This letter uncovers the relationship between distortion energy in RDWT and original signals under additive noise, indicating implications for signal processing.
The behavior under additive noise of the redundant discrete wavelet transform (RDWT), which is 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 letter, a precise relationship between RDWT-domain and original-signal-domain distortion for additive white noise in the RDWT domain is derived.
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James E. Fowler (2005) studied this question.
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