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A confidence-set approach to signal denoising

Boris Ryabko 1 Daniil Ryabko 2
2 SEQUEL - Sequential Learning
LIFL - Laboratoire d'Informatique Fondamentale de Lille, Inria Lille - Nord Europe, LAGIS - Laboratoire d'Automatique, Génie Informatique et Signal
Abstract : The problem of filtering of finite-alphabet stationary ergodic time series is considered. A method for constructing a confidence set for the (unknown) signal is proposed, such that the resulting set has the following properties. First, it includes the unknown signal with probability , where is a parameter supplied to the filter. Second, the size of the confidence sets grows exponentially with a rate that is asymptotically equal to the conditional entropy of the signal given the data. Moreover, it is shown that this rate is optimal. We also show that the described construction of the confidence set can be applied to the case where the signal is corrupted by an erasure channel with unknown statistics.
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Submitted on : Tuesday, December 3, 2013 - 2:29:58 PM
Last modification on : Thursday, January 20, 2022 - 4:12:33 PM



Boris Ryabko, Daniil Ryabko. A confidence-set approach to signal denoising. Statistical Methodology, Elsevier, 2013, 15, pp.115--120. ⟨10.1016/j.stamet.2013.05.003⟩. ⟨hal-00913253⟩



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