A discrete denoising algorithm estimates the input sequence to a discrete memoryless channel (DMC) based on the observation of the entire output sequence. For the case in which the DMC is known and the quality of the reconstruction is evaluated with a given single-letter fidelity criterion, we propose a discrete denoising algorithm that does not assume knowledge of statistical properties of the input sequence. Yet, the algorithm is universal in the sense of asymptotically performing as well as the optimum denoiser that knows the input sequence distribution, which is only assumed to be stationary and ergodic. Moreover, the algorithm is universal also in a semi-stochastic setting, in which the input is an individual sequence, and the randomness is due solely to the channel noise.

We develop a code length principle which is invariant to the choice of parameterization on the model distributions. An invariant approximation formula for easy computation of the marginal distribution is provided for gaussian likelihood models. We provide invariant estimators of the model parameters and formulate conditions under which these estimators are essentially posteriori unbiased for gaussian models. An upper bound on the coarseness of discretization on the model parameters is deduced. We introduce a discrimination measure between probability distributions and use it to construct probability distributions on model classes. The total code length is shown to be closely related to the NML code length of Rissanen when choosing Je#reys prior distribution on the model parameters together with a uniform prior distribution on the model classes. Our model selection principle is applied to a gaussian estimation problem for data in a wavelet representation and its performance is tested and compared to alternative wavelet-based estimation methods in numerical experiments. Copyright c 2004 by Eirik Fossgaard 1.