# Compressed BC-LISTA via Low-Rank Convolutional Decomposition

arXiv: https://arxiv.org/abs/2601.23148 · HTML: https://mlsanity.com/paper/2601.23148/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 33 references that are in the map.
- First posted on arXiv 30 Jan 2026.

## Builds on (most cited first, 17 of 17)

- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [Knowledge Distillation: A Survey](https://mlsanity.com/paper/2006.05525/) (2020)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Compressed Sensing using Generative Models](https://mlsanity.com/paper/1703.03208/) (2017)
- [Exploiting Linear Structure Within Convolutional Networks for Efficient Evaluation](https://mlsanity.com/paper/1404.0736/) (2014)
- [Speeding up Convolutional Neural Networks with Low Rank Expansions](https://mlsanity.com/paper/1405.3866/) (2014)
- [Model-Based Deep Learning](https://mlsanity.com/paper/2012.08405/) (2020)
- [Provable Benefit of Orthogonal Initialization in Optimizing Deep Linear Networks](https://mlsanity.com/paper/2001.05992/) (2020)
- [Learning Filter Basis for Convolutional Neural Network Compression](https://mlsanity.com/paper/1908.08932/) (2019)
- [Generalized optimal sub-pattern assignment metric](https://mlsanity.com/paper/1601.05585/) (2016)
- [Learning Sub-Sampling and Signal Recovery with Applications in Ultrasound Imaging](https://mlsanity.com/paper/1908.05764/) (2019)
- [Jointly Learning Selection Matrices For Transmitters, Receivers And Fourier Coefficients In Multichannel Imaging](https://mlsanity.com/paper/2402.19023/) (2024)
- [Structured LISTA for Multidimensional Harmonic Retrieval](https://mlsanity.com/paper/2102.11663/) (2021)
- [Learning to Sample: Data-Driven Sampling and Reconstruction of FRI Signals](https://mlsanity.com/paper/2106.14500/) (2021)
- [Efficient Convolutional Forward Modeling and Sparse Coding in Multichannel Imaging](https://mlsanity.com/paper/2403.09505/) (2024)
- [Learning Structured Compressed Sensing with Automatic Resource Allocation](https://mlsanity.com/paper/2410.18954/) (2024)

## Abstract (arXiv)

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.