Combined modeling of sparse and dense noise for improvement of Relevance Vector Machine

TL;DR

This paper introduces a robust Relevance Vector Machine that models both sparse and dense noise simultaneously, improving signal recovery and computational efficiency in various applications.

Contribution

A novel RVM approach that combines sparse and dense noise modeling without estimating sparse noise separately, extending to block-sparse signals.

Findings

Enhanced recovery of sparse and block-sparse signals.

Improved computational efficiency over existing methods.

Effective in applications like housing price prediction and image denoising.

Abstract

Using a Bayesian approach, we consider the problem of recovering sparse signals under additive sparse and dense noise. Typically, sparse noise models outliers, impulse bursts or data loss. To handle sparse noise, existing methods simultaneously estimate the sparse signal of interest and the sparse noise of no interest. For estimating the sparse signal, without the need of estimating the sparse noise, we construct a robust Relevance Vector Machine (RVM). In the RVM, sparse noise and ever present dense noise are treated through a combined noise model. The precision of combined noise is modeled by a diagonal matrix. We show that the new RVM update equations correspond to a non-symmetric sparsity inducing cost function. Further, the combined modeling is found to be computationally more efficient. We also extend the method to block-sparse signals and noise with known and unknown block structures. Through simulations, we show the performance and computation efficiency of the new RVM in several applications: recovery of sparse and block sparse signals, housing price prediction and image denoising.