Motion Compensation Improves Medical Ultrasound Image Quality

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1 Motion Compensation Improves Medical Ultrasound Image Quality Lian Yu, 1 Nicola Neretti, 2 Leon Cooper, 2 and Nathan Intrator 3 Abstract Internal noise degrades the quality of a medical ultrasound imaging and thus, reduces its usefulness as a diagnostic tool. We study the effect of fusing multiple ultrasound pings on improving the quality of the ultrasound image. This approach is limited by the relative motion between the sensor array and internal organs, a problem which reduces the effect of the fusion. We present a robust motion estimation algorithm that relies on multiple receivers. We further demonstrate that fusion of multiple ping images following motion compensation improves the ultrasound image quality and removes the degrading effect of tissue motion. Finally, we demonstrate that ultrasound imaging can be enhanced by the use of image processing methods and by overlaying the skeleton on the analog image. Index Terms Ultrasound image, motion compensation, image processing I. INTRODUCTION The current challenge of ultrasonic systems is to scan deeply without sacrificing the accuracy, which is strongly dependent on the background noise. With higher scanning frequency and increasing penetration depth, the returning ultrasound signal is attenuated, and therefore more affected by noise. In fact, when the noise level is above a certain threshold, accuracy falls rapidly [1]. One possible solution to this problem is to average returns over multiple ultrasonic pings. Such averaging is likely to reduce the effect of noise by a factor of 1/ n, where n is the number of successive pings. This approach can be useful when there is no tissue or sensor motion. When using synthetic aperture ultrasound techniques, tissue motion during data acquisition may cause significant degradation in image resolution since each image pixel is reconstructed by coherent summation of echo signals from multiple pings. Synthetic aperture ultrasonic imaging attempts to increase image resolution using a small number of array elements in the ultrasound data collection. It has the potential to improve image quality beyond that obtained by imaging techniques like phased array imaging. This method, which has been investigated over the last decade [2],[3] suffers from two main problems which limit the quality of synthetic aperture imaging: low signal-to-noise ratio (SNR), and sensitivity to tissue motion. Motion compensation has been proposed to address tissue motion problems [4],[5]. Most of the studies on motion compensation for synthetic aperture imaging are based on correlation measurements [4]-[7]. The cross-correlation of reference signals uses position sensitive signal processing mainly depends on the correlation level between reference signals. The performance of the shift estimation technique after cross-correlation relies heavily on the choice of the time-delay estimation kernels. A detailed comparison of the different time-delay estimation kernels is given in [8]. In this paper, we propose a novel robust motion estimation method. We then explore adaptive imaging fusion with motion compensation. We present a robust motion estimation algorithm that relies on multiple receivers. We further demonstrate that fusion of multiple ping images following motion compensation improves the ultrasound image quality and removes the degrading effect of tissue motion. Finally, we demonstrate that ultrasound imaging can be enhanced by the use of image processing methods and by overlaying the skeleton on the analog image. A.. Motion estimation and compensation II. METHODOLOGY 1 Lian Yu is with the Department of Mathematics, Beijing Normal University, 19 Xinjiekouwai St., Beijing , P. R. China. 2 Nicola Neretti and Leon Cooper are with the Institute for Brain and Neural Systems and Dept. of Physics, Brown University 3 Nathan Intrator is with the school of Computer Science, Tel-Aviv University, Ramat Aviv 69978, Israel. 1

