on and off, due to the difference of power consumption of the transmitters. These may result in some negative values in the noise debiased blood PD image, PD_B(x, z). In this study, we forced the negative values in PD_B(x, z) to zero since PD signals, by definition, should be non-negative.

In this study, the noise equalization method was also conducted to provide a benchmark for comparison, based on the same set of in vivo kidney data. Details of the noise equalization method have been provided in [16]. Briefly, a full SVD was first performed on the original data S₀(x, z, i) and the highest-order singular value and singular vector were used for an inverse SVD calculation, followed by the same PD calculation process to obtain a noise field. A 2D median filter (50 pixels × 50 pixels) was applied to heavily smooth the noise field before noise equalization. The final noise equalized PD image was achieved by dividing the original PD image (Fig. 1b) by the derived noise field.

C. Evaluation of different transmitting voltages and TGC settings

To evaluate the feasibility of the proposed method under various SNR situations, different acoustic transmitting voltages and TGCs were used to perform UMI on a blood flow phantom (Model 1425, Gammex, Middleton, WI, USA). The oblique vessel channel (diameter = 5 mm) was scanned along longitudinal direction. Two relatively low transmitting one-sided voltages (half of the peak-to-peak voltages) were utilized (i.e. 10 V and 5 V, respectively) for the phantom experiment to produce low SNR scenarios. For each transmitting voltage, three TGC settings were used (as shown in Fig. 2): the first was identical to the original TGC used for in vivo imaging in this study (referred to as TGC 1); the second one was with TGC gain turned off (referred to as TGC 2); and the third one was with the TGC gain set to be maximum for all depths (referred to as TGC 3). TGC 2 (TGC off) was used to evaluate the proposed method under extremely low SNR situations. The rest of the imaging parameters were kept identical to those in the in vivo study. Noise data were collected and applied similarly as in in vivo imaging for the three TGC setups. For quantitative performance evaluation, the SNR of the PD image was defined as:

$$SNR=\frac{{\overline{S}}_{blood}}{{\overline{S}}_{background}}$$ (6)

where ${\overline{S}}_{blood}$ is the mean power of the blood flow signal within a certain region-of-interest (ROI), and ${\overline{S}}_{background}$ is the mean power of the background noise. The ROIs for ${\overline{S}}_{blood}$ and ${\overline{S}}_{background}$ calculation will be defined separately for the phantom and in vivo kidney images, and the blood SNR was shown in a logarithmic scale (i.e., 10log₁₀(SNR)).

Fig. 2.

Different TGC settings used in this study.

D. Evaluation of noise power estimation

Collecting more noise frames will provide a more accurate estimation of the noise field, and result in better noise bias suppression. However, collecting a smaller number of noise ensembles may be advantageous for the purpose of real-time applications. To study the minimal number of noise ensembles required to achieve robust noise suppression, various numbers of noise ensembles (M from 5 to 300) were tested on both phantom data and in vivo kidney data. Before subtraction of noise power, the noise power image E [PD_n (x, z)] estimated based on equation 5 can also be smoothed by a spatial smoothing filter to provide a more robust and accurate estimation. in this study, a spatial median filter with size of 10 pixels × 10 pixels (3.45 mm × 3.45 mm) was used for both phantom and in vivo kidney data as an illustration.

E. Combining debiasing-based noise suppression with accelerated SVD based clutter filtering

An accelerated SVD method based on randomized SVD (rSVD) and randomized spatial downsampling (rSD) was previously proposed for real-time implementation of UMI [15]. In this study, the performance of the proposed debiasing-based noise suppression method applied to both the rSVD and the combination of rSVD and rSD was evaluated based on the in vivo kidney data. Similar to global SVD clutter filtering, for rSVD noise debiasing, an experimentally measured noise power image can be subtracted from the noise-contaminated PD image to achieve noise suppression. In this study, a noise ensemble of 300 frames was used. To test the performance of the combination of rSVD and rSD with noise debiasing, the original ultrasound data matrix was decomposed into 16 smaller sub-matrices based on the randomized spatial downsampling method proposed in [15]. Briefly, as shown in Fig. 3, rows of the original 2D Casorati matrix (N_z × N_x by N_t) were randomly drawn for each downsampled sub-matrix (the ‘randperm.m’ function of MATLAB was used). For each downsampled sub-matrix, rSVD was performed to reject tissue clutter, and the clutter filtered sub-matrices were then placed back in their original positions to reconstruct the clutter filtered 2D Casorati matrix, which was then reshaped for PD image generation. Noise debiasing was then achieved by subtracting the measured noise power image from the reconstructed noise-contaminated PD image. For clutter filter processing time comparisons, a PC workstation with 4 CPU cores [Intel(R) Core(TM) i5–6500 CPU at 3.20 GHz] was used in this study with the different clutter filter algorithms coded in Matlab (version R2017b, MathWorks, Inc., Natick, MA, USA). The processing time of each clutter filter method was repeated five times to provide an average. For rSVD combined with rSD, only the processing time for calculating a single subset of data was evaluated, ignoring the computational overhead for parallel processing.

