Gradient-Adaptive Normalized Convolution

Signal estimation for sparsely and irregularly sampled signals can be carried out using either noniterative methods, or iterative methods or methods that deal with irregular samples and their uncertainty, through normalized convolution. The latter is a general method for filtering incomplete or uncertain data and is based on the separation of both data and operator into a signal part and a certainty part. It has been proven that normalized convolution yields a local description which is optimal both in an algebraic and a least-squares sense. In this letter, we employ the normalized convolution concept to formulate a novel reconstruction method for irregularly sampled signals, utilizing an anisotropic, rotated applicability filter. Our experimental results demonstrate performance gains in a least-squares sense, retaining edge and contour information, especially in sparsely sampled areas on the image plane.