2 Coherent summation of the successive images is necessary for reducing the effect of noise in ultrasound images. If the successive images are not phase aligned, the summation produces a blurred and fuzzy image. This affects the SNR, spatial resolution, and contrast resolution. The phase misalignment is induced by tissue and sensor motion between each pinging. Thus, motion estimation and compensation is required to maintain image quality. The motion estimation and compensation method that is presented here is based on cross-correlation of match filtered successive ultrasound ping returns. The method is illustrated in Fig. 1 using two ultrasound pings. Two successive pinging signals of all aperture elements are collected. We assume that there may be some rigid tissue motion between successive pings. As the time between two pings is short, the translation distance and rotation angle of tissue motion is expected to be small. In this case, the motion can be assumed as a line motion relative to the sensor array. Then the signal of the same line in two successive pings is similar, but out of phase. The phase differences are approximately on a straight line across the ping return lines. The line has an angle with the aperture array due to possible rotation of the tissue (Fig 1). The translation distance and rotation angle should be estimated for motion compensation. We estimate the translation distance and rotation angle simultaneously. First the returns from two pings are cross-correlated. Then the peak of the cross-correlation is estimated. The peak location should provide an estimation of the phase delay between the two pings along the same beam-formed line. The essential assumption, which makes this robust delay estimation possible, is the fact that the sensor array is mounted on a rigid body, and thus the movement between the sensor array and the tissue should fall on a straight line (see Fig. 2). Thus, the estimated time delays of the peaks of all returns to the different sensor elements should be located around a straight line. The variability around this line results from errors in the estimation that is due to noise. A straight line can be fitted through all these time delay peaks (Fig. 2). The center of the fitting line is the estimated translation distance of the tissue and the angle between the fitting line and the aperture array is the estimated rotation angle relative to the tissue. The estimated phase shift of each image line is the value of the estimated delay at the respective position. After compensating the phase shift to each sensor line of the successive ping, the two pings become aligned in phase and can be used to build a fused image from the multiple pings. The estimation of the line which indicates the estimated shift of sensor array relative to the tissue between successive pings is not straightforward. The simplistic approach is the least square line fitting (LSLF). The problem of this approach is its sensitivity to outliers. The estimation of phase delays suffers from big outliers, when the peak of the cross correlation is incorrectly found due to background noise. Thus, a method that is less sensitive to possible outliers is required. We present below a more robust line fitting method which uses an improved mode of a distribution to estimate the location of the line (IMLF) for underwater sonar system [9]. The method can be used for ultrasound system without any modification. Consider a set of points from 1 to N. Consider all the lines which go through at least two points (with some limitation on the tilt degree of the line). For each line, we compute a bin with a certain width that is centered at that line. Comparing the number of points falling inside the bin, the line which contains the largest number of points in its bin is estimated to be the fitting line through the points. The steps of the algorithm are Step 0: Input a set of points p ( i) = ( x( i), y( i)), i = 1... N, N is the number of points, select an engaged gap e as the width of the bin which is centered around a selected line, select a degree suitable line, set k = 1 { } Step 1: Select a pair of points p( i), p( j), i, j = 1,..., N, i j p( i), p( j) Step 2: Compute the line l through the point pair { } θ max as the maximum tilt degree of a Step 3: Calculate the tilt degree θ between line l and x direction abs( θ ) > θ if max, then ignore line l, go to step 1 else keep line l and put l L in the suitable line set as k, continue step 4 L Step 4: Search the points whose distance to line k is less than e, save the number of these points as num( k), k = k + 1 Step 5: Iterate step 1-4 for all the point pairs L Step 6: Search the line K which contains the maximum number of points as 2

3 K = arg max{ num( k)} k Step 7: Output line LK as the fitting line of the point set p B. Image processing For improving the quality of the image fusion result, we robustified the images by bounding the intensity values of the image to be between the 3 percentile to 97 percentile of the image intensity values. This made a better use of the intensity level scheme by removing outliers in intensity level. Improvement in image quality is demonstrated in the simulation results. To further enhance on ultrasound image, we present a skeleton extraction approach which utilizes the multiple image fusion following motion compensation. Suppose there are multiple ultrasound images which are realigned by motion compensation. It