Balancing Sparsity and Rank Constraints in Quadratic Basis Pursuit

TL;DR

This paper explores the balance between sparsity and low-rank constraints in matrix recovery problems, providing a new analysis method that guides parameter adjustment and improves performance evaluation in phase retrieval and calibration tasks.

Contribution

It introduces a novel approach to analyze the trade-off between sparsity and low-rank constraints, aiding in parameter tuning and performance assessment.

Findings

The proposed method aligns well with existing approaches in phase retrieval and calibration.

Simulation results demonstrate the effectiveness of the trade-off analysis.

Adjusting weights impacts the performance in predictable ways.

Abstract

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.