Bayesian Hypothesis Testing for Sparse Representation

TL;DR

This paper introduces a Bayesian Hypothesis Testing Algorithm for sparse signal representation, improving upon the Iterative Detection Estimation method by deriving thresholds from Bayesian hypothesis testing, resulting in high accuracy but increased computational complexity.

Contribution

It presents a novel Bayesian hypothesis testing framework that enhances the IDE algorithm for sparse representation, providing a more principled thresholding approach.

Findings

Hard-version achieves high estimation accuracy

Algorithm outperforms in accuracy compared to existing methods

Increased computational complexity due to Bayesian testing

Abstract

In this paper, we propose a Bayesian Hypothesis Testing Algorithm (BHTA) for sparse representation. It uses the Bayesian framework to determine active atoms in sparse representation of a signal. The Bayesian hypothesis testing based on three assumptions, determines the active atoms from the correlations and leads to the activity measure as proposed in Iterative Detection Estimation (IDE) algorithm. In fact, IDE uses an arbitrary decreasing sequence of thresholds while the proposed algorithm is based on a sequence which derived from hypothesis testing. So, Bayesian hypothesis testing framework leads to an improved version of the IDE algorithm. The simulations show that Hard-version of our suggested algorithm achieves one of the best results in terms of estimation accuracy among the algorithms which have been implemented in our simulations, while it has the greatest complexity in terms of simulation time.