2008/07/22 by Kamakshi Sivaramakrishnan, Sivaramakrishnan, Kamakshi, Tsachy Weissman +1
Computer Science · Engineering · Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #H.1.1 #Image and Signal Denoising Methods #Information Theory (cs.IT) #Machine Learning (cs.LG) #Medical Image Segmentation Techniques #Sparse and Compressive Sensing Techniques #Statistics Theory (math.ST) #cs.IT #cs.LG #math.IT #math.ST #stat.TH
paper · pdf · doi:10.48550/arxiv.0807.3396
56 pages
arxiv created 2008/07/22 · openalex publication_date 2008/07/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the problem of reconstructing a discrete-time signal (sequence) with continuous-valued components corrupted by a known memoryless channel. When performance is measured using a per-symbol loss function satisfying mild regularity conditions, we develop a sequence of denoisers that, although independent of the distribution of the underlying `clean' sequence, is universally optimal in the limit of large sequence length. This sequence of denoisers is universal in the sense of performing as well as any sliding window denoising scheme which may be optimized for the underlying clean signal. Our results are initially developed in a ``semi-stochastic'' setting, where the noiseless signal is an unknown individual sequence, and the only source of randomness is due to the channel noise. It is subsequently shown that in the fully stochastic setting, where the noiseless sequence is a stationary stochastic process, our schemes universally attain optimum performance. The proposed schemes draw from nonparametric density estimation techniques and are practically implementable. We demonstrate efficacy of the proposed schemes in denoising gray-scale images in the conventional additive white Gaussian noise setting, with additional promising results for less conventional noise distributions.