Technical Report

J. E. Fowler, “The Redundant Discrete Wavelet Transform and Additive Noise,” Tech. Rep. MSSU-COE-ERC-04-04, Mississippi State ERC, Mississippi State University, March 2004.

• Abstract:
  The behavior under additive noise of the redundant discrete wavelet transform, a frame expansion that is essentially an undecimated discrete wavelet transform, is studied. Known prior results in the form of inequalities bound distortion energy in the original signal domain from additive noise in frame-expansion coefficients. In this paper, a more precise relationship between RDWT-domain and original-signal-domain distortion is developed. Specifically, it is determined that the contribution to distortion in the original signal domain from white noise in a single RDWT subband depends only on the decomposition scale at which the subband resides. Furthermore, the total noise distortion due to all subbands is found to be an equality rather than a bounding relationship involving frame bounds, which are shown, in fact, to widen as the number of decomposition scales increases.
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