Adaptive Context for a Discrete Universal Denoiser
Statistical analysis of spatially uniform signal contexts allows Discrete Universal Denoiser (DUDE) to effectively correct signal errors caused by a discrete symmetric memoryless transmission channel. The analysis sets no limits on a probability signal model apart from stationarity and ergodicity. Statistics of signal contexts are used first to learn the probability of errors and then to detect and correct the errors. Therefore a proper choice of context is an essential prerequisite to the practical use of DUDE. We propose to use the maximum likelihood estimate of context assuming the signals are modelled with a nonparametric generic Markov–Gibbs random chain or field. The model adds to stationarity and ergodicity only one more condition, namely, pairwise dependences between each signal and its context. Experiments with noisy binary images confirm a feasibility of such adaptive context, show some advantages of DUDE over more conventional median filtering, and relate the choice of a proper context size to the maximum entropy of the context statistics used for image denoising.
KeywordsMaximum Entropy White Area Image Denoising Signal Array Signal Context
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