The conjugated null space method of blind PSF estimation and deconvolution optimization

TL;DR

This paper introduces a novel conjugated null space method for blind PSF estimation and deconvolution, utilizing spectral domain optimization and dynamic regularization for high-resolution image reconstruction.

Contribution

It proposes a new null space-based approach for blind PSF and inverse PSF estimation, with innovative regularization techniques for improved deconvolution.

Findings

Fast convergence of iterative schemas for high-resolution image reconstruction

Effective PSF and IPSF estimation using null space eigenfunctions

Regularization methods that prevent image smoothing and enhance detail

Abstract

We have shown that the vector of the point spread function (PSF) lexicographical presentation belongs to the left side conjugated null space (NS) of the autoregression (AR) matrix operator on condition the AR parameters are common for original and blurred images. The method of the PSF and inverse PSF (IPSF) evaluation in the basis of the NS eigenfunctions is offered. The optimization of the PSF and IPSF shape with the aim of fluctuation elimination is considered in NS spectral domain and image space domain. The function of surface area was used as the regularization functional. 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 convolutions with the PSF and IPSF to obtaining iterative schema of image optimization. The variations balance is providing by dynamic regularization basing on condition of the iteration process convergence. The regularization has dynamic character because depends on current and previous image estimate variations. The second method implements the regularization of the deconvolution optimization in curved space with metric defined on image estimate surface. The given iterative schemas have fast convergence and therefore can be used for reconstruction of high resolution images series in real time. The NS can be used for design of denoising bilateral linear filter which does not introduce image smoothing.