# Sparse Solutions of an Undetermined Linear System

## TL;DR

This paper explores methods for finding sparse solutions to underdetermined linear systems, focusing on compressive sensing techniques using l_1 and l_q approaches, and proposes an algorithm based on restricted Isometry to ensure solution uniqueness.

## Contribution

It introduces a new algorithm leveraging restricted Isometry for solving underdetermined systems to achieve sparse, unique solutions.

## Key findings

- The l_1 and l_q approaches effectively recover sparse solutions.
- The proposed algorithm improves solution uniqueness under restricted Isometry conditions.
- Application potential in compressive sensing and signal processing.

## Abstract

This work proposes a research problem of finding sparse solution of undetermined Linear system with some applications. Two approaches how to solve the compressive sensing problem: using l_1 approach , the l_q approach with 0 < q < 1. Compressive sensing algorithms are designed to cope with ambiguities introduced by undersampling. We propose an algorithm for restricted Isometry and how it can be used to constrain the undetermined linear system to eventually get a unique solution.