The Whittaker Smoother and the Moore-Penrose Inverse in Signal Reconstruction
نویسندگان
چکیده
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. 1206 S. Chountasis, V. N. Katsikis, D. Pappas and A. Perperoglou Mathematics Subject Classification: 15A09, 65D10, 94A12
منابع مشابه
An Efficient Schulz-type Method to Compute the Moore-Penrose Inverse
A new Schulz-type method to compute the Moore-Penrose inverse of a matrix is proposed. Every iteration of the method involves four matrix multiplications. It is proved that this method converge with fourth-order. A wide set of numerical comparisons shows that the average number of matrix multiplications and the average CPU time of our method are considerably less than those of other methods.
متن کاملThe reverse order law for Moore-Penrose inverses of operators on Hilbert C*-modules
Suppose $T$ and $S$ are Moore-Penrose invertible operators betweenHilbert C*-module. Some necessary and sufficient conditions are given for thereverse order law $(TS)^{ dag} =S^{ dag} T^{ dag}$ to hold.In particular, we show that the equality holds if and only if $Ran(T^{*}TS) subseteq Ran(S)$ and $Ran(SS^{*}T^{*}) subseteq Ran(T^{*}),$ which was studied first by Greville [{it SIAM Rev. 8 (1966...
متن کاملHermitian solutions to the system of operator equations T_iX=U_i.
In this article we consider the system of operator equations T_iX=U_i for i=1,2,...,n and give necessary and suffcient conditions for the existence of common Hermitian solutions to this system of operator equations for arbitrary operators without the closedness condition. Also we study the Moore-penrose inverse of a ncross 1 block operator matrix and. then gi...
متن کاملOn the duality of quadratic minimization problems using pseudo inverses
In this paper we consider the minimization of a positive semidefinite quadratic form, having a singular corresponding matrix $H$. We state the dual formulation of the original problem and treat both problems only using the vectors $x in mathcal{N}(H)^perp$ instead of the classical approach of convex optimization techniques such as the null space method. Given this approach and based on t...
متن کاملApplications of the Moore-Penrose Inverse in Digital Image Restoration
This paper presents a fast computational method that finds application in a broad scientific field such as digital image restoration. The proposed method provides a new approach to the problem of image reconstruction by using the Moore-Penrose inverse. The resolution of the reconstructed image remains at a very high level but the main advantage of the method was found on the computational load ...
متن کامل