# Joint Sparse Recovery With Semisupervised MUSIC

## TL;DR

This paper introduces SS-MUSIC, a semisupervised approach to joint sparse recovery that enhances the classical MUSIC algorithm by leveraging unlabeled atoms, improving performance especially in rank-defective scenarios.

## Contribution

It proposes a novel semisupervised MUSIC algorithm that iteratively refines classification by utilizing both labeled and unlabeled data, addressing rank deficiency issues in joint sparse recovery.

## Key findings

- SS-MUSIC outperforms traditional MUSIC and greedy algorithms in recovery probability.
- It requires fewer iterations for convergence.
- It demonstrates robustness in rank-defective and coherent measurement scenarios.

## Abstract

Discrete multiple signal classification (MUSIC) with its low computational cost and mild condition requirement becomes a significant noniterative algorithm for joint sparse recovery (JSR). However, it fails in rank defective problem caused by coherent or limited amount of multiple measurement vectors (MMVs). In this letter, we provide a novel sight to address this problem by interpreting JSR as a binary classification problem with respect to atoms. Meanwhile, MUSIC essentially constructs a supervised classifier based on the labeled MMVs so that its performance will heavily depend on the quality and quantity of these training samples. From this viewpoint, we develop a semisupervised MUSIC (SS-MUSIC) in the spirit of machine learning, which declares that the insufficient supervised information in the training samples can be compensated from those unlabeled atoms. Instead of constructing a classifier in a fully supervised manner, we iteratively refine a semisupervised classifier by exploiting the labeled MMVs and some reliable unlabeled atoms simultaneously. Through this way, the required conditions and iterations can be greatly relaxed and reduced. Numerical experimental results demonstrate that SS-MUSIC can achieve much better recovery performances than other MUSIC extended algorithms as well as some typical greedy algorithms for JSR in terms of iterations and recovery probability.