The whittaker smoother and the moore-penrose inverse in signal reconstruction

The aim of this work is to propose a method based on B-splines for signal filtering and signal reconstruction. The proposed approach consists of applying the Moore-Penrose inverse for the reconstruction of noisy signals and the use of smoothing techniques with a Whittaker smoother to control the roughness of variation in order to extract the signal from a noisy series. The advantages of this method over the conventional filtering and reconstruction methods are the continuous control over smoothness, the automatically interpolating, as well as computationally efficient leave-one-out cross-validation.