  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.
