Fast Randomized Singular Value Decomposition-Based Clutter Filtering for Shear Wave Imaging

The mechanical properties of soft tissues can be quantitatively characterized through the estimation of shear wave velocity (SWV) using various motion estimation methods, such as the commonly used block matching (BM) methods. However, such methods suffer from slow computational speed and many tunable parameters. In order to solve these problems, Butterworth filter-based clutter filter wave imaging (BW-CFWI) is recently proposed to detect the mechanical wave propagation by highlighting the tissue velocity induced by mechanical wave, without using any motion estimation methods. In this study, in order to improve the SWV estimation performance of the clutter filter wave imaging (CFWI) method, we propose singular value decomposition (SVD)-based clutter filter for CFWI (SVD-CFWI) and further accelerate it using a randomized SVD (rSVD)-based clutter filter (rSVD-CFWI). Homogeneous phantoms with different Young's moduli are used to investigate the influences of the cutoff order of singular value and iteration time on the performance of SWV estimation. An elasticity phantom with stepped cylindrical inclusions is tested for comparison of rSVD-CFWI, SVD-CFWI, BW-CFWI, and normalized cross-correlation (NCC)-based BM (NCC-BM). The performances of the proposed methods are also evaluated on data acquired from the bicipital muscle in vivo. The results of phantom experiments show that rSVD-CFWI and SVD-CFWI reconstruct SWV maps with improved shape of the inclusions. For the softest inclusion with a diameter of 10.40 mm, the contrast-to-noise ratios (CNRs) between the inclusions and background obtained with rSVD-CFWI (3.78 dB) and SVD-CFWI (3.71 dB) are higher than those obtained with BW-CFWI (0.55 dB) and NCC-BM (0.70 dB). For the stiffest inclusion with a diameter of 10.40 mm, higher CNRs are also achieved by rSVD-CFWI (5.68 dB) and SVD-CFWI (5.07 dB) than by BW-CFWI (2.92 dB) and NCC-BM (2.36 dB). In the in-vivo experiments, more homogeneous SWV maps and smaller standard deviations of SWVs are obtained with rSVD-CFWI and SVD-CFWI than with BW-CFWI and NCC-BM. Besides, RSVD-CFWI has lower computational complexity than SVD-CFWI and NCC-BM and has lower memory space requirement than SVD-CFWI. The computational speed of rSVD-CFWI is comparable to that of BW-CFWI and over 10 times higher than that of SVD-CFWI. Therefore, RSVD-CFWI is demonstrated to be a competitive tool for fast shear wave imaging.