%0 Journal Article
%T Sparse Representation by Frames with Signal Analysis
%A Christopher Baker
%J Journal of Signal and Information Processing
%P 39-48
%@ 2159-4481
%D 2016
%I Scientific Research Publishing
%R 10.4236/jsip.2016.71006
%X 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 <img src=\"Edit_5bc9b7a7-718a-4884-9975-7aab342695fc.bmp\" alt=\"\" />&nbsp;is used in fulfilling the definition of D-RIP. It is proved that
k-sparse signals can be reconstructed if <img src=\"Edit_1e2fb150-c793-49e6-947b-ac2f588f5931.bmp\" alt=\"\" />&nbsp;by using a concise and transparent
argument1. The approach could be extended to obtain other D-RIP bounds (i.e. <img src=\"Edit_794ae530-738b-4ab7-9bc7-ba1c04c602d7.bmp\" alt=\"\" />).
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.
%K Compressed Sensing
%K Total Variation Minimization
%K l&lt
%K sub&gt
%K 1&lt
%K /sub&gt
%K -Analysis
%K D-Restricted Isometry Property
%K Tight Frames
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=63986