  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.
