Tight is better: Performance Improvement of the Compressive Classifier Using Equi-Norm Tight Frames

TL;DR

Transforming sensing matrices into Equi-Norm Tight Frames significantly enhances the performance of compressive classifiers by making them more effective at detecting known sparse signals in noisy measurements.

Contribution

This paper proves that converting arbitrary sensing matrices into Equi-Norm Tight Frames improves compressive classifier performance, offering a practical method for designing better sensing matrices.

Findings

Equi-Norm Tight Frames improve classifier accuracy

Transformation into tight frames is easy and practical

Enhanced detection performance demonstrated

Abstract

Detecting or classifying already known sparse signals contaminated by Gaussian noise from compressive measurements is different from reconstructing sparse signals, as its objective is to minimize the error probability which describes performance of the detectors or classifiers. This paper is concerned about the performance improvement of a commonly used Compressive Classifier. We prove that when the arbitrary sensing matrices used to get the Compressive Measurements are transformed into Equi-Norm Tight Frames, i.e. the matrices that are row-orthogonal, The Compressive Classifier achieves better performance. Although there are other proofs that among all Equi-Norm Tight Frames the Equiangular tight Frames (ETFs) bring best worst-case performance, the existence and construction of ETFs on some dimensions is still an open problem. As the construction of Equi-Norm Tight Frames from any arbitrary matrices is very easy and practical compared with ETF matrices, the result of this paper can also provide a practical method to design an improved sensing matrix for Compressive Classification. We can conclude that: Tight is Better!