Comparison of Several Sparse Recovery Methods for Low Rank Matrices with Random Samples

TL;DR

This paper compares IMAT and LASSO methods for sparse signal recovery in linear models with random missing data, demonstrating IMAT's superior performance through simulations in big data contexts.

Contribution

It introduces a comparative analysis of IMAT and LASSO for sparse recovery under missing data conditions, highlighting IMAT's advantages in such scenarios.

Findings

IMAT outperforms LASSO in sparse recovery with missing data

Simulations confirm IMAT's robustness in big data applications

The study provides insights into sparse recovery methods for incomplete datasets

Abstract

In this paper, we will investigate the efficacy of IMAT (Iterative Method of Adaptive Thresholding) in recovering the sparse signal (parameters) for linear models with missing data. Sparse recovery rises in compressed sensing and machine learning problems and has various applications necessitating viable reconstruction methods specifically when we work with big data. This paper will focus on comparing the power of IMAT in reconstruction of the desired sparse signal with LASSO. Additionally, we will assume the model has random missing information. Missing data has been recently of interest in big data and machine learning problems since they appear in many cases including but not limited to medical imaging datasets, hospital datasets, and massive MIMO. The dominance of IMAT over the well-known LASSO will be taken into account in different scenarios. Simulations and numerical results are also provided to verify the arguments.