Analysis of displacement errors in high-resolution image reconstruction with multisensors

An image-acquisition system composed of an array of sensors, where each sensor has a subarray of sensing elements of suitable size, has recently been popular for increasing the spatial resolution with high signal-to-noise ratio beyond the performance bound of technologies that constrain the manufacture of imaging devices. Small perturbations around the ideal subpixel locations of the sensing elements (responsible for capturing the sequence of undersampled degraded frames), because of imperfections in fabrication, limit the performance of the signal-processing algorithms for processing and integrating the acquired images for the desired enhanced resolution and quality. The contributions of this paper include an analysis of the displacement errors on the convergence rate of the iterative approach for solving the transform based preconditioned system of equations. Subsequently, it is established that the use of the MAP, L₂ norm or H₁ norm regularization functional leads to a proof of linear convergence of the conjugate gradient method in terms of the displacement errors caused by the imperfect subpixel locations. Results of simulation support the analytical results