Sparse Representation by Frames with Signal Analysis

The use of frames is analyzed in Compressed Sensing (CS) through proofs and experiments. First, a new generalized Dictionary-Restricted Isometry Property (D-RIP) sparsity bound constant for CS is established. Second, experiments with a tight frame to analyze sparsity and reconstruction quality using several signal and image types are shown. The constant  is used in fulfilling the definition of D-RIP. It is proved that k-sparse signals can be reconstructed if  by using a concise and transparent argument1. The approach could be extended to obtain other D-RIP bounds (i.e. ). Experiments contrast results of a Gabor tight frame with Total Variation minimization. In cases of practical interest, the use of a Gabor dictionary performs well when achieving a highly sparse representation and poorly when this sparsity is not achieved.