# Entropy-Based Learning of Sensing Matrices

## TL;DR

This paper introduces an entropy-maximization learning approach to design orthogonal sensing matrices for compressed sensing, improving signal recovery accuracy and efficiency across various signal types.

## Contribution

It presents a novel learning scheme that constructs sensing matrices by maximizing measurement entropy, with bounds for unique recovery and superior performance compared to existing methods.

## Key findings

- Enhanced recovery accuracy for synthetic, speech, and image signals.
- Reduced number of measurements needed for accurate reconstruction.
- Outperforms existing sensing matrix construction methods.

## Abstract

This paper proposes a learning method to construct an efficient sensing (measurement) matrix, having orthogonal rows, for compressed sensing of a class of signals. The learning scheme identifies the sensing matrix by maximizing the entropy of measurement vectors. The bounds on the entropy of the measurement vector necessary for the unique recovery of a signal are also proposed. A comparison of the performance of the designed sensing matrix and the sensing matrices constructed using other existing methods is also presented. The simulation results on the recovery of synthetic, speech, and image signals, compressively sensed using the sensing matrix identified, shows an improvement in the accuracy of recovery. The reconstruction quality is better, using less number of measurements, than those measured using sensing matrices identified by other methods.