Optimized projections for compressed sensing via rank-constrained nearest correlation matrix
This work addresses the problem of enhancing signal recovery efficiency in compressed sensing applications, though it appears incremental as it builds on existing algorithms.
The paper tackled optimizing acquisition matrices for compressed sensing with overcomplete dictionaries by formulating it as a rank-constrained nearest correlation matrix problem, resulting in notable improvements and superior robustness in sparse signal recovery.
Optimizing the acquisition matrix is useful for compressed sensing of signals that are sparse in overcomplete dictionaries, because the acquisition matrix can be adapted to the particular correlations of the dictionary atoms. In this paper a novel formulation of the optimization problem is proposed, in the form of a rank-constrained nearest correlation matrix problem. Furthermore, improvements for three existing optimization algorithms are introduced, which are shown to be particular instances of the proposed formulation. Simulation results show notable improvements and superior robustness in sparse signal recovery.