Universal Lossless Compression-based Denoising

In a discrete denoising problem, if the denoiser knows the clean source distribution, the Bayes optimal denoiser is the Bayes response of the posterior distribution of the source given the noisy observations. However, in many applications the source distribution is unknown. We consider the Bayes response based on the approximate posterior distribution induced by a universal lossless compression code. Motivated by this approach, we present the empirical conditional entropy-based denoiser. Simulations show that when the source alphabet is small, the proposed denoiser achieves the performance of the Universal Discrete DEnoiser ( DUDE). Furthermore, if the alphabet size increases, the proposed denoiser degrades more gracefully than the DUDE.