  We propose and study the single-frame anisoplanatic deconvolution problem
associated with image classification using machine learning algorithms, named
the nonuniform defocus removal (NDR) problem. Mathematical analysis of the NDR
problem is done and the so-called defocus removal (DR) algorithm for solving it
is proposed. Global convergence of the DR algorithm is established without
imposing any unverifiable assumption. Numerical results on simulation data show
significant features of DR including solvability, noise robustness,
convergence, model insensitivity and computational efficiency. Physical
relevance of the NDR problem and practicability of the DR algorithm are tested
on experimental data. Back to the application that originally motivated the
investigation of the NDR problem, we show that the DR algorithm can improve the
accuracy of classifying distorted images using convolutional neural networks.
The key difference of this paper compared to most existing works on
single-frame anisoplanatic deconvolution is that the new method does not
require the data image to be decomposable into isoplanatic subregions.
Therefore, solution approaches partitioning the image into isoplanatic zones
are not applicable to the NDR problem and those handling the entire image such
as the DR algorithm need to be developed and analyzed.
