Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On MMSE and MAP Denoising Under Sparse Representation Modeling Over a
  Unitary Dictionary   Among the many ways to model signals, a recent approach that draws
considerable attention is sparse representation modeling. In this model, the
signal is assumed to be generated as a random linear combination of a few atoms
from a pre-specified dictionary. In this work we analyze two Bayesian denoising
algorithms -- the Maximum-Aposteriori Probability (MAP) and the
Minimum-Mean-Squared-Error (MMSE) estimators, under the assumption that the
dictionary is unitary. It is well known that both these estimators lead to a
scalar shrinkage on the transformed coefficients, albeit with a different
response curve. In this work we start by deriving closed-form expressions for
these shrinkage curves and then analyze their performance. Upper bounds on the
MAP and the MMSE estimation errors are derived. We tie these to the error
obtained by a so-called oracle estimator, where the support is given,
establishing a worst-case gain-factor between the MAP/MMSE estimation errors
and the oracle's performance. These denoising algorithms are demonstrated on
synthetic signals and on true data (images).

5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org