TITLE:
Sparse Representation by Frames with Signal Analysis
AUTHORS:
Christopher Baker
KEYWORDS:
Compressed Sensing, Total Variation Minimization, l1-Analysis, D-Restricted Isometry Property, Tight Frames
JOURNAL NAME:
Journal of Signal and Information Processing,
Vol.7 No.1,
February
29,
2016
ABSTRACT: 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.