# Efficient Convolutional Forward Modeling and Sparse Coding in Multichannel Imaging

arXiv: https://arxiv.org/abs/2403.09505 · HTML: https://mlsanity.com/paper/2403.09505/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Mar 2024.

## Built on by (most cited first, 2 of 2)

- [Learning Structured Compressed Sensing with Automatic Resource Allocation](https://mlsanity.com/paper/2410.18954/) (2024)
- [Compressed BC-LISTA via Low-Rank Convolutional Decomposition](https://mlsanity.com/paper/2601.23148/) (2026)

## Abstract (arXiv)

This study considers the Block-Toeplitz structural properties inherent in traditional multichannel forward model matrices, using Full Matrix Capture (FMC) in ultrasonic testing as a case study. We propose an analytical convolutional forward model that transforms reflectivity maps into FMC data. Our findings demonstrate that the convolutional model excels over its matrix-based counterpart in terms of computational efficiency and storage requirements. This accelerated forward modeling approach holds significant potential for various inverse problems, notably enhancing Sparse Signal Recovery (SSR) within the context LASSO regression, which facilitates efficient Convolutional Sparse Coding (CSC) algorithms. Additionally, we explore the integration of Convolutional Neural Networks (CNNs) for the forward model, employing deep unfolding to implement the Learned Block Convolutional ISTA (BC-LISTA).