Blind PSF estimation and methods of deconvolution optimization

TL;DR

This paper introduces novel methods for blind PSF estimation and image deconvolution optimization that improve convergence speed, enabling real-time high-resolution image reconstruction.

Contribution

It presents a new approach to blind PSF estimation using the null space of the AR matrix and develops two innovative deconvolution optimization methods with faster convergence.

Findings

Inverse PSF evaluation with surface area regularization.

Two optimization methods with dynamic and curved space regularization.

Faster convergence compared to existing algorithms.

Abstract

We have shown that the left side null space of the autoregression (AR) matrix operator is the lexicographical presentation of the point spread function (PSF) on condition the AR parameters are common for original and blurred images. The method of inverse PSF evaluation with regularization functional as the function of surface area is offered. The inverse PSF was used for primary image estimation. Two methods of original image estimate optimization were designed basing on maximum entropy generalization of sought and blurred images conditional probability density and regularization. The first method uses balanced variations of convolution and deconvolution transforms to obtaining iterative schema of image optimization. The variations balance was defined by dynamic regularization basing on condition of iteration process convergence. The regularization has dynamic character because depends on current and previous image estimate variations. The second method implements the regularization of deconvolution optimization in curved space with metric defined on image estimate surface. It is basing on target functional invariance to fluctuations of optimal argument value. The given iterative schemas have faster convergence in comparison with known ones, so they can be used for reconstruction of high resolution images series in real time.