is possible to fuse these images by averaging over the motion compensated images. For each ping return of the fused image, a threshold can be assigned, to detect regions with strong ping return. The threshold can be determined using the mean of the beam plus a certain standard deviation. Regions in the beam with a value larger than the threshold are selected. The strong ping returns, usually represent a tissue boundary which we are trying to enhance. In particular, this can be useful for tracking arteries. Once the mean ping return is above the threshold, we use the temporal mean of peak locations from the collection of returns to determine the exact position of fused image peak in a manner similar to [9]. III. SIMULATION AND RESULTS A. System setup A set of simulations using Field II ultrasound simulator [10] have been performed for investigating the image fusion effect following motion compensation based on several line fitting algorithms. We used one ultrasound transmitter and 32 receivers of linear array making up the beamformer. The element height was 5mm, the width was half wavelength of ping signal and the kerf was 0.05 mm. We used a Hanning apodization [10] for emission and reception. The focusing scheme used multiple emission and reception zones which focused at every 2 mm. For analog beamformers this is a small zone size. For digital beamformers it is a large zone size. This focusing scheme was used to obtain high-detail and high-contrast resolution preferably constant for all depths. The pinging signal was created by timing a Hanning window on a sinusoidal signal. It was a Mexican hat at a center frequency of 3MHz with 6.7µs duration. Both the pinging signal and its auto-correlation had a sharp peak and two symmetric negative part with lower magnitude. For simplicity, the motion was considered relative to the array location at the first ping. The translate distance of the motion was modeled by a uniformly distributed random displacements in the range [-2λ, 2λ] where λ is the wave length of the pinging signal. The rotation angel of the motion was modeled as uniformly distributed between [-2º, 2º]. White Gaussian noise was added to each received signal. The SNR was measured in decibels as a function of the ratio between the total energy of the echo (measured in Ws), and the spectral density of the noise (measured in W/Hz). The noise energy was further colored by the spectral density of the signal so that the effect of the noise be maximal (see [11] for further details). Using this measurement of SNR, the spectrum of the noise which actually influences the detection of the signal becomes equal to the spectrum of the signal. The SNR level was 10db. The received data of each receiver was contaminated by noise as raw data. The image was reconstructed using back projection technique [12] for each ping from the raw data. No interpolation and filter were used for back projection. The resolution of the image was 200x800. B. Motion estimation simulation The motion estimation method was evaluated by using a point reflector surrounded by 10,000 scatterers. The motion between two pings was estimated using least-square-line-fitting (LSLF) method and by our Improved Mode Line Fitting (IMLF) method. Following motion estimation and compensation, an image was reconstructed. The multiple ping fusion was achieved by averaging 50 (motion compensation) reconstructed images. Fig. 3 demonstrates the differences between the motion estimation schemes. Fig. 3a depicts a reconstructed image from a single ping returns. The target is almost completely covered by the background noise. Fig. 3b depicts fusion of reconstructed images of jittering ultrasound pings without motion compensation. It is evident that such fusion of images does not improve the quality of the image beyond a single ping reconstructed image. Fig. 3c depicts image fusion following motion compensation that the motion has been estimated using the classical LSLF method. Fig. 3d depicts the same fusion when the motion has been estimated via our proposed IMLF algorithm. It is clear that the 3

