An Efficient Method for Robust Projection Matrix Design

Our objective is to efficiently design a robust projection matrix $\Phi$ for the Compressive Sensing (CS) systems when applied to the signals which are not exactly sparse. The optimal projection matrix design is obtained by mainly minimizing the average coherence of the equivalent dictionary. In order to drop the requirement of the sparse representation error (SRE) for a set of training data as in [8] [9], we introduce a novel penalty function independent to a particular SRE matrix. Without requiring of training data, the robust sensing matrix can be efficiently designed and utilized for most of CS systems, like a CS system with a conventional wavelet dictionary for image processing. Simulation results demonstrate the efficiency and effectiveness of the proposed approach comparing with the state-of-the-art methods. In addition, we experimentally demonstrate with natural images that under similar compression rate, a CS system with a learned dictionary in high dimensions outperforms the one with a learned dictionary in low dimensions in terms of reconstruction accuracy. This together with the fact that our proposed method can efficiently work in high dimensions suggests that a CS system can potentially go beyond the small patches in sparsity-based signal and image processing.