Geodesic
Discrete optimal filtering
Diskretnaya Matematika, Tome 10 (1998) no. 4, pp. 88-103

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We consider a problem of discrete optimal filtering: using the symbols of an observed binary sequence $\{\eta_{t}\}$, to construct a binary sequence $\{w_{t}^*\}$ which is in a sense the best estimate of a non-observable deterministic (non-random) binary sequence $\{\vartheta_{t}\}$ related to the sequence $\{\eta_{t}\}$ by the equalities $$ \eta _{t}= \xi_{t}\oplus \vartheta _{t}, \qquad t=1,2,\ldots,N, $$ where $\{\xi_{t}\}$ is a random stationary binary sequence and $\oplus$ means the addition modulo 2. We demonstrate an applications of the discrete optimal filtering in the cases where the sequence $\{\vartheta_{t}\}$ is an encoded black-and-white facsimile or television image transmitted through some channel with noise. 
@article{DM_1998_10_4_a5,
     author = {B. V. Gladkov and A. N. Datsenko-Chigorin},
     title = {Discrete optimal filtering},
     journal = {Diskretnaya Matematika},
     pages = {88--103},
     publisher = {mathdoc},
     volume = {10},
     number = {4},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_1998_10_4_a5/}
}
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B. V. Gladkov; A. N. Datsenko-Chigorin. Discrete optimal filtering. Diskretnaya Matematika, Tome 10 (1998) no. 4, pp. 88-103. http://geodesic.mathdoc.fr/item/DM_1998_10_4_a5/