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Compressed BC-LISTA via Low-Rank Convolutional Decomposition

Han Wang, Yhonatan Kvich, Eduardo Pérez, Florian Römer, Yonina C. Eldar

TL;DR

This work tackles sparse signal recovery for time-delay-based, multichannel imaging by introducing a compressed forward model built from a low-rank convolutional decomposition. The forward operator is factorized as $\mathbf{W}\approx \mathbf{C}\mathbf{B}$ using OMP-selected basis filters from the analytic convolutional kernels, and realized as a two-layer CNN module to form the Compressed BC-LISTA (C-BC-LISTA). The approach is evaluated on synthetic 32-channel FMC ultrasound data, where C-BC-LISTA achieves competitive reconstruction accuracy with substantially fewer parameters and faster convergence than state-of-the-art LISTA variants, with analytic initialization and deeper blocks providing notable benefits. The results demonstrate that exploiting the linear-operator structure via structure-aware compression yields practical gains in memory, training efficiency, and recovery performance for large-scale sparse inverse problems in time-delay-based multichannel imaging.

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.

Compressed BC-LISTA via Low-Rank Convolutional Decomposition

TL;DR

This work tackles sparse signal recovery for time-delay-based, multichannel imaging by introducing a compressed forward model built from a low-rank convolutional decomposition. The forward operator is factorized as using OMP-selected basis filters from the analytic convolutional kernels, and realized as a two-layer CNN module to form the Compressed BC-LISTA (C-BC-LISTA). The approach is evaluated on synthetic 32-channel FMC ultrasound data, where C-BC-LISTA achieves competitive reconstruction accuracy with substantially fewer parameters and faster convergence than state-of-the-art LISTA variants, with analytic initialization and deeper blocks providing notable benefits. The results demonstrate that exploiting the linear-operator structure via structure-aware compression yields practical gains in memory, training efficiency, and recovery performance for large-scale sparse inverse problems in time-delay-based multichannel imaging.

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.
Paper Structure (11 sections, 7 equations, 3 figures, 1 table)

This paper contains 11 sections, 7 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction and Related Work
  2. Methodology
  3. Slice-Wise Convolutional Forward Model
  4. Low-Rank Approximation
  5. Low-Rank CNN Decomposition
  6. Compressed BC-LISTA
  7. Evaluation
  8. Training Strategy
  9. Quantitative Comparisons
  10. Ablation Analysis
  11. Conclusion

Figures (3)

  • Figure 1: Illustration of the convolutional forward model.
  • Figure 2: Low-rank CNN decomposition and architecture of C-BC-LISTA.
  • Figure 3: Training validation loss comparison in different settings.