4 fusion of reconstructed images which used the IMLF motion estimation is significantly better than LSLF. For comparison, Fig. 3e demonstrates an image fusion of the same number of noisy image when no relative motion between the receiver and tissue exists. It can be seen that the motion compensated image fusion using IMLF method is close to the optimal quality that can be achieved if no motion exists. It is also clear that the image fusion (Fig. 3d) leads to far better results than a single image reconstruction (Fig. 3a). For quantitative testing of the improvement of the image quality, we tested the contrast resolution (CR) and the contrast-to-noise-ratio (CNR) of the images. The CR calculation is described in [7]: It Ib CR = (1) Ib where I t and I b are the intensity of the target and the background respectively. I t is calculated by finding a target region and calculating its intensity. I b is calculated by finding a region of no target in the image and calculating its averaged intensity. The CNR is given by [13] µ t µ b (2) CNR = 2 2 σ + σ / where ( ) 2 t b µ and t σ t are the mean and standard deviation of the intensity of the target, and µ and b σ b are the mean and standard deviation of the intensity of the background. These values are estimated from different regions in the image as described above. The CR and CNR are computed for each of the five images in Fig.3. The result is summarized in Table I. It can be seen that the image without motion compensation (Fig 3b) has the lowest contrast resolution (even lower than the single ping image, Fig 3a). Both motion estimation methods (LSLF, Fig 3c and IMLF, Fig 3d) increase the contrast resolution. The IMLF (Fig 3d) leads to the best improvement, it s CR value (0.4385) is close to the ideal (Fig 3e) CR value (0.4585), which is calculated without motion. The CNR results support the same conclusion. C. Image processing simulation A more realistic demonstration of the effect of motion estimation and compensation is provided in Fig. 4 and 5. In these figures, a phantom organ is reconstructed via realistic ultrasound parameters. Fig. 5 takes the process a step further to extract only the skeleton of the organ from the ultrasound image. This is important for example, when following arteries in medical imaging. Image processing effects were compared using the Filed II simulator on an artificial anatomic phantom of a left kidney. Simulated tissue boundaries were introduced by forming curved lines in the scattering map along which strong scatterers were placed. This is marked by white lines shown in Fig. 4a. The model is two-dimensional and consists of 10,000 scatterers. The multiple ping ultrasound images were created from 50 pings. Fig. 4b shows a conventional ultrasound image. The image was constructed using a Hilbert transform (energy envelope) of single ping returns following cross-correlation (matched filter) between the returned echoes and the pinging signal. Fig. 4c shows a fused ultrasound image of the analog mean of multiple pings before motion compensation. Fig. 4d is a robust Hilbert envelop on fused ultrasound image of the analog mean of multiple pings (MHR) after motion compensation using IMLF motion estimation. Note the bright regions where the boundary of the kidney is orthogonal to the ultrasound and thus a large signal is received. In the single ping image (Fig. 4b) the boundary can be seen, but in (Fig. 4c) the boundary is blurred due to tissue motion. After motion compensation, the boundary becomes clear again (Fig. 4d). Note also the fuzziness of the boundaries which are parallel to the transmitted ultrasound. They can not be seen in the single ping case or the multiple pings without alignment (Fig. 4b,4c). The boundaries are clear after realignment of multiple pings (Fig. 4d) even though they are weaker than the orthogonal boundary. It follows that a compensation based on the proposed robust motion estimation of each ping return achieves near optimal (no motion case) results and removes substantial amount of image blur. Fig. 4e-g depict a comparison of different image processing methods. Fig. 4e depicts a Hilbert envelop image of the analog mean of multiple pings divided by the standard deviation of the multiple pings pixel by pixel, and the quotient is robustified to get the image (MHDR). This method can be modified (Fig. 4f) by calculating the robustified Hilbert envelop of each realigned ping data, followed by calculation of the analog mean of the multiple pings, finally using a robustified average to get the image (RHMR). The third image processing method (Fig. 4g) is a robust version of MHDR (Fig. 4e), where the echo location distribution of each ping return is calculated locally and based on that, outliers are removed prior to the calculation of a Hilbert envelop of the analog mean (RMHDR). It is easily seen that while MHDR and RHMR (Fig. 4e,f) improve the contrast of the image to some extent, RMHDR (Fig. 4g) achieves the best contrast and the most clearly image of the kidney structure (Note especially the 4

