[Paper Review] Compressed BC-LISTA via Low-Rank Convolutional Decomposition

Han Wang, Yhonatan Kvich+3 more|arXiv (Cornell University)|Jan 30, 2026

Ultrasound Imaging and Elastography0 citations

TL;DR

The paper proposes a compressed forward model for multichannel sparse signal recovery by a low-rank convolutional decomposition and uses it to build C-BC-LISTA, a lightweight, efficient LISTA-based solver that outperforms state-of-the-art baselines in multichannel ultrasound imaging with fewer parameters and faster convergence.

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.

Motivation & Objective

• Motivate sparse signal recovery under compressed forward and backward operators in time delay-based measurements.
• Develop a compressed forward model using low-rank convolutional decomposition of analytic operators.
• Instantiate a lightweight LISTA variant (C-BC-LISTA) leveraging the compressed forward model for multichannel imaging.
• Demonstrate improved reconstruction accuracy and reduced parameter count and storage compared to SOTA baselines.
• Provide ablations to identify the impact of initialization, number of basis filters, and trainability of forward/backward models.

Proposed method

• Formulate a slice-wise convolutional forward model for time delay-based FMC multichannel ultrasound measurements.
• Factorize the forward filter weight matrix W as W ≈ C B with B consisting of M basis filters selected via OMP and C containing mixing coefficients.
• Realize the factorization as a two-layer low-rank CNN module: first layer uses basis filters B; second layer performs 1x1 convolution with mixing coefficients C.
• Apply OMP and (optionally) SVD to obtain the compressed basis B and mixing C, with B rows drawn from W to preserve interpretability.
• Extend BC-LISTA to C-BC-LISTA by replacing each ISTA step with the two-layer compressed convolutional module, maintaining exact adjoints for backward operations.
• Trainable options include whether forward/backward kernels are fixed or trainable, and whether block parameters are shared or per-block.

Experimental results

Research questions

• RQ1 Can a low-rank, convolutional decomposition of the forward model enable compressed but accurate sparse signal recovery in multichannel imaging?
• RQ2 Does a compressed BC-LISTA enable similar or better reconstruction with far fewer parameters and storage than existing LISTA variants?
• RQ3 What initialization and compression strategy (e.g., OMP-based basis selection) yields the best training efficiency and convergence behavior?
• RQ4 How does C-BC-LISTA perform under noiseless and various SNR conditions in multichannel ultrasound imaging?
• RQ5 What is the impact of the number of basis filters on convergence speed and reconstruction accuracy?

Key findings

• C-BC-LISTA achieves substantially fewer parameters and smaller model size than SOTA methods while improving reconstruction accuracy.
• OMP-initialized structured compression performs best among ablations, yielding efficient training and better convergence.
• Increasing the number of basis filters accelerates convergence but mainly affects speed rather than the error floor, with BF-16 frequently yielding strong performance.
• Analytic initialization of both forward and backward models leads to stable and fast convergence; freezing the forward model slows training.
• C-BC-LISTA generally outperforms MLP-LISTA, ALISTA, and BC-LISTA in convergence speed and validation loss.
• The compressed variant achieves competitive performance with significantly reduced memory requirements.