The conjugated null space method of blind deconvolution

Abstract

The method of blind deconvolution for a problem of image deblurring solution is suggested. The method includes estimation of the point spread function (PSF), evaluation of optimized inverse PSF and optimization of original image estimate. It was shown that the left side null space of the autoregression (AR) matrix operator is the lexicographical presentation of the 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. The first method uses balanced variations of convolution and deconvolution transforms to obtaining iterative schema of image optimization. The variations balance is joined with 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.