5 two circle structures in the center of the images). Comparing the weak boundary regions in both sides of the image in each plot, Fig. 4g gives a brighter and more details of the boundary. We also measured the image quality by CR and CNR for each of the six images (Fig 4b-g) using formula (1) and (2) respectively. The results are summarized in Table II. The results of the complex kidney phantom appears in agreement with the results from the point reflection target experiment. Without motion compensation, the phantom image (Fig 4c) has the lowest CR and CNR, it s contrast resolution is worse than that of the single ping image (Fig 4b). After motion compensation, both contrast resolution and CNR of the image (Fig 4d) are improved. The last three columns in the table demonstrate the effect of the three different fusion methods (Fig 4e-g). RMHDR (Fig 4g) gives the best value in both CR and CNR. D. Skeleton extraction simulation In medical applications, it is useful to follow lines in the image which often describe veins. We are demonstrating here that an improved skeletonization can also be archived with the robust fusion of multiple ultrasound pings. The effect of skeleton extraction from multiple images of a fetus phantom is shown in Fig. 5. Simulated phantom of the fetus were introduced by making lines in the scatterer map along which the strong reflectors were placed. The original skeleton image is marked by completely white lines shown in Fig. 5a. The model is two-dimensional and consists of 10,000 scatterers. The images are fused from 50 pings. Fig. 5b shows a single ping image contaminated by additive noise. Fig. 5d and 5c are the images of the analog mean of multiple pings with and without motion compensation respectively. The skeleton in Fig. 5d is extracted based on multiple images using the method discussed in section IIB. The skeleton is superposed on the image and shown in Fig. 5e by red lines. After motion compensation and image fusion, the SNR of the image is improved compare to single ping image (Fig. 5b and 5d) and furthermore, the motion compensated image has sharp contrast and high resolution. After superposition of the skeleton on the image (Fig. 5e), some details can be enhanced and the skeleton can be used for further image analysis. IV. CONCLUSIONS We have demonstrated that current ultrasound image reconstruction can be improved utilizing multiple ping returns from the same target. The use of multiple ping returns leads to a sharper ultrasound image with significant improvement of the Contrast to the Noise Ratio (CNR). This improvement is possible when compensation of the motion of each ping return is performed before fusing the multiple pings together. This paper continues the recently introduced motion estimation in underwater sonar [9]. The method utilizes the rigid motion property of the receiving sensor. In this paper, we demonstrate that the motion of the ultrasound sensor can be compensated in a similar way, and we further demonstrate its effect on enhancing the ultrasound image. We have further demonstrated that motion estimation which relies on the mode of the returning distribution (over the sensor array) leads to better estimation of the translation and rotation of the ultrasound sensor in the presence of noise (Fig. 3). We then demonstrated that the ultrasound can be further enhanced by utilizing a robust statistics of the intensity profile resulting from the multiple ping returns and by extracting the energy from the average of the returns (using a Hilbert transform) (Fig. 4). Finally we demonstrated that analog averaging of the multiple ping returns following motion compensation leads to a dramatic improvement in ultrasound image, which can be further enhanced, by overlaying the temporal average of the ultrasound returns on the analog image (Fig. 5). The proposed scheme does not require any change in the transmitting or receiving hardware of the ultrasound sensor. It enables the use of lower energy exploration as the multiple returns lead to effective increase in SNR, thus reducing potential tissue damage by using lower peak ultrasound energy. The method establishes the fact that ultrasound imagery can be enhanced by observing a certain tissue for longer time and fusing an increasing number of ultrasound returns. It is expected that the improvement of ultrasound image resolution may lead to increased use of ultrasound imagery, which is less harmful than technology that is based on radiation and is much cheaper than technology based on magnetic resonance. 