Lower Limits of Discrete Universal Denoising

Following recent work by Weissman et al, in the spirit of results on universal compression, we compare the performance of universal denoisers on discrete memoryless channels to that of the best k-th order omniscient denoiser, namely one that is tuned to the transmitted noiseless sequence. We show that the additional loss incurred in the worst case by any denoiser on a length-n sequence grows like Omega(c ^k/radicn), where c > 1 is a constant depending on the channel parameters and the loss function. This shows that for fixed k, the additional loss incurred by the discrete universal denoiser (DUDE) is no larger than a constant multiplicative factor of the best possible