Fig. 3.

Schematic plot of randomized spatial downsampling (rSD).

III. Results

A. Debiasing-based noise suppression in global SVD clutter filtering

After noise suppression with debiasing, the contrast of the PD image is greatly improved, as shown in Fig. 1d. Figure 4 shows a zoomed image of Fig. 1d for better visualization of the kidney cortical blood flow signal and for manual ROI selection. The white dashed line indicates the ROI for ${\overline{S}}_{blood}$ calculation, and green dashed line indicates the ROI for ${\overline{S}}_{background}$ calculation. The same set of ROIs will be utilized throughout the study for in vivo performance evaluation. The quantitative SNR measurement of the PD images before (Fig. 1b) and after (Fig. 1d) noise suppression was 3.8 dB and 17.2 dB, respectively. Subtle details of microvessel structure within the cortical region (as indicated by the ROI within the white dashed line in Fig. 4) can be better discerned after noise suppression. Power Doppler profiles from the PD image of the kidney data along a horizontal direction (indicated by the white dashed line in Fig. 1d) and a vertical direction (indicated by the light blue dashed line in Fig. 1d) are shown in Figs. 5a and 5b, respectively. One can observe that a much higher contrast can be achieved with the proposed noise debiasing method. With the removal of noise bias, the low blood flow signals (as indicated by the red arrows in Fig. 5b) can be better differentiated, even at a depth of around 55 mm, which might otherwise be easily submerged into the background noise.

Fig. 4.

A magnified display of the cortical region of the in vivo kidney PD image as indicated in Fig.1d. The regions inside the dashed white and green lines were manually selected for evaluation of the PD SNR.

Fig. 5.

(a) Power Doppler profiles of the in vivo kidney data along the white dashed line indicated in Fig. 1(d). (b) Power Doppler profiles along the light blue dashed line indicated in Fig. 1(d). The blue profiles represent the power Doppler profiles without noise debiasing, while the orange ones represent the corresponding power Doppler profiles with noise debiasing. The red arrows in (b) indicate the positions of two adjacent small vessels at a depth around 55 mm, which can be better differentiated with higher contrast using the noise debiasing method.

As a comparison, the results from the noise equalization method are shown in Fig. 6. Figure. 6a shows the noise field derived from the highest-order singular values for noise equalization, and Fig. 6b is the corresponding noise-equalized PD image of the same kidney data. The SNR measurement of the noise equalized image is 6.5 dB, which is 2.7 dB higher than the non-equalized image (Fig. 1b) but still much lower than the noise debiased image (Fig. 1d), as detailed in Table I. In addition, while noise equalization can markedly improve the visualization of the kidney blood signals by equalizing the noise field, residual tissue clutters in the near field can be significantly amplified, as indicated by the arrows in Fig. 6b.

Fig. 6.

(a) Noise field derived from the highest-order singular value for noise equalization. (b) Power Doppler image obtained with noise equalization method by dividing noise-contaminated PD image (Fig. 1b) by the smoothed noise field (Fig. 6a).

TABLE I.

Blood Signal-to-Noise-Ratio (SNR) Measurements and Processing Performance for Different Clutter Filtering and Noise Suppression Methods

	SNR (dB)	Processing time (s)	Processing rate (Hz)
Full SVD	3.8	3.40 ± 0.04	0.29
Full SVD + noise equalization	6.5	4.59 ± 0.02	0.22
Full SVD + noise debiasing	17.2	3.74 ± 0.12	0.27
rSVD	3.8	1.01 ± 0.13	0.99
rSVD + noise debiasing	15.4	1.30 ± 0.09	0.77
rSVD + randomized downsampling + noise debiasing	13.6	0.101 ± 0.007*	9.90*

^*indicates processing time/processing rate for calculating a single subset of matrix for the rSVD + randomized downsampling + noise debiasing method, which may be considered as the processing time/rate for the parallel processing of all the datasets, if computational overhead for parallel processing is ignored. It should be noted that the processing time and processing rate were calculated based on the data with a large field-of-view (FOV) (80 mm × 100 mm) and long ensemble (300 frames). For real-time implementation, a much smaller FOV and shorter ensemble length would be used.

