An iterative method of restoring degraded images was developed by treating images, point spread functions, and degraded images as probability-frequency functions and by applying Bayes’s theorem. The method functions effectively in the presence of noise and is adaptable to computer operation.

/pdf/bayesian-based-iterative-method-of-image-restoration-41ifp80ljc.pdf

Bayesian-Based Iterative Method of Image Restoration

Jaynes's principle of maximum entropy and Kullbacks principle of minimum cross-entropy (minimum directed divergence) are shown to be uniquely correct methods for inductive inference when new information is given in the form of expected values. Previous justifications use intuitive arguments and rely on the properties of entropy and cross-entropy as information measures. The approach here assumes that reasonable methods of inductive inference should lead to consistent results when there are different ways of taking the same information into account (for example, in different coordinate system). This requirement is formalized as four consistency axioms. These are stated in terms of an abstract information operator and make no reference to information measures. It is proved that the principle of maximum entropy is correct in the following sense: maximizing any function but entropy will lead to inconsistency unless that function and entropy have identical maxima. In other words given information in the form of constraints on expected values, there is only one (distribution satisfying the constraints that can be chosen by a procedure that satisfies the consistency axioms; this unique distribution can be obtained by maximizing entropy. This result is established both directly and as a special case (uniform priors) of an analogous result for the principle of minimum cross-entropy. Results are obtained both for continuous probability densities and for discrete distributions.

/pdf/axiomatic-derivation-of-the-principle-of-maximum-entropy-and-28m2oeiysp.pdf

Axiomatic derivation of the principle of maximum entropy and the principle of minimum cross-entropy

Since the development of the entropy theory by Shannon in the late 1940s and of the principle of maximum entropy (POME) by Jaynes in the late 1950s there has been a proliferation of applications of entropy in a wide spectrum of areas, including hydrological and environmental sciences. The real impetus to entropy-based hydrological modelling was provided by Amorocho and Espildora in 1972. A great variety of entropy applications in hydrology and water resources have since been reported, and new applications continue to unfold. This paper reviews the recent contributions on entropy applications in hydrology and water resources, discusses the usefulness and versatility of the entropy concept, and reflects on the strengths and limitations of this concept. The paper concludes with comments on its implications in developing countries. #1997 by John Wiley & Sons, Ltd.

The use of entropy in hydrology and water resources

Data mining techniques are provided which are effective and efficient for discovering useful information from an amorphous collection or data set of records. For example, the present invention provides for the mining of data, e.g., of several or many records, to discover interesting associations between entries of qualitative text, and covariances between data of quantitative numerical types, in records. Although not limited thereto, the invention has particular application and advantage when the data is of a type such as clinical, pharmacogenomic, forensic, police and financial records, which are characterized by many varied entries, since the problem is then said to be one of “high dimensionality” which has posed mathematical and technical difficulties for researchers. This is especially true when considering strong negative associations and negative covariance, i.e., between items of data which may so rarely come together that their concurrence is never seen in any record, yet the fact that this is not expected is of potential great interest.

Method and apparatus for data mining to discover associations and covariances associated with data

Bayesian deconvolution I: Convergent properties

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