A Transform Learning Based Deconvolution Technique with Super-Resolution and Microscanning Applications

We deal with reconstruction of convolved images with known point spread functions. We adopt a feature enhanced deconvolution method. Instead of using a pre-designed sparsifying transform, we use an online transform learning based method, and reconstruct images along with a sparsifying transform. To avoid circular effects, we implement non-circular convolution operator using FFT based convolution and dead pixels. We use a coordinate descent type algorithm and derive the associated update steps for both circular and non-circular deconvolution. Moreover, we show single image super-resolution extension for non-circular deconvolution. We compare the proposed method to other feature enhanced deconvolution alternatives, as well as conventional methods such as Lucy-Richardson method. Finally, we demonstrate the effectiveness of the algorithm for circular deconvolution, non-circular deconvolution, and single-image super-resolution applications.