Normalized averaging using adaptive applicability functions with application in image reconstruction from sparsely and randomly sampled data

In this paper we describe a new strategy for using local structure adaptive filtering in normalized convolution. The shape of the filter, used as the applicability function in the context of normalized convolution, adapts to the local image structure and avoids filtering across borders. The size of the filter is also adaptable to the local sampling density to avoid unnecessary smoothing over high certainty regions. We compare our adaptive interpolation technique with the conventional normalized averaging methods. We found that our strategy yields a result that is much closer to the original signal both visually and in terms of MSE, meanwhile retaining sharpness and improving the SNR.