Sparse Representation by Frames with Signal Analysis

Christopher Baker
2016 Journal of Signal and Information Processing  
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 k δ is used in fulfilling the definition of D-RIP. It is proved that k-sparse signals can be reconstructed if 2 2 3 k δ < by using a concise
more » ... using a concise and transparent argument 1 . The approach could be extended to obtain other D-RIP bounds (i.e. tk δ ). 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.
doi:10.4236/jsip.2016.71006 fatcat:v56oelyaqbbqxiugktfwgfdwb4