# MREM: Multiresolution Regularized Expectation Maximization Algorithm
for Image Reconstruction of Poisson Data

### D. D. Dixon

### J. Knödlseder

### R. Diehl

## Abstract

The Expectation Maximization Maximum Likelihood (EMML) algorithm
(also known as Richardson-Lucy) provides a Maximum Likelihood (ML)
image estimate from Poisson data affected by a non-trivial instrumental
response (e.g., PSF). However, like all such ML estimates, it suffers from
noise amplification, necessitating some degree of regularization to extract
scientifically useful data. Here, we describe a regularization utilizing wavelet
threshholding of the EM correction factors, coupled with progressive
admittance of wavelets from large to small scales. We term the
resultant iteration Multiresolution Regularized Expectation Maximization,
or MREM.

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On 16 Jul 1999, 09:19.