Efficient multiframe super-resolution for imagery with lateral shifts.

Trade studies used to design optical imaging systems frequently result in systems being undersampled. The resolution of such systems is limited by the finite size of the detector pixels rather than the cutoff spatial frequency of the optical system. Multiframe super-resolution techniques can be used to combine a number of spatially displaced images from such systems into a single, high-resolution image. Nonlinear optimization techniques have frequently been used to solve this problem. Such techniques define an objective function and use numerical optimization methods to obtain a solution. These numerical methods are often more efficient when derivatives of the objective function with respect to the variables can be calculated analytically rather than numerically. We demonstrate for the simple motion model of pure lateral translation that the derivatives of the objective function with respect to the image lateral shifts can be calculated analytically to speed optimization calculations.