Improving Imprecise Compressive Sensing Models

TL;DR

This paper introduces a new theoretical framework for compressive sensing that accounts for imprecise recovery and uncertainty in the number of sparse components, improving the understanding of recovery success in dynamic systems.

Contribution

It presents a novel model that better predicts recovery success and quality under uncertainty, extending traditional CS theory to more realistic scenarios.

Findings

The new model accurately predicts recovery success in dynamic systems.

Relaxed recovery success criteria improve practical applicability.

Experimental results validate the model's effectiveness.

Abstract

Random sampling in compressive sensing (CS) enables the compression of large amounts of input signals in an efficient manner, which is useful for many applications. CS reconstructs the compressed signals exactly with overwhelming probability when incoming data can be sparsely represented with a few components. However, the theory of CS framework including random sampling has been focused on exact recovery of signal; impreciseness in signal recovery has been neglected. This can be problematic when there is uncertainty in the number of sparse components such as signal sparsity in dynamic systems that can change over time. We present a new theoretical framework that handles uncertainty in signal recovery from the perspective of recovery success and quality. We show that the signal recovery success in our model is more accurate than the success probability analysis in the CS framework. Our model is then extended to the case where the success or failure of signal recovery can be relaxed. We represent the number of components included in signal recovery with a right-tailed distribution and focus on recovery quality. Experimental results confirm the accuracy of our model in dynamic systems.