  We investigate the methods that simultaneously enforce sparsity and low-rank
structure in a matrix as often employed for sparse phase retrieval problems or
phase calibration problems in compressive sensing. We propose a new approach
for analyzing the trade off between the sparsity and low rank constraints in
these approaches which not only helps to provide guidelines to adjust the
weights between the aforementioned constraints, but also enables new simulation
strategies for evaluating performance. We then provide simulation results for
phase retrieval and phase calibration cases both to demonstrate the consistency
of the proposed method with other approaches and to evaluate the change of
performance with different weights for the sparsity and low rank structure
constraints.

Numerical Analysis;Machine Learning