B. Influence of transmitting voltages and TGC settings

The PD images of blood flow phantom obtained with the global SVD filtering using different transmitting voltages and TGCs are shown in Fig. 7. The ROIs indicated in the first figure of Fig. 7 are used to calculate the blood flow SNR, where the white dashed rectangle indicates the ROI for background noise, and back dashed rectangle indicates the ROI for the blood flow. It is clear that a higher transmitting voltage is associated with a higher SNR for all TGC settings, as shown in Fig. 7. At each voltage level (1^st column and 3^rd column in Fig. 7), a lower TGC reduces SNR, which agrees with the results reported in a previous study [16]. When TGC gain is turned off (second row in Fig. 7), the blood flow signal becomes less discernible at the voltage of 10 V (SNR = 1.1 dB). With voltage reduced to 5 V, the blood signal is almost indistinguishable from the background noise, and SNR is as low as 0.2 dB. The second fourth columns in Fig. 7 show the corresponding noise-suppressed PD images with the proposed method, revealing a significant improvement of SNR. Even for the lowest SNR case (TGC 2, 5V), an increase of 6.5 dB of SNR can be achieved, and the weak blood flow signal can be better visualized with noise floor removal. However, for the deeper region (> 60 mm) where no blood signal is detected with TGC turned off, removal of noise bias does not improve the SNR. Therefore, a higher TGC is always preferred for blood flow detection. For TGC 3, all the TGC values were set to maximum, and thus noise level was elevated in the near field, as compared with TGC1. In this study, both TGC1 and TGC 3 values were already set to maximums in the deeper region (approximately 40 mm and beyond) and thus the SNR measured from below 40 mm for the two TGC cases are similar, as shown in Fig. 7. These results demonstrate the feasibility of the proposed method in noise suppression under different SNR situations.

Fig. 7.

Power Doppler images of blood flow phantom based on global SVD clutter filtering with or without noise debiasing under different transmitting voltages and TGC settings. The ROIs for blood flow SNR calculation are selected at the same depth, as indicated in the first image. TGC1: original TGC for in vivo image; TGC 2: TGC off; TGC 3: TGC maximum. All images are displayed under the same color scale (−30 dB ~ 0 dB).

C. Study of noise ensemble size

The effect of noise ensemble size was first evaluated based on a phantom data set (transmitting voltage of 10 V, TGC 1), and the results are shown in Fig. 8. A global full SVD clutter filter was used in this part of the study. According to Fig. 8, one can see that without noise power smoothing, PD SNR begins to plateau beyond a noise ensemble length of 50. With spatial smoothing, a better blood SNR can be achieved for all noise ensemble lengths. The green line in Fig. 8 indicates the blood SNR of the PD image without noise suppression, which shows that even with the lowest number of noise ensembles, a substantial improvement can still be achieved with the proposed noise suppression method. More importantly, collecting 5 noise ensembles only requires 10 ms based on the 500 Hz PRF used in this study, which should have negligible impact in practice. For the in vivo kidney data, quantitative blood SNR was estimated based on the ROIs shown in Fig. 4, and similar findings are observed. Examples of noise power images estimated without or with spatial smoothing (10×10 pixel 2D median filter) using different number of noise ensembles are shown in the first row of Fig. 9, and the corresponding noise-suppressed PD images are shown in the second and third row of Fig. 9. With increased noise ensemble lengths, one can see an improved noise power estimation and improved quality of the corresponding noise-suppressed PD images. Figure 10 shows the quantitative resulting blood SNR measurements, which is in good agreement with the phantom experiment (Fig. 8).

Fig. 8.

Blood SNR measurements of the blood flow phantom PD images debiased with different noise ensemble lengths. The green line indicates the blood SNR of the PD image without debiasing-based noise suppression.

Fig. 9.

Study of the impact of different noise ensemble lengths on noise suppression for UMI PD images. (a) Noise power images estimated without and with spatial smoothing using different noise ensemble lengths (indicated in the title of each figure). (b) Noise-suppressed PD images using the corresponding noise power images in (a). (c) Magnified images of the corresponding small regions indicated by the dashed white rectangles in (b). All images are displayed under the same color scale (−30 dB ~ 0 dB).

