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Analysis versus synthesis in signal priors (2005)
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@TECHREPORT{Elad05analysisversus,
author = {Michael Elad and Peyman Milanfar and Ron Rubinstein},
title = {Analysis versus synthesis in signal priors},
institution = {},
year = {2005}
}
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Abstract
The concept of prior probability for signals plays a key role in the successful solution of many inverse problems. Much of the literature on this topic can be divided between analysis-based and synthesis-based priors. Analysis-based priors assign probability to a signal through various forward measurements of it, while synthesisbased priors seek a reconstruction of the signal as a combination of atom signals. In this paper we describe these two prior classes, focusing on the distinction between them. We show that although when reducing to the complete and under-complete formulations the two become equivalent, in their more interesting overcomplete formulation the two types depart. Focusing on the ℓ1 denoising case, we present several ways of comparing the two types of priors, establishing the existence of an unbridgeable gap between them. 1.
Keyphrases
signal prior analysis versus synthesis under-complete formulation successful solution interesting overcomplete formulation denoising case various forward measurement unbridgeable gap prior class key role atom signal several way synthesis-based prior prior probability analysis-based prior many inverse problem
