Multi-Resolution Reconstruction of Irregularly Sampled Signals with Compactly Supported Radial Basis Functions

We propose a novel method for reconstructing d dimensional signals with irregular samples, without any restriction on their positions. We develop a multi-resolution approximation scheme using compactly supported radial basis functions (CSRBFs). Samples are first clustered using principal component analysis and their centroids define CSRBF centers. The mean square error is minimized by selecting centers where the largest local error at the previous level is. We shall prove the effectiveness of our algorithm in one-and two-dimensional cases with Gaussian noise