Compactly Supported Non-Uniform Spline Wavelet for Irregularly Sub-Sampled Image Representation

This paper investigates the mathematical framework of the two-dimensional multiresolution analysis adapted to irregularly spaced data. This two-dimensional multiresolution is related on separable multiresolution analysis using non-uniform B-spline functions. For any arbitrary degree of the spline function, we propose an orthonormalization procedure of the scaling and wavelet bases. These orthonormal basis functions satisfy the important features required by a traditional multiresolution analysis such as: (i) the continuity conditions of the scaling and wavelet functions and (ii) the compact support of the scaling and wavelets functions. We show that the orthogonal decomposition is implemented using filter banks where the coefficients depend on the location of the samples on the image grid.