Jensen-Generalized Discrete Fisher Information, Its Generating Function, and Applications to Image Processing and Contaminated Models

In this work, we first introduce a discrete version of generalized Fisher information measure and develop some new results for it. We then propose Jensen-generalized discrete Fisher (Jensen-GDF) information as a generalized measure, based on the convexity property of generalized discrete Fisher information measure. We further introduce generating functions for generalized discrete Fisher information and Jensen-GDF information measures and use them to develop some results. We also propose a new correlation coefficient in terms of the generalized discrete Fisher information and discuss some of its properties. Finally, to demonstrate the usefulness of the Jensen-generalized discrete Fisher information measure and the proposed correlation coefficient, we apply them to two real-world examples in image processing and forms of contaminated data, and present corresponding numerical results. Our findings show that the Jensen-GDF information measure and the correlation coefficient introduced here are effective criteria for quantifying similarity between two images in image processing settings and for analyzing contaminated data.