You probably recall recently these posts:
- Nonlinear Basis Pursuit - implementation -
- Sparse phase retrieval via group-sparse optimization
- Blind Identification via Lifting - implementation -
all parts of the more generic nonlinear Nonlinear Compressive Sensing family of solvers, well we have a newcomer and its implementation in that area:
Balancing Sparsity and Rank Constraints in Quadratic Basis Pursuit by Cagdas Bilen , Gilles Puy, Rémi Gribonval , Laurent Daudet
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.
The codes for the MATLAB implementations of the proposed method has been provided in
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