Discrete Denoising with Shifts

We introduce S-DUDE, a new algorithm for denoising Discrete Memoryless Channel (DMC)-corrupted data. The algorithm, which generalizes the recently introduced DUDE (Discrete Universal DEnoiser), aims to compete with a genie that has access, in addition to the noisy data, also to the underlying clean data, and that can choose to switch, up to m times, between sliding window denoisers in a way that minimizes the overall loss. When the underlying data form an individual sequence, we show that the S-DUDE performs essentially as well as this genie, provided that m is sub-linear in the size of the data. When the clean data are emitted by a piecewise stationary process, we show that the S-DUDE achieves the optimum distribution-dependent performance, provided that the same sub-linearity condition is imposed on the number of switches. To further substantiate the universal optimality of the S-DUDE, we show that when the number of switches is allowed to grow linearly with the size of the data, an...

• Type: Journal
• Year: 2007
• Where: CORR
• Authors: Taesup Moon, Tsachy Weissman
• Keywords: Clean Data, CORR 2007, Discrete Memoryless Channel, Discrete Universal DEnoiser, Education