Optimizing Multitemporal Data Regression for Minimizing Residual Entropy

Comparison of two images of the same object or phenomenon taken some time apart is a bit complicated due to fact that, there may be sensor variation, illumination variation, non-uniform attenuation, atmospheric absorption or any other environmental effects which may render some changes. That eventually makes it quite difficult to achieve a good compression rate in terms of any prediction based approach. That’s why optimizing the functional relation between two distinct time satellite image is the basic and prerequisite for many studies in the sequential transmission of remote sensed data. Shannon's entropy represents an absolute limit on the best possible lossless compression of any communication. In the sequential transmission of the remote sensed data the images will be available frequently, so we need to achieve the lowest entropy of the data to be sent. We want to have an optimization process that will minimize the residual entropy of any regression based prediction approach. Minimizing the entropy of the residual for any prediction will in fact make the residual symbol’s probability as independent as possible (decor related). In this paper we have used simple linear model to be optimized by the modified objective function of entropy minimization rather that sum square based least square approach. We have used brute force search or exhaustive search for the optimization process. Considering our objective function, optimization search techniques like Simulated Annealing, Tabu search, Genetic algorithm, Cross Entropy method are the best candidates for this procedure. From the experimental results we can easily differentiate our procedure from the SSE based regression analysis. In fact in most of the cases of the image pairs our optimization method achieves lower entropy than that of the least square regression analysis. Key-Words: Entropy, Regression, Residual, Temporal, REM and Optimization.