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 sublinear 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 sublinearity 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,
any
(sequence of) scheme(s) fails to compete in the above sense. Using dynamic programming, we derive an efficient implementation of the S-DUDE, which has complexity (time and memory) growing linearly with the data size and the number of switches
m
. Preliminary experimental results are presented, suggesting that S-DUDE has the capacity to improve on the performance attained by the original DUDE in applications where the nature of the data abruptly changes in time (or space), as is often the case in practice.