Fig. 10.

Blood SNR measurements of the in vivo kidney PD images debiased with different noise ensemble lengths. The green line indicates the SNR of the PD image without debiasing-based noise suppression.

D. Debiasing-based noise suppression in accelerated SVD clutter filtering

This section shows the implementation of the noise suppression method in accelerated SVD clutter filtering, with the purpose of real-time and noise-debiased UMI. Figure 11a shows the PD image obtained using rSVD clutter filtering without noise debiasing. Similar to the global SVD clutter filtered results, the ramp-shaped background noise can be clearly observed. The SNR measurement of the rSVD clutter filtered image is 3.8 dB, which is similar to the result of the full SVD clutter filter (Fig. 1b, Table I). With noise debiasing, rSVD can produce a PD image with significantly improved SNR (15.4 dB, Fig. 11b), which is almost identical to the full SVD filtered PD image with noise debiasing (17.2 dB, Fig. 1d).

Fig. 11.

Power Doppler images processed with (a) rSVD clutter filtering, (b) rSVD clutter filtering with noise debiasing, and (c) rSVD and rSD with noise debiasing.

As shown in Table I, the added computational cost of the debiasing-based noise suppression is small. Specifically, the noise power estimation and subtraction shows to add about 10 % of processing time to the full SVD processing (3.40 ± 0.04 s versus 3.74 ± 0.12, Table I) and about 30 % of processing time to the the rSVD processing (1.01 ± 0.13 s versus 1.30 ± 0.09 s, Table I). Figure 11c shows the noise suppressed PD image obtained using the combination of rSVD and rSD, where the original data set was randomly divided into 16 subsets and processed with rSVD separately. The SNR measurement in this case slightly drops to 13.6 dB, but it is still significantly higher than that of the non-debiased PD image (3.8 dB, Fig. 11a). The computational performance for rSVD and rSD combined is approximately 10x faster than rSVD alone and 30x faster than full SVD, which can justify the slight loss in SNR in practice.

IV. Discussion

In this paper, we proposed a debiasing-based noise suppression method that can effectively suppress noise-induced bias in ultrafast UMI and facilitate robust real-time SVD-based clutter filtering based on rSVD and rSD. One major challenge of ultrafast UMI is the presence of depth-dependent noise resulting from the weak ultrasound signals in deep regions of the tissue with unfocused ultrasound transmission. The proposed method addresses this challenge by removing the noise-induced bias from PD images to improve ultrafast UMI quality. The effectiveness of the proposed debiasing method was demonstrated in vivo, showing a marked improvement of PD image SNR. With suppression of the additive noise bias, subtle details of vessel structure within the cortex region of the kidney data can be clearly resolved at a depth up to 6 cm in this study. Figure. 12 shows two additional in vivo cases of liver PD images, further demonstrating the performance of the proposed technique for noise suppression and better vasculature visualization.

Fig. 12.

Two cases of in vivo liver PD images. (a) and (c) are PD images obtained based on global SVD clutter filtering without noise debiasing. (b) and (d) are the corresponding noise debiased PD images obtained by the proposed method.

The noise equalization method previously proposed in [16] cannot provide improvement in SNR by definition, since both the blood signal and background noise are divided by the same equalizing factor (i.e., the noise field). Although in Table I the SNR values vary slightly before and after using this method, this is simply because the ROis used to quantify the SNR for the in vivo kidney data were selected at different depths (as indicated in Fig. 4) where the noise-determined equalizing factors are different. The ROIs for blood flow and background were preferable to be at the same depth, but in this study their selection was limited by the in vivo distribution of blood vessel. Even though a full SVD may not be necessary to derive the noise field for noise equalization (there are other fast ways for noise field estimation like the proposed experimental measurement method), the equalization process may amplify the residue tissue clutter in the near field and deteriorate the imaging performance. Unlike noise equalization, the debiasing-based noise suppression method proposed in this study estimates the noise bias directly from experimentally collected noise ensembles, and removes this bias, yielding a much improved SNR. Even for very low SNR situation, the proposed method can still improve the visualization of weak blood flow signal that is otherwise submerged in the strong background noise, as indicated in the phantom experiment (second row, Fig. 7). For the in vivo kidney data, the power Doppler profile before and after noise debiasing also provide evidence of improved visualization of weak blood flow signal at a depth of around 55 mm (as indicated by the arrows in Fig. 5b). However, it is noted that the underlying principle of the proposed method to improve blood flow PD SNR is based on reducing the noise bias, as opposed to increasing blood flow signal. Therefore, removing the noise floor does not improve the blood flow SNR if no blood flow signal is detected at all. This is reflected in the second row of Fig. 7 for the deeper region (> 60 mm) where the ultrasound SNR was too low to detect any blood signal. Therefore, according to the results, a higher acoustic power (voltage) and TGC gain would always be desired to increase the overall ultrasound SNR and to detect weak blood flow signal.

