# Technical Reports

## HPL-2011-205

**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 *k _{n}*, 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*<

*k*than the sequence of DUDEs with parameter

_{n}*k*.

_{n}37 Pages

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

Internal Posting Date: October 22, 2011 [Fulltext]