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We extend the stochastic gradient optimization used in a mutual information-based registration algorithm to include second-order (Hessian) effects with the aim of accelerating its convergence rate. We consider images, which are misaligned by a four parameter rigid transformation, consisting of scale, rotation and/or x- and y-translations, and we present the results of optimization using a second-order stochastic derivative. The algorithm is applied to a pair of multi-temporal satellite images, and is implemented in a multi-resolution manner using wavelets. Results are presented for an implementation, which switches after a fixed number of iterations, from the first-order scheme to the second-order one.