Translations:Model used for deconvolution/14/en

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An inherent feature of any inverse problem is randomness. As we will see, randomness may be associated with various parts of our quest, but there can certainly be no doubt that noise always associated with the observations is indeed random. Thus, our approach must be statistical in nature. Statistics, to many, imply probabilities. Probabilities, at least to us, imply Bayes. This is not the only view; in fact, we consider two quite different views. In the first, we consider the model parameters to be a realization of a random variable. In the second, we treat the parameters as nonrandom. Probability theory and statistics are different. The former refers to the quest of predicting properties of observations from probability laws that are assumed known. The latter is, in a sense, the inverse. We observe data and wish to infer the underlying probability law. In general, inverse problems are more complex to solve than forward problems. They are often ill posed or nonunique.