Blind PSF estimation and methods of deconvolution optimization
This work addresses image deblurring for applications like real-time high-resolution imaging, but it appears incremental as it builds on existing deconvolution methods with improved convergence.
The paper tackles the problem of blind point spread function (PSF) estimation for image deconvolution by proposing a method based on the null space of an autoregression matrix and introducing two optimization techniques using regularization and maximum entropy principles. The result is iterative schemas with faster convergence, enabling high-resolution image reconstruction in real time.
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.