Technical Reports

HPL-2011-205

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Twice-universal denoising

Ordentlich, Erik; Viswanathan, Krishnamurthy; Weinberger, Marcelo J.
HP Laboratories

HPL-2011-205

Keyword(s): Universal denoising; universal data compression; loss estimation

Abstract: We propose a sequence of universal denoisers motivated by the goal of extending the notion of twice-universality from universal data compression theory to the sliding window denoising setting. Given a sequence length n and a denoiser, the k-th order regret of the latter is the maximum excess expected denoising loss relative to sliding window denoisers with window length 2k+1, where, for a given clean sequence, the expectation is over all channel realizations and the maximum is over all clean sequences of length n. We define the twice-universality penalty of a denoiser as its excess k-th order regret when compared to the k-th order regret of the DUDE with parameter k, and we are interested in denoisers with a small penalty for all k simultaneously. We consider a class of denoisers that apply one of a number of constituent denoisers based on minimizing an estimated denoising loss and establish a formal relationship between errors in the estimated denoising loss and the twice-universality penalty of the resulting denoiser. Given a sequence of window parameters kn, increasing in n sufficiently fast, we use this approach to construct and analyze a specific sequence of denoisers that achieves a much smaller twice--universality penalty for k < kn than the sequence of DUDEs with parameter kn.

37 Pages

External Posting Date: October 22, 2011 [Fulltext]. Approved for External Publication
Internal Posting Date: October 22, 2011 [Fulltext]

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