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Universal denoising for the finite-input general-output channel

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2 Author(s)
Dembo, A. ; Depts. of Math. & Stat., Stanford Univ., CA, USA ; Weissman, T.

We consider the problem of reconstructing a finite-alphabet signal corrupted by a known memoryless channel with a general output alphabet. The goodness of the reconstruction is measured by a given loss function. We (constructively) establish the existence of a universal (sequence of) denoiser(s) attaining asymptotically the optimum distribution-dependent performance for any stationary source that may be generating the noiseless signal. We show, in fact, that there is a whole family of denoiser sequences with this property. These schemes are shown to be universal also in a semistochastic setting, where the only randomness assumed is that associated with the channel noise. The scheme is practical, requiring O(n1+ε) operations (for any ε>0) and working storage size sublinear in the input data length. This extends recent work that presented a discrete universal denoiser for recovering a discrete source corrupted by a discrete memoryless channel (DMC).

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Information Theory, IEEE Transactions on  (Volume:51 ,  Issue: 4 )