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6 inhomogenities - part II: effects of and correction for motion, IEEE Trans. Ultrason., Ferroelec., Freq.Contr., vol. 39, pp , [5] M. Karaman, H. S. Bilge, and M. O Donnell, Adaptive multi-element synthetic aperture imaging with motion and phase aberation correction, IEEE Trans. Ultrason., Ferroelec., Freq. Contr., vol. 42, pp , [6] K.W.Rigby, C.L. Chalek, B.H. Haider, R.S. Lewandowski, M. O'Donnell, L.S. Smith, and D.G. Wildes, "Improved in vivo abdominal image quality using real-time estimation and correction of wavefront arrival time errors", in Proc. IEEE Ultrason. Symp., 2000, vol.3, pp , [7] K. L. Gammelmark and J. A. Jensen, Multielement synthetic transmit aperture imaging using temporal encoding, IEEE Trans. Med. Imag., vol. 22, no. 4, pp , [8] F. Viola, W.F. Walker, "A comparison of the performance of time-delay estimators in medical ultrasound,", IEEE Trans Ultrason Ferroelectr Freq Control, 50, 4, , Apr., 2003 [9] L. Yu, N. Neretti, N. Intrator, "Multiple ping sonar accuracy improvement using robust motion estimation and ping fusion,", JASA, 119 (4), pp , [10] J. A. Jensen, Field: A program for simulating ultrasound systems, Med. Biol. Eng. Comp. 10th Nordic-Baltic Conference on Biomedical Imaging, Vol. 4, Supplement 1, Part 1, pp , 1996b. [11] N. Neretti, N. Intrator and Leon N Cooper, Robust statistics from multiple pings improves noise tolerance in sonar, Submitted for publication. [12] S. Lockwood, A. Brown, and H. Lee, Backward propagation image reconstruction techniques for bistatic synthetic-aperture radar imaging systems with circular-aperture configurations, In Signals, Systems and Computers, Conference Record of the Thirty-Fifth Asilomar Conference, Vol.1, pp , [13] F. N. Ucar, M. Karaman, Beam space processing for low-cost scanners, in Proc. IEEE Ultrason. Symp. pp ,

7 FIGURE CAPTION Fig. 1 Image fusion with motion compensation. Following successive returns from multiple pings, a motion estimation scheme (see text) is employed and estimates the relative motion between the transmitter/receiver and tissue between pings. Then motion compensation is applied to returned signal so that the two successive pings are realigned and can be fused together. Fig. 2 The sketch of improved mode line fitting method. The sensor array is aligned along x-direction. The position along y-direction of each point expresses the displacement of each sensor s signal between two pings. Black points p (i) and p ( j) are the selected pair of points. Solid line L k is the fitting line through p (i) and p ( j). The gap between two dashed line is the bin of L k. The distance e between solid line and dashed line is the width of the bin. θ is the tilt degree between line L k and x-direction. Dot points are the points inside the bin. Circle points are the points outside the bin. Fig. 3 Motion compensation effects in high noise background. Reconstructed images based on different motion estimation methods at 10db SNR noise. For each ping, the image is reconstructed by using back projection method for the raw data of 10 receivers. The multiple ping images are averaged to create the fusion image. The different motion estimation methods are applied and the results are showed at each plot. Plot a is the single ping reconstructed image. Plot b is the average of multiple ping images with jitter but without motion compensation. Plot c and d are the average of multiple ping images corrected for LSLF and IMLF motion estimation method respectively. Plot e is the average of ideal multiple ping images where there is no motion between pings. The resolution of image is 200x800. Fig. 4 Image processing methods comparison by kidney phantom simulation. Plot a is original phantom of a left kidney. Plot b is the image of single ping. The data was robust Hilbert envelop of the single ping data. Plot c is the image of multiple pings before alignment. The data was robust Hilbert envelop of the analog mean of the multiple pings data before alignment. Plot d is the image of multiple pings after alignment. The data was robust Hilbert envelop of the analog mean of the multiple pings data after alignment (MHR). Plot e is the image of the robust data which was the quotient of the Hilbert envelop to the analog mean of multiple pings data divided by the standard deviation of the multiple pings data pixel by pixel (MHDR). Plot f is the image of the robust data which was the analog mean of processed multiple pings data. The processed data was the robust Hilbert envelop of each ping s data (RHMR). Plot g is the image of the robust Hilbert of the analog mean of the robust multiple pings data (RMHDR). Fig. 5 Skeleton extraction demonstration on fetus phantom simulation. Plot a is the phantom of fetus. Plot b is single ping image with noise. Plot c and d are analog mean of multiple pings without motion compensation and analog mean of multiple pings after motion compensation respectively. Plot e is the temporal mean of multiple pings peaks detected in the regions based on motion compensated multiple images. 7

