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MAP versus MMSE Estimation

In: Sparse and Redundant Representations

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  • Michael Elad

    (The Technion – Israel Institute of Technology, Computer Science Department)

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.

Suggested Citation

  • Michael Elad, 2010. "MAP versus MMSE Estimation," Springer Books, in: Sparse and Redundant Representations, chapter 0, pages 201-225, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4419-7011-4_11
    DOI: 10.1007/978-1-4419-7011-4_11
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