Clutter suppression in ultrasound: performance evaluation and review of low-rank and sparse matrix decomposition methods

Abstract

Vessel diseases are often accompanied by abnormalities related to vascular shape and size. Therefore, a clear visualization of vasculature is of high clinical significance. Ultrasound color flow imaging (CFI) is one of the prominent techniques for flow visualization. However, clutter signals originating from slow-moving tissue are one of the main obstacles to obtain a clear view of the vascular network. Enhancement of the vasculature by suppressing the clutters is a significant and irreplaceable step for many applications of ultrasound CFI. Currently, this task is often performed by singular value decomposition (SVD) of the data matrix. This approach exhibits two well-known limitations. First, the performance of SVD is sensitive to the proper manual selection of the ranks corresponding to clutter and blood subspaces. Second, SVD is prone to failure in the presence of large random noise in the dataset. A potential solution to these issues is using decomposition into low-rank and sparse matrices (DLSM) framework. SVD is one of the algorithms for solving the minimization problem under the DLSM framework. Many other algorithms under DLSM avoid full SVD and use approximated SVD or SVD-free ideas which may have better performance with higher robustness and less computing time. In practice, these models separate blood from clutter based on the assumption that steady clutter represents a low-rank structure and that the moving blood component is sparse. In this paper, we present a comprehensive review of ultrasound clutter suppression techniques and exploit the feasibility of low-rank and sparse decomposition schemes in ultrasound clutter suppression. We conduct this review study by adapting 106 DLSM algorithms and validating them against simulation, phantom, and in vivo rat datasets. Two conventional quality metrics, signal-to-noise ratio (SNR) and contrast-to-noise ratio (CNR), are used for performance evaluation. In addition, computation times required by different algorithms for generating clutter suppressed images are reported. Our extensive analysis shows that the DLSM framework can be successfully applied to ultrasound clutter suppression.

Keywords: Clutter suppression; Low-rank and sparse matrix decomposition; Ultrasound color flow imaging; Vessel visualization.

Fig. 1

A set of comparison images showing CFI with and without clutter filters. a CFI raw data in Brightness mode. b The same data after clutter suppression by SVD. In the upper right window, the raw CFI data contain a lot of tissue clutter in the background, which is suppressed by SVD in the second image

Fig. 2

A set of pictures showing the threshold selection of SVD. a The original simulation data in brightness mode. b–e The processed images by SVD with different thresholds. Parameters b and e represent the selected rank of blood and noise signal, respectively. The full rank of the data is 20

Fig. 3

The schematic diagram of DLSM framework. DLSM framework contains 5 branches, which are models (or called math formulations), decomposition problems, minimization problems, loss functions, solvers (or called algorithms). Examples are shown beside the branches

Fig. 4

The illustration of tensor decomposition

Fig. 5

The illustration of Tucker decomposition

Fig. 6

The illustration of CANDECOMP/PARAFAC (CP) decomposition

Fig. 7

The illustration of the simulation data. a The simulation cube with tissue scatterers and blood scatterers. The red blood scatterers are in the middle and moving to the right. The simulated sound waves focus in the center. b A series of simulation data frames obtained from simulation experiments

Fig. 8

The illustration of the phantom experiments. a The illustration of phantom data collection experiment. b The B-mode image of the first frame in phantom data

Fig. 9

The illustration of the in vivo rat experiments. a The illustration of the in vivo rat data collection experiment. b A schematic representation of sparse component of the in vivo rat data

Fig. 10

The output result images of simulation data. a The output of sparse component obtained by the IALM algorithm on original simulated RF data. It is a typical good result representing correct decomposition and pure sparse components. b The output of sparse component obtained by the ADM algorithm on original simulated RF data. It is a typical noisy result with background noise as sparse components. c The output of sparse component obtained by the OSTD algorithm on processed simulated RF data with larger dynamic range. The algorithms with a CNR less than 1 in Table 3 give such results with pure background because they only show the sparsest parts

Fig. 11

Three typical output results of phantom experiments. a A typical good result showing pure sparse components without noise. This image is obtained by ALM algorithm on original phantom data. b A typical output affected by bright edge structures. This image is obtained by APG algorithm on original phantom data. Because the pixel values of bright edges are 1000 times larger than the pixel values in the rest of the image, the flow sparse component in the middle of the tube cannot be observed. c A typical noisy result showing sparse components with indivisible noise. This image is obtained by RSTD algorithm on original phantom data

Fig. 12

The examples of the results of rat experiments. a The B-mode image of rat data for comparison. b is obtained by ALM algorithm on original rat data. The dynamic background and noise are filtered out relatively well. c is obtained by APG algorithm on original rat data. Large areas of dynamic tissue are classified as sparse components. Since there is no ground truth for in vivo rat data, the results are described using relatively good and relatively noisy