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MAP versus MMSE Estimation

  • Michael Elad
Chapter

Abstract

So far we kept the description of the pursuit algorithms on a deterministic level, as an intuitive optimization procedure. We mentioned in Chapter 9 that these algorithms correspond to an approximation of the Maximum-A’posteriori-Probability (MAP) estimator, but this connection was not explicitly derived. In this chapter we make this claim exact by defining the quest for sparse representations as an estimation task. As we shall see, this calls for a clear and formal definition of the stochastic model assumed to generate the sparse representation vector. A benefit of such treatment is an ability to derive the Minimum-Mean-Squared-Error (MMSE) estimator as well, and this in turn leads to the need to approximate it. These and more are the topics we cover in this chapter.

Keywords

Sparse Representation Multivariate Gaussian Distribution Estimation Task Sparse Vector MMSE Estimation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Computer Science DepartmentThe Technion – Israel Institute of TechnologyHaifaIsrael

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