Comparison of several sparse recovery methods for low rank matrices with random samples

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 random 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 mainly focus on comparing the power of Iterative Method of Adaptive Thresholding (IMAT) in reconstruction of the desired sparse signal with that of 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 in the absence of time-consuming matrix completion methods will be taken into account in terms of RMSE and computational complexity. Simulations and numerical results are also provided to verify the arguments.