Nonlinear processing of a shift-invariant discrete wavelet transform (DWT) for noise reduction

Markus Lang; Haitao Guo; Jan Erik Odegard; C. Sidney Burrus; Raymond O. Wells Jr.

doi:10.1117/12.205427

6 April 1995 Nonlinear processing of a shift-invariant discrete wavelet transform (DWT) for noise reduction

Markus Lang, Haitao Guo, Jan Erik Odegard, C. Sidney Burrus, Raymond O. Wells Jr.

Proceedings Volume 2491, Wavelet Applications II; (1995) https://doi.org/10.1117/12.205427
Event: SPIE's 1995 Symposium on OE/Aerospace Sensing and Dual Use Photonics, 1995, Orlando, FL, United States

Abstract

A novel approach for noise reduction is presented. Similar to Donoho, we employ thresholding in some wavelet transform domain but use a nondecimated and consequently redundant wavelet transform instead of the usual orthogonal one. Another difference is the shift invariance as opposed to the traditional orthogonal wavelet transform. We show that this new approach can be interpreted as a repeated application of Donoho's original method. The main feature is, however, a dramatically improved noise reduction compared to Donoho's approach, both in terms of the l₂ error and visually, for a large class of signals. This is shown by theoretical and experimental results, including synthetic aperture radar (SAR) images.

Citation Download Citation

Markus Lang, Haitao Guo, Jan Erik Odegard, C. Sidney Burrus, and Raymond O. Wells Jr. "Nonlinear processing of a shift-invariant discrete wavelet transform (DWT) for noise reduction", Proc. SPIE 2491, Wavelet Applications II, (6 April 1995); https://doi.org/10.1117/12.205427

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