Abstract
Compressed sensing is a novel signal sampling theory based on the sparsity of signals. To recover a sparse signal from fewer measurements, it is desired that measurement matrices have low coherence and low spectral norm. For this purpose, a progressive coherence and spectral norm minimization (PCSNM) scheme is proposed by dividing the optimization problem into several ℓ∞-minimization problems with orthogonality constraints. Utilizing the smoothing technique and penalty function method, these non-smooth constrained problems are transformed into unconstrained approximate optimization problems and solved by a gradient-type based alternating minimization approach. Simulation results demonstrate that the proposed scheme outperforms some previous methods, especially in decreasing the spectral norm.
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