Adaptive approximation of multi-dimensional irregularly sampled signals with compactly supported radial basis functions

We propose two novel methods for reconstructing d-dimensional signals with irregular samples, without any restriction on their positions. First approach is an approximation with a fixed number of compactly supported radial basis functions (CSRBFs). Whereas the second one is a multiresolution approach with a fixed error bound, in which we only add CSRBFs where the largest local error at the previous level is. For both approaches, we compute an adaptive local support size for each CSRBFs. We prove the effectiveness of our algorithm in two-dimensional cases