The fusion of different resolution SAR images

We explore the possibility of using different data sets relative to the same scene to obtain a better knowledge of the scene than the one obtained using only one data set. In particular we concentrate on the fusion of two different spatial resolution images, although the method we propose can be regarded as a method of more general interest. The fused image has the least mean square deviation from the finer resolution image, subject to the constraints imposed by the knowledge of the coarser resolution image. Fusion is obtained by solving a constrained quadratic highly parallelizable minimization problem. Explicit formulas for the solution of the minimization problem are given. The number of elementary operations required is proportional to the number of pixels of the finer resolution image. We test our method on a class of simulated images that reproduce some features of synthetic aperture radar (SAR) images. As an example we consider the problem of detection of point scatterers in a uniform background. The results obtained show that the information from the coarser resolution image can significantly improve the quality of the reconstructed scene obtained from the finer resolution image.