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Signal restoration with overcomplete wavelet transforms: comparison of analysis and synthesis priors

Selesnick, I. ; Figueiredo, M. A. T.

Signal restoration with overcomplete wavelet transforms: comparison of analysis and synthesis priors, Proc SPIE Wavelets XIII, San Diego, United States, Vol. 7446, pp. - , August, 2009.

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Abstract
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 `1-norm regularization with overcomplete transforms for denoising and deconvolution.