# Generalized orthogonal matching pursuit for multiple measurements - A structural approach

## TL;DR

This paper introduces a generalized orthogonal matching pursuit algorithm tailored for multiple measurement vectors, emphasizing the preservation of data structures and demonstrating improved approximation in signal processing applications.

## Contribution

It presents a novel structural approach to MMV sparse approximation, focusing on data structure preservation rather than just approximation accuracy.

## Key findings

- Numerical comparisons show improved performance over existing methods.
- The approach effectively preserves complex data structures.
- Applications demonstrate practical benefits in signal processing tasks.

## Abstract

Sparse data approximation has become a popular research topic in signal processing. However, in most cases only a single measurement vector (SMV) is considered. In applications, the multiple measurement vector (MMV) case is more usual, i.e., the sparse approximation problem has to be solved for several data vectors coming from closely related measurements. Thus, there is an unknown inter-vector correlation between the data vectors. Using SMV methods typically does not return the best approximation result as the correlation is ignored. In the past few years several algorithms for the MMV case have been designed to overcome this problem. Most of these techniques focus on the approximation quality while quite strong assumptions to the type of inter-vector correlation are made. While we still want to find a sparse approximation, our focus lies on preserving (possibly complex) structures in the data. Structural knowledge is of interest in many applications. It can give information about e.g., type, form, number or size of objects of interest. This may even be more useful than information given by the non-zero amplitudes itself. Moreover, it allows efficient post processing of the data. We numerically compare our new approach with other techniques and demonstrate its benefits in two applications.