Wavelet transform and maximum entropy method

Eric Pantin; Jean-Luc Starck

doi:10.1117/12.224171

9 October 1995 Wavelet transform and maximum entropy method

Eric Pantin, Jean-Luc Starck

Proceedings Volume 2570, Experimental and Numerical Methods for Solving Ill-Posed Inverse Problems: Medical and Nonmedical Applications; (1995) https://doi.org/10.1117/12.224171
Event: SPIE's 1995 International Symposium on Optical Science, Engineering, and Instrumentation, 1995, San Diego, CA, United States

Abstract

In 1994, to overcome the difficulties encountered by the maximum entropy method (MEM) to restore images containing both high and low frequencies, Bonteoke et al. introduced the Pyramid Maximum Entropy Deconvolution. However, this method presents several drawbacks such as parameters estimation (model, alpha). Furthermore, in their method they don't minimize any functional. Following these ideas, we propose the multiresolution maximum entropy method which is based on the concept of multiscale entropy derived from the wavelet decomposition of a signal into different frequency bands. It leads to a method which is flux conservative, and the use of a multiresolution support solves the problem of MEM to choose the (alpha) parameter, i.e. relative weight between the goodness-of-fit and the entropy. We also show that our algorithm is efficient for filtering astronomical images.

Citation Download Citation

Eric Pantin and Jean-Luc Starck "Wavelet transform and maximum entropy method", Proc. SPIE 2570, Experimental and Numerical Methods for Solving Ill-Posed Inverse Problems: Medical and Nonmedical Applications, (9 October 1995); https://doi.org/10.1117/12.224171

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