On Jensen- divergence measure

Abstract The purpose of this paper is twofold. The first part is to introduce relative- $\chi_{\alpha}^{2}$ , Jensen- $\chi_{\alpha}^{2}$ and (p, w)-Jensen- $\chi_{\alpha}^2$ divergence measures and then examine their properties. In addition, we also explore possible connections between these divergence measures and Jensen–Shannon entropy measure. In the second part, we introduce $(p,\eta)$ -mixture model and then show it to be an optimal solution to three different optimization problems based on $\chi_{\alpha}^{2}$ divergence measure. We further study the relative- $\chi_{\alpha}^{2}$ divergence measure for escort and arithmetic mixture densities. We also provide some results associated with relative- $\chi_{\alpha}^{2}$ divergence measure of mixed reliability systems. Finally, to demonstrate the usefulness of the Jensen- $\chi_{\alpha}^{2}$ divergence measure, we apply it to a real example in image processing and present some numerical results. Our findings in this regard show that the Jensen- $\chi_{\alpha}^{2}$ is an effective criteria for quantifying the similarity between two images.

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