Implicit Image Differentiation and Filtering with Applications to Image Sharpening
Alexander G. Belyaev · SIAM Journal on Imaging Sciences · 2013
This paper demonstrates potential advantages of using implicit finite differencing and filtering schemes for fast, accurate, and reliable differentiating and filtering of multidimensional signals defined on regular grids. In particular, applications to image enhancement and Gaussian image deblurring are considered. The theoretical contribution of the paper is threefold. The first adapts the Fourier--Padé--Galerkin approximation approach for constructing compact implicit finite difference schemes with desirable spectral resolution properties. The second establishes a link between implicit and explicit finite differences used for gradient estimation. Finally, the third one consists of introducing new implicit finite difference schemes with good spectral resolution properties.