Subpixel image reconstruction using nonuniform defocused images

This paper considers the problem of reconstructing an object with high-resolution using several low-resolution images, which are degraded due to nonuniform defocus effects caused by angular misalignment of the subpixel motions. The new algorithm, indicated by the Superresolution And Nonuniform Defocus Removal (SANDR) algorithm, simultaneously performs the nonuniform defocus removal as well as the superresolution reconstruction. The SANDR algorithm combines non-sequentially the nonuniform defocus removal method recently developed by Thao et al. and the least squares approach for subpixel image reconstruction. Hence, it inherits global convergence from its two component techniques and avoids the typical error amplification of multi-step optimization contributing to its robustness. Further, existing acceleration techniques for optimization have been proposed that assure fast convergence of the SANDR algorithm going from rate O(1/k) to O(1/k^2) compared to most existing superresolution (SR) techniques using the gradient descent method. An extensive simulation study evaluating the new SANDR algorithm has been conducted. As no algorithms are available to address the combined problem, in this simulation study we restrict the comparison of SANDR with other SR algorithms neglecting the defocus aberrations. Even for this case the advantages of the SANDR algorithm have been demonstrated.