Constrained Total Least-Squares Computations for High-Resolution Image Reconstruction with Multisensors

摘要

Multiple undersampled images of a scene are often obtained by using a charge-coupled device (CCD) detector array of sensors that are shifted relative to each other by subpixel displacements. This geometry of sensors, where each sensor has a subarray of sensing elements of suitable size, has been popular in the task of attaining spatial resolution enhancement from the acquired low-resolution degraded images that comprise the set of observations. With the objective of improving the performance of the signal processing algorithms in the presence of the ubiquitous perturbation errors of displacements around the ideal subpixel locations (because of imperfections in fabrication), in addition to noisy observation, the errors-in-variables or the total least-squares method is used in this paper. A regularized constrained total least-squares (RCTLS) solution to the problem is given, which requires the minimization of a nonconvex and nonlinear cost functional. Simulations indicate that the choice of the regularization parameter influences significantly the quality of the solution. The L-curve method is used to select the theoretically optimum value of the regularization parameter instead of the unsound but expedient trial-and-error approach. The expected superiority of this RCTLS approach over the conventional least-squares theory-based algorithm is substantiated by example.