Multigrid techniques and wavelet representations in image superresolution

Mariappan S. Nadar; Bobby R. Hunt; Philip J. Sementilli

doi:10.1117/12.185884

16 September 1994 Multigrid techniques and wavelet representations in image superresolution

Mariappan S. Nadar, Bobby R. Hunt, Philip J. Sementilli

Proceedings Volume 2308, Visual Communications and Image Processing '94; (1994) https://doi.org/10.1117/12.185884
Event: Visual Communications and Image Processing '94, 1994, Chicago, IL, United States

Abstract

The Expectation Maximization algorithm for Poisson data, the Poisson-MLE algorithm, and the Simultaneous Multiplicative Algebraic Reconstruction Technique are three iterative solutions to minimum Kullback-Leibler (KL) distance methods. It has been noted empirically that the performance of the three minimum KL distance methods rely on the sparseness of the object. In a previous work, ad hoc object representation schemes were reported that improved the performance of these algorithms, for objects with a significantly high background. In addition to the limitation on the nature of the object estimated, these algorithms have a slow convergence rate. Multigrid methods and wavelet decompositions are two closely related concepts. Multigrid methods were proposed to improve the convergence rates of some iterative methods by appending corrections from coarse grids to an approximate estimate at the fine grid. Wavelet representations, on the other hand, have achieved tremendous success in signal compression applications. This is a direct consequence of the fact that the wavelet transform redistributes the energy in the signal to small number of transform coefficients, thus making the wavelet representation approximately sparse. In addition, the spaces spanned by the wavelet bases comprise of elements with a significant number of near zero sample values. In this paper we expound on the similarities and differences of the two concepts as pertaining to the imaging equation. This leads to a multigrid formulation based on the wavelet subspaces. The goal of this paper is to use this new formulation to overcome two deficiencies of minimum KL distance methods, viz., ringing artifacts due to significant background values in the object and slow convergence of the iterative methods.

Citation Download Citation

Mariappan S. Nadar, Bobby R. Hunt, and Philip J. Sementilli "Multigrid techniques and wavelet representations in image superresolution", Proc. SPIE 2308, Visual Communications and Image Processing '94, (16 September 1994); https://doi.org/10.1117/12.185884

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