By Joseph Noonan
The target of this e-book is to offer a unified information-theoretic method of remedy estimation difficulties more often than not confronted in sign processing functions. The authors offer new techniques to this challenge, in addition to new interpretations for current suggestions. significant purposes of this paintings comprise snapshot recovery, communique channel estimation, textual content recovery, and method modeling. A basic method of fixing a couple of detection and estimation difficulties using ideas from details conception is built, and the theoretical improvement of the strategy - in addition to vital functions - is given.
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Extra resources for Signal and Image Restoration: Information-Theoretic Approaches
Sample text
Then, their divergence distance D(p p ) may be written in terms of their potential functions as D(p p ) = Ep log(p/p ) = Ep log p − Ep log p = φ(τ ) + ψm (α ) − α , τ . 5 Information projection Let pm (x, α) ∈ Pm , then its projection to the k-dimensional subspace Pk is defined by a PDF from Pk as pk (x, β) = arg min{D(p q) : q(x) ∈ Pk }. 10) Now, let Mk (pm ) denote the set of all densities from an exponential family having the same set of k moments as pm on a set of k statistics, a subset of the set of m statistics that generates pm .
3) subject to the condition that the constraint in Eq. 2) is satisfied. 5 An example of such an operator is the gradient. We note here that the constraint presented in this section is of importance to our work since the same constraint is used in deriving the GMF. 4 Bayesian Restoration It is possible to formulate the problem of image restoration as an estimation problem. Using this formulation one may then bring to the problem established techniques from estimation theory such as ML estimation and MAP estimation.
Noonan and P. Basu, “On estimation error using maximum entropy density estimates,” Kybernetes 36(1), 52–64 (2007). 9. H. Akaike, “A new look at the statistical model identification,” IEEE Transactions on Automatic Control 19(6), 716–723 (1974). 1) where x and y are the original and observed signals, respectively, and n is the additive noise due to the measuring device. Signal restoration is the process of inferring the best estimate for the target signal x given the observed signal y and some prior knowledge, if available, about the target.
