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

Area of Science:

• Signal Processing
• Machine Learning
• Optimization

Background:

• Large models face challenges with interpretability, generality, and data limitations.
• Traditional iterative methods in Compressed Sensing (CS) offer interpretability but lack efficiency and quality at low sampling rates.

Purpose of the Study:

• Introduce Coefficients Learning (CL), a novel training-free framework for sparse reconstruction.
• Enhance the accuracy and efficiency of traditional iterative CS methods without requiring extensive training data.

Main Methods:

• CL utilizes ultra-small neural models with $n$ parameters for length-$n$ signals.
• It integrates automatic differentiation and prior knowledge into model losses within a residual-based solving process.
• CL was evaluated using CLOMP and implemented on classic iterative CS methods (convex optimization, message-passing, greedy algorithms).

Main Results:

• CL maintains the generality of iterative methods while significantly improving reconstruction accuracy.
• Efficiency gains of 100x to 1000x were observed for greedy algorithms.
• On diverse image datasets, CL improved median reconstruction accuracy by 163%, 78%, and 35% at sampling rates of 0.04, 0.25, and 0.5, respectively.

Conclusions:

• CL offers a powerful, training-free solution for sparse reconstruction, addressing limitations of existing methods.
• This framework can significantly benefit industrial and medical applications reliant on sparse signal solutions.