In this study, only the processing time for a single subset of data was evaluated for the combination of rSVD and rSD method with noise suppression, which may be considered as the theoretical processing time for parallel processing if the associated overhead is ignored. Realistically, the computational performance of parallel processing on an entire power Doppler data set depends on the number of available CPU cores, the number of subsets and the associated overheads. More information can be found in a previous publication [15]. It should also be noted that only the processing time for different methods based on a workstation and Matlab was used to compare different methods in this study, which may be influenced by factors such as the architecture of the processing unit, memory management, algorithm optimization and programming language. Thus the processing time serves only as an approximation of computational cost. The purpose of this study, however, is to propose a simple and effective noise debiasing method that can be combined with the previous proposed accelerated SVD methods to provide both fast and high-quality microvessel imaging. Therefore, the study focused on evaluating the blood flow SNR improvement and the added computational cost of the proposed method, instead of the computational complexity of the accelerated SVD methods. A thorough evaluation of the accelerated SVD methods has been provided in a previous study where the computational complexity has been compared and the real-time feasibility of the technique has been shown [15]. The results here indicate a slight drop of SNR when rSD was included, as shown in the Fig. 11c, which might be a limitation of the real time implementation of the technique. The minor compromise of image quality, however, is acceptable since the SNR of the PD image is still much higher than those without noise suppression (Fig. 11c versus 11a), while the computational speed can be up to 30x faster. Furthermore, the test data used in this study have a large FOV (dimension: 80 mm × 100 mm) and a long ensemble length (300 frames). In practice, a predefined ROI with size of 40 mm × 40 mm and a shorter ensemble (say 50 frames) would probably be sufficient for most real-time applications. This reduction of data size would further boost the computational speed.

For real-time implementation, integrating the blood flow imaging sequence and noise ensemble collection sequence is practically feasible. Our results show that even the lowest noise ensemble tested in this study (5 ensemble length) can provide a substantially improved UMI with noise debiasing. This would only require 10 ms for a 500 Hz frame rate and 5 ms for a 1000 Hz PRF in practice. The noise frames do not need to be continuously acquired (because noise is uncorrelated from frame to frame), and thus any noise frame combination can be applied to estimate a robust noise profile. Meanwhile, the electronic noise collected for noise debiasing is target-independent because no acoustic energy is transmitted during noise ensemble acquisitions. Therefore, a new measurement of noise ensembles is only required when the imaging settings (including TGC, beamforming processes etc.) are changed. Thus in practice, it is still feasible to collect a long noise ensemble with the same length as the actual UMI imaging sequence (e.g. 300 ensemble lengths). In addition, a lookup table of the noise fields for all possible combinations of the imaging sequences and system configurations could be established, from which the scanner can automatically select the noise power image without acquiring new noise frames and thus facilitating real-time implementation.

This study only focused on removing the bias in the power Doppler image induced by the additive electronic noise, which is a major source of deterioration of the microvessel images. By suppressing this bias, the SNR of the microvessel image can be substantially improved, and the microvessel signal can be better visualized, as indicated by the results. However, the multiplicative noise (such as speckle noise) and artifacts (such as side lobe artifacts) are not removed, which is a limitation of the proposed method. Another limitation of the current study is the lack of a reference standard for the in vivo data used for the evaluation of the proposed method. Considering the difficulties of constructing realistic small vessel imaging phantoms, using the same in vivo data set throughout the study was considered to be a good alternative. Human kidney data was chosen as the preferred in vivo test data since it has a well-organized vessel hierarchy, which can be used to determine if the reconstructed microvessel image concurs with anatomical expectation. In addition, the kidney includes the cortex region with rich microvessels and the renal pyramid region without blood signal to serve as the background contrast, which facilitated the calculation of SNR for the study.

