Compressed BC-LISTA via Low-Rank Convolutional Decomposition

TL;DR

This paper introduces a low-rank convolutional decomposition approach for compressed multichannel imaging, enhancing sparse signal recovery with fewer parameters and improved accuracy, demonstrated in ultrasound imaging simulations.

Contribution

It proposes a novel compressed measurement model using low-rank CNN decomposition, combined with OMP-based filter selection, to improve efficiency and accuracy in multichannel imaging reconstruction.

Findings

C-BC-LISTA outperforms state-of-the-art methods in ultrasound imaging.

OMP initialization yields the best performance and training efficiency.

The proposed method reduces model size while maintaining high reconstruction accuracy.

Abstract

We study Sparse Signal Recovery (SSR) methods for multichannel imaging with compressed {forward and backward} operators that preserve reconstruction accuracy. We propose a Compressed Block-Convolutional (C-BC) measurement model based on a low-rank Convolutional Neural Network (CNN) decomposition that is analytically initialized from a low-rank factorization of physics-derived forward/backward operators in time delay-based measurements. We use Orthogonal Matching Pursuit (OMP) to select a compact set of basis filters from the analytic model and compute linear mixing coefficients to approximate the full model. We consider the Learned Iterative Shrinkage-Thresholding Algorithm (LISTA) network as a representative example for which the C-BC-LISTA extension is presented. In simulated multichannel ultrasound imaging across multiple Signal-to-Noise Ratios (SNRs), C-BC-LISTA requires substantially fewer parameters and smaller model size than other state-of-the-art (SOTA) methods while improving reconstruction accuracy. In ablations over OMP, Singular Value Decomposition (SVD)-based, and random initializations, OMP-initialized structured compression performs best, yielding the most efficient training and the best performance.