Based on the thin plate spline approximation theory, we propose in this paper an efficient regularization algorithm for the reconstruction of numerical derivatives from two-dimensional scattered noisy data. An error estimation that deduces a good regularization parameter is given. Numerical results show that the proposed method is efficient and stable.

The solution of the linear system of equations Ax ≈ b arising from the discretization of an ill-posed integral equation with a square integrable kernel H(s, t) is considered. The Tikhonov regularized solution x is found as the minimizer of J(x) = {‖Ax − b‖2 + λ‖Lx‖2} and depends on regularization parameter λ which trades off the fidelity of the solution data fit and its smoothing norm, determin...

This work addresses the problem of error concealment in video transmission systems over noisy channels employing Bregman divergences along with regularization. Error concealment intends to improve the effects of disturbances at the reception due to bit-errors or cell loss in packet networks. Bregman regularization gives accurate answers after just some iterations with fast convergence, better a...

Regularization is a standard statistical technique to deal with ill-conditioned parameter estimation problems. We discuss in this contribution what possibilities and advantages regularization ooers in system identiication. In the rst place regularization reduces the variance error of a model, but at the same time it introduces a bias. The familiar trade-oo between bias and variance error for th...

In this paper, we show that the parametric simplex method is an efficient algorithm for solving various statistical learning problems that can be written as linear programs parametrized by a so-called regularization parameter. The parametric simplex method offers significant advantages over other methods: (1) it finds the complete solution path for all values of the regularization parameter by ...

natural signals are continues, therefore, digitizing is an essential task enabling us to use computing tools to process them. according to the nyquist/shannon sampling theory, the sampling frequency must be at least twice the maximum frequency contained in the signal which is being sampled; otherwise, some high frequencies may be aliased and result in a bad reconstruction. the nyquist sampling ...

This thesis investigates the generalization problem in artificial neural networks, attacking it from two major approaches: regularization and model selection. On the regularization side, under the framework of Kullback–Leibler divergence for feedforward neural networks, we develop a new formula for the regularization parameter in Gaussian density kernel estimation based on available training da...

This paper focuses on comb-type or scattered pilot arrangement in OFDM systems with a frequency guard band under the time-variant channel. If the maximum channel delay is large, there is a nearly singular matrix problem when a receiver adopts the Frequency Domain LS (FDLS) method to estimate the data subcarrier channel frequency response. This problem renders FDLS channel estimation more sensit...