A Generalized Beta Prime Distribution as the Ratio Probability Density Function for Change Detection Between Two SAR Intensity Images With Different Number of Looks

In the framework of the comparison of synthetic aperture radar (SAR) imagery from the Magellan space mission and the VISAR and VenSAR radar instruments which will be onboard the forthcoming VERITAS and EnVision missions to Venus, the problem of the disparity between the resolutions of the images arises when attempting to define a test statistic with which to detect changes. Reliable change detection requires equivalent spatial resolutions which, for the two different images, inevitably involve different equivalent numbers of looks after speckle-reduction processing. This study presents a method to address this scenario using a generalized beta prime distribution as a probability density function (pdf) which is fit to the histogram of the ratio between the two intensity images. The work demonstrates and verifies the properties of the function, highlights its most useful traits, and elaborates on the mathematical procedure required to achieve a meaningful change detection in line with the classic theory of an equal number of looks. The results show that the method accurately describes the ratio histogram of two SAR-intensity images with different numbers of looks. Furthermore, they demonstrate the adaptability of the method to the presence of high pixel correlation between the images and validate its robustness in the presence of textural complexity when the texture patterns of the images are similar.