Unsupervised Unfolded rPCA (U2-rPCA): Deep Interpretable Clutter Filtering for Ultrasound Microvascular Imaging

TL;DR

This work tackles clutter filtering in ultrasound microvascular imaging by introducing U2-rPCA, an unsupervised unfolded network derived from IRLS-rPCA with a sparse-enhancement unit to bolster sparse micro-flow features. The model preserves mathematical interpretability through Frobenius-norm formulations and layer-wise data-consistency losses while enabling trainable, data-driven feature learning without ground-truth labels. Experiments on in-silico kidney-mimicking phantoms and public in-vivo datasets (kidney and tumor) show superior CNR/SNR versus SVD, rPCA baselines, and a DL filter, with ablations confirming the SEU’s contribution. The approach offers a real-time, interpretable clutter-filtering solution for contrast-free ultrasound microvascular imaging, with potential extensions to semi-supervised learning and improved simulators for ground-truth-like training data.

Abstract

High-sensitivity clutter filtering is a fundamental step in ultrasound microvascular imaging. Singular value decomposition (SVD) and robust principal component analysis (rPCA) are the main clutter filtering strategies. However, both strategies are limited in feature modeling and tissue-blood flow separation for high-quality microvascular imaging. Recently, deep learning-based clutter filtering has shown potential in more thoroughly separating tissue and blood flow signals. However, the existing supervised filters face the challenges of interpretability and lack of in-vitro and in-vivo ground truths. While the interpretability issue can be addressed by algorithm deep unfolding, the training ground truth remains unsolved. To this end, this paper proposes an unsupervised unfolded rPCA (U2-rPCA) method that preserves mathematical interpretability and is insusceptible to learning labels. Specifically, U2-rPCA is unfolded from an iteratively reweighted least squares (IRLS) rPCA baseline with intrinsic low-rank and sparse regularization. A sparse-enhancement unit is added to the network to strengthen its capability to capture the sparse micro-flow signals. U2-rPCA is like an adaptive filter that is trained with part of the image sequence and then used for the following frames. Experimental validations on a in-silico dataset and public in-vivo datasets demonstrated the outperformance of U2-rPCA when compared with the SVD-based method, the rPCA baseline, and another deep learning-based filter. Particularly, the proposed method improved the contrastto-noise ratio (CNR) of the power Doppler image by 2 dB to 10 dB when compared with other methods. Furthermore, the effectiveness of the building modules of U2-rPCA was validated through ablation studies.

Figures (13)

• Figure 1: The framework of the U2-rPCA clutter filter. (a) is the realization in the $k$-th layer. (b) is the architecture of the sparse-enhancement unit.
• Figure 2: Configurations of the in-silico kidney-mimicking phantom. (a) illustrates the basic flow unit and its variants. (b) is the geometry of this phantom and the velocities in the flow units. (c) shows the finite-element-analysis (FEA)-based axial-compression strain curve and the lateral and axial displacements applied to the phantom. (d) presents the ground-truth power Doppler image and Doppler velocity image
• Figure 3: ULM density maps and axial velocity components (references of the Doppler velocity estimations) of (a) the kidney dataset and (b) the tumor dataset obtained from the PALA scripts and data.
• Figure 4: (a) Power Doppler images of the in-silico kidney-mimicking phantom obtained by U2-rPCA, IRLS-rPCA, SVD, and 3D-Res-UNet. (b) Doppler velocity images obtained by U2-rPCA, IRLS-rPCA, and SVD. (c) The color bars illustrate the dynamic range and velocity range.
• Figure 5: Power Doppler images of the kidney obtained by (a) U2-rPCA, (b) IRLS-rPCA, (c) SVD, and (d) 3D-Res-UNet.