Wavelet analysis of random fields and multiresolution Wiener filtering

Kevin West Bowman; Christian Houdre

doi:10.1117/12.217586

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1 September 1995 Wavelet analysis of random fields and multiresolution Wiener filtering

Kevin West Bowman, Christian Houdre

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Proceedings Volume 2569, Wavelet Applications in Signal and Image Processing III; (1995) https://doi.org/10.1117/12.217586
Event: SPIE's 1995 International Symposium on Optical Science, Engineering, and Instrumentation, 1995, San Diego, CA, United States

Abstract

We explore the relationship between random processes and wavelets in multiple dimensions and their application to statistical signal processing. To this end, we introduce a multiresolution Wiener filter (MWF) that is applied to the wavelet coefficients of a random process. The MWF is based upon the multiresolution Wiener-Hopf (MWH) equation, which is derived using orthogonal projection theorem on a Hilbert space. The MWH is applied to the solution of the signal estimation problem for both stationary and fractional Brownian motion (fBm) processes. A theoretical mean square error is calculated for the MWF and its values compared to experimental data.

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Kevin West Bowman and Christian Houdre "Wavelet analysis of random fields and multiresolution Wiener filtering", Proc. SPIE 2569, Wavelet Applications in Signal and Image Processing III, (1 September 1995); https://doi.org/10.1117/12.217586

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