Extracting a multivariate nonlinear physical model from a set of satellite images is considered as a multivariate nonlinear regression problem. Multiple local solutions often prevent gradient type algorithms from obtaining global optimal solutions. A method of solving this problem is presented based on the simultaneous perturbation stochastic approximation (SPSA) algorithm. The method is applied to a problem of estimating the distribution of energetic ion populations in the magnetosphere from global images of the magnetosphere. The approach uses multiple objective functions: single image errors and the summation of square image errors. The algorithm is demonstrated on simulated energetic- neutral atom (ENA) images. Within a reasonable number of function evaluations, the process converges and reconstructs the images with a mean square error less than or equal to 0.1% of the original image. Also, the SPSA method is compared with results obtained from simulated annealing (SAN) in a single objective function setting. In the comparison study, SPSA has a 3:1 advantage over SAN in both accuracy and efficiency measures.