Denoising via MCMC-Based Lossy Compression

It has been established in the literature, in various theoretical and asymptotic senses, that universal lossy compression followed by some simple postprocessing results in universal denoising, for the setting of a stationary ergodic source corrupted by additive white noise. However, this interesting theoretical result has not yet been tested in practice in denoising simulated or real data. In this paper, we employ a recently developed MCMC-based universal lossy compressor to build a universal compression-based denoising algorithm. We show that applying this iterative lossy compression algorithm with appropriately chosen distortion measure and distortion level, followed by a simple derandomization operation, results in a family of denoisers that compares favorably (both theoretically and in practice) with other MCMC-based schemes, and with the discrete universal denoiser DUDE.