The variational approach to signal restoration calls for the minimization of a cost function that is the sum of a data fidelity term and a regularization term, the latter term constituting a 'prior'. A synthesis prior represents the sought signal as a weighted sum of 'atoms'. On the other hand, an analysis prior models the coefficients obtained by applying the forward transform to the signal. For orthonormal transforms, the synthesis prior and analysis prior are equivalent; however, for overcomplete transforms the two formulations are different. We compare analysis and synthesis ℓ₁-norm regularization with overcomplete transforms for denoising and deconvolution.

Date Published: 4 September 2009
PDF: 15 pages
Proc. SPIE 7446, Wavelets XIII, 74460D (4 September 2009); doi: 10.1117/12.826663

Published in SPIE Proceedings Vol. 7446:
Wavelets XIII
Vivek K. Goyal; Manos Papadakis; Dimitri Van De Ville, Editor(s)