Training-free Ultra Small Model for Universal Sparse Reconstruction in Compressed Sensing

TL;DR

This paper introduces a training-free, ultra-small neural model called CLOMP for rapid and accurate sparse reconstruction in compressed sensing, outperforming traditional methods in efficiency and accuracy.

Contribution

The paper proposes a novel minimal-parameter neural model that enables training-free, interpretable, and highly efficient sparse reconstruction, bridging traditional iterative methods and AI techniques.

Findings

CLOMP improves efficiency by 100 to 1000 times over traditional methods.

CLOMP enhances image reconstruction quality with up to 292% SSIM increase.

The method works effectively on both synthetic and real signals across various datasets.

Abstract

Pre-trained large models attract widespread attention in recent years, but they face challenges in applications that require high interpretability or have limited resources, such as physical sensing, medical imaging, and bioinformatics. Compressed Sensing (CS) is a well-proved theory that drives many recent breakthroughs in these applications. However, as a typical under-determined linear system, CS suffers from excessively long sparse reconstruction times when using traditional iterative methods, particularly with large-scale data. Current AI methods like deep unfolding fail to substitute them because pre-trained models exhibit poor generality beyond their training conditions and dataset distributions, or lack interpretability. Instead of following the big model fervor, this paper proposes ultra-small artificial neural models called coefficients learning (CL), enabling training-free and rapid sparse reconstruction while perfectly inheriting the generality and interpretability of traditional iterative methods, bringing new feature of incorporating prior knowledges. In CL, a signal of length $n$ only needs a minimal of $n$ trainable parameters. A case study model called CLOMP is implemented for evaluation. Experiments are conducted on both synthetic and real one-dimensional and two-dimensional signals, demonstrating significant improvements in efficiency and accuracy. Compared to representative iterative methods, CLOMP improves efficiency by 100 to 1000 folds for large-scale data. Test results on eight diverse image datasets indicate that CLOMP improves structural similarity index by 292%, 98%, 45% for sampling rates of 0.1, 0.3, 0.5, respectively. We believe this method can truly usher CS reconstruction into the AI era, benefiting countless under-determined linear systems that rely on sparse solution.