Reconstruction of One-Dimensional Signals and Two-Dimensional Images Through the Use of Sobolev-Type Orthogonal Moments

We propose an innovative approach for the reconstruction of 1D signals and 2D images utilizing Sobolev-type orthogonal moments, specifically Krawtchouk-Sobolev moments KSOMs. This method capitalizes on unique discrete measures, leveraging the connection relations and difference equations that characterize these polynomial families. The weighted polynomials derived from Krawtchouk polynomials KOPs are applied in a sophisticated reconstruction algorithm. This approach significantly enhances accuracy and efficiency compared to traditional techniques, emphasizing the structural relationships and recurrent properties of the polynomials. The efficacy and performance of this technique are demonstrated through rigorous testing, marking a significant advancement in the field of signal processing and digital imaging.