Orthonormal quadratic B-spline wavelet bases family on an irregular sampling partition

This paper is devoted to the construction of orthonormal wavelet bases family in the multiresolution orthogonal decomposition context. The study is carried out within the framework where the signal sample positions are known but not equally spaced. The scaling basis in this multiresolution approach is generated from quadratic non- uniform B-spline functions. We impose a multiplicity of order three on each sequence knot. We show that the wavelet and the scaling functions, are not deduced from a unique prototype function which is dilated and translated as in the traditional multiresolution scheme. The filter coefficients are not constants any more at different scales. They depend closely on the sample positions on the sequence. This approach can be used to interpolate irregularly sampled signals in an efficient way, by keeping the multiresolution approach.