No abstract

This paper investigates the mathematical framework of multiresolution analysis based on irregularly spaced knots sequence. Our presentation is based on the construction of nested nonuniform spline multiresolution spaces. From these spaces, we present the construction of orthonormal scaling and wavelet basis functions on bounded intervals. For any arbitrary degree of the spline function, we provide an explicit generalization allowing the construction of the scaling and wavelet bases on the nontraditional sequences. We show that the orthogonal decomposition is implemented using filter banks where the coefficients depend on the location of the knots on the sequence. Examples of orthonormal spline scaling and wavelet bases are provided. This approach can be used to interpolate irregularly sampled signals in an efficient way, by keeping the multiresolution approach.

No abstract

This paper is concerned with the problem of recovering a discrete signal from a set of irregular spaced samples at known locations. We propose a local interpolation method based on non-uniform B-spline functions. Under specific constraints (multiplicity order imposed on each knot), we generalize the non-uniform B-spline functions for any degree of the interpolation function. We show that whatever the degree of the interpolation function, only few knots are enough to reconstruct the discrete signal. We provide a new and general scheme for the implementation of the reconstruction method. The results of simulation are satisfactory.

No abstract