A regularization-based reconstruction algorithm for band-limited signals

This paper investigates the problem of reconstructing band-limited signals from their samples. The concepts of ill-posed problems and regularization operators are introduced, and the ill-posedness of the reconstruction problem is analyzed in the presence of noisy sampling data. A regularized reconstruction algorithm is proposed by modifying the sinc function through the removal of discontinuities in its Fourier transform. The convergence properties and error estimates of the proposed algorithm are established theoretically for noisy sampling data. Numerical experiments are presented to compare the proposed method with several existing reconstruction algorithms, demonstrating its improved performance in the presence of noise.