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This paper proposes a new method for a measure of coherent similarity between temporal multichannel synthetic aperture radar (SAR) images and its implementation to change detection application. The method is based on mutual information (MI) from information theory. The MI measures the amount of information in common between coherent temporal multichannel SAR acquisitions. In order to develop an algorithm for all kinds of SAR images, such as interferometric SAR, polarimetric-interferometric SAR (PolInSAR), and partial PolInSAR, first, the joint density function of temporal multichannel images based on their second-order statistics has been derived. Then, the derived joint density function is used to calculate an analytical expression for the MI between temporal images, which is assumed to be maximal if the temporal images are identical. Although, in this paper, a new coherent similarity measure has analytically been derived for temporal polarimetric SAR images based on complex Wishart process in time, since the mathematical formulation is general, it can equally well be implemented into any kind of multivariate remote sensing data, such as multispectral optical and interferometric images after small continuation. This derived quantity has been implemented for change detection application whose aim is to characterize the temporal behavior of the acquisitions. A comparison between the proposed and the other well-known change detection methods by means of scene characterization is shown, describing the advantages due to the fact that the proposed change detector involves almost every facet of applied change detection.