8 ping k-1 Matched filter ping k Matched filter Motion estimation Motion compensation Motion compensation Image construction Image construction Coherent summation for image fusion Fig. 1 Image fusion with motion compensation. Following successive returns from multiple pings, a motion estimation scheme (see text) is employed and estimates the relative motion between the transmitter/receiver and tissue between pings. Then motion compensation is applied to returned signal so that the two successive pings are realigned and can be fused together. 8

9 Fig. 2 The sketch of improved mode line fitting method. The sensor array is aligned along x-direction. The position along y-direction of each point expresses the displacement of each sensor s signal between two pings. Black points p(i) p( j) L is the fitting line through p(i) p( j). The and are the selected pair of points. Solid line k and L gap between two dashed line is the bin of k. The distance e between solid line and dashed line is the width of the L bin. θ is the tilt degree between line k and x-direction. Dot points are the points inside the bin. Circle points are the points outside the bin. 9

10 Fig. 3 Motion compensation effects in high noise background. Reconstructed images based on different motion estimation methods at 10db SNR noise. For each ping, the image is reconstructed by using back projection method for the raw data of 10 receivers. The multiple ping images are averaged to create the fusion image. The different motion estimation methods are applied and the results are showed at each plot. Plot a is the single ping reconstructed image. Plot b is the average of multiple ping images with jitter but without motion compensation. Plot c and d are the average of multiple ping images corrected for LSLF and IMLF motion estimation method respectively. Plot e is the average of ideal multiple ping images where there is no motion between pings. The resolution of image is 200x

11 (a) Fig. 4 Image processing methods comparison by kidney phantom simulation. Plot a is original phantom of a left kidney. Plot b is the image of single ping. The data was robust Hilbert envelop of the single ping data. Plot c is the image of multiple pings before alignment. The data was robust Hilbert envelop of the analog mean of the multiple pings data before alignment. Plot d is the image of multiple pings after alignment. The data was robust Hilbert envelop of the analog mean of the multiple pings data after alignment (MHR). Plot e is the image of the robust data which was the quotient of the Hilbert envelop to the analog mean of multiple pings data divided by the standard deviation of the multiple pings data pixel by pixel (MHDR). Plot f is the image of the robust data which was the analog mean of processed multiple pings data. The processed data was the robust Hilbert envelop of each ping s data (RHMR). Plot g is the image of the robust Hilbert of the analog mean of the robust multiple pings data (RMHDR). 11

12 Fig. 5 Skeleton extraction demonstration on fetus phantom simulation. Plot a is the phantom of fetus. Plot b is single ping image with noise. Plot c and d are analog mean of multiple pings without motion compensation and analog mean of multiple pings after motion compensation respectively. Plot e is the temporal mean of multiple pings peaks detected in the regions based on motion compensated multiple images. 12

13 Table I. Calculated CR and CNR for the motion estimation simulation Method Single ping Without LSLF IMLF Idea motion estimation CR CNR Table II. Calculated CR and CNR of images from motion compensation and image processing on kidney phantom simulation Method Single ping Without motion compensation With IMLF motion compensation MHR MHDR RHMR RMHDR CR CNR Table I. Calculated CR and CNR for the point reflection motion estimation simulation. First row is the contrast resolution (CR) value. Second row is the contranst-to-noise-ratio(cnr) value. Both CR and CNR are calculated on each of five images in Fig. 3a-e and showed in columns. The columns are respectively single ping image, multiple ping image without motion compensation, motion compensated multiple ping image using LSLF motion estimation, motion compensated multiple ping image using IMLF motion estimation and the idea case which is the multiple ping image without motion. Table II. Calculated CR and CNR of images from the motion compensation and image processing on kidney phantom simulation. CR and CNR numbers are showed in rows respectively. Both CR and CNR are calculated on each of six images in Fig. 4b-g and showed in columns. The first column is for single ping image. The second column is for multiple ping image without motion compensation. Column 3-6 are results of multiple ping image fused after motion compensation using IMLF motion estimation method and compare between different image processing method. The image processing methods are MHR, MHDR, RHMR, RMHDR respectively. 13