While we focus on UMI based on SVD clutter filtering, the proposed noise suppression method can also be applied to noise-contaminated PD images obtained by other types of tissue clutter filters, such as temporal high-pass filters. Although the proposed method is elaborated in the context of 2D imaging, the idea can be readily applied to 3D blood flow imaging, where 3D noise power volume can be estimated and subtracted as described in this study. Finally, the study focuses on UMI without injection of ultrasound contrast agents, while the underlying principle can be extended to contrast-enhanced ultrasound imaging (CEUS) for further enhancement of imaging performance.

V. Conclusion

A noise debiasing method was proposed in this study that estimates and removes the noise bias present in SVD clutter filtered UMI experimentally by acquiring separate noise-only data frames. The proposed method can be readily combined with accelerated SVD methods, is computationally inexpensive, and requires only a small amount of additional data acquisition. Substantial improvement of blood flow SNR in UMI was shown in vivo for accelerated SVD clutter filtering when combined with the proposed debiasing-based noise suppression method. The proposed method has great potential for real-time implementation of high quality ultrafast UMI based on SVD clutter filtering, facilitating its implementation in a wide range of clinical applications.

Biographies

Chengwu Huang received the B.S. degree in biomedical engineering from Beihang University, Beijing, China, in 2012, and the Ph.D. degree from the Department of Biomedical Engineering at Tsinghua University, Beijing, China, in 2017. He is now with the Department of Radiology, Mayo Clinic College of Medicine, Rochester, Minnesota, USA. His current research interests include ultrasound microvessel imaging and ultrasound elastogrpahy.

Pengfei Song (IEEE/S’09/M’14) received the B.Eng. degree in Biomedical Engineering from the Huazhong University of Science and Technology, Wuhan, China, in 2008; the M.S. degree in Biological Systems Engineering from the University of Nebraska-Lincoln, Lincoln, NE, in 2010; and the Ph.D. degree in Biomedical Sciences-Biomedical Engineering from the Mayo Graduate School, Mayo Clinic College of Medicine, Rochester, MN, in 2014. He is currently an Assistant Professor in the Department of Radiology, Mayo Clinic College of Medicine, Rochester, MN. His current research interests are ultrasound microvessel imaging and ultrasound shear wave elastography. Dr. Song is a member of IEEE, AIUM, and Sigma Xi.

Ping Gong received the B.Sc degree from Tianjin University, China, majoring Biomedical Engineering in 2010. She completed her M.Sc. degree in the Department of Electrical and Computer Engineering at Lakehead University, Canada in 2012 and Ph.D. in Biomedical Physics, Ryerson University in 2016. She is now with the Department of Radiology, Mayo Clinic College of Medicine, Rochester, Minnesota, USA. Her research focuses on developing ultrasound transmission and beamforming algorithms to improve ultrasound image quality.

Joshua D. Trzasko (IEEE/M’99/SM’2014) received the B.S. degree in Electrical and Computer Engineering in 2003 from Cornell University and the Ph.D. degree in Biomedical Engineering from Mayo Graduate School in 2009. He is currently an Associate Consultant in the Division of Medical Physics and Assistant Professor of Radiology and Biomedical Engineering at Mayo Clinic. Dr. Trzasko’s research focuses on the development and application of statistical signal processing methods for medical imaging, including: quantitative imaging, artifact correction, and limited data reconstruction in magnetic resonance imaging (MRI); radiation dose reduction in x-ray computed tomography (CT); and ultrasound (US) microvasculature imaging.

Armando Manduca (SM’89) received the B.S. degree in mathematics from the University of Connecticut, Mansfield, CT, USA, in 1974, and the Ph.D. degree in astronomy from the University of Maryland, College Park, MD, USA, in 1980. He is currently a Professor of Biomedical Engineering and Radiology, and the Chair of the Division of Biomathematics and Translational Engineering with Mayo Clinic, Rochester, MN, USA. His research interests include the development of algorithms for the analysis of MR and ultrasound elastography data, image denoising for CT data to reduce radiation dose, and ultrasound microvessel imaging.

Shigao Chen (IEEE/M’02) received the B.S. and M.S. degrees in biomedical engineering from Tsinghua University, China, in 1995 and 1997, respectively, and the Ph.D. degree in biomedical imaging from the Mayo Graduate School, Rochester, MN, in 2002. He is currently an Associate Professor of the Mayo Clinic College of Medicine. His research interest is noninvasive quantification of the viscoelastic properties of soft tissue using ultrasound, and ultrasound microvessel imaging.