Multiwavelets are briefly reviewed and preprocessing and postprocessing for such wavelets are introduced. Least squares curve fitting of irregularly sampled data is achieved by means of unshifted and shifted multiscaling functions. This preprocessing procedure combined with multiwavelet neural networks for data-adaptive curve fitting is shown to perform well in the case of high resolution. In t...

helicopter-borne electromagnetic (hem) is a fast and high resolution airborne electromagnetic (aem) method that is frequently used for imaging of the subsurface resistivity structures. this is a versatile and cost effective method, frequently has used in mineral and groundwater exploration and various environmental problems. modern frequency-domain hem systems utilize small electromagnetic, mag...

Developed in [Deng and Lin, 2014], Least-Squares Progressive Iterative Approximation (LSPIA) is an efficient iterative method for solving B-spline curve and surface least-squares fitting systems. In [Deng and Lin 2014], it was shown that LSPIA is convergent when the iterative matrix is nonsingular. In this paper, we will show that LSPIA is still convergent even the iterative matrix is singular.

This paper adresses the problem of least-square fitting with rational pole curves. The issue is to minimize a sum of squared Euclidean norms with respect to three types of unknowns: the control points, the node values, and the weights. A new iterative algorithm is proposed to solve this problem. The method alternates between three steps to converge towards a solution. One step uses the projecti...

In this paper, we present a novel scheme for parsing images into medium level vision representation: contour curve and region texture. This scheme is integrated with piecewise iterative curve fitting and texture synthesis, in which an original image is analyzed at the representation side so as to obtain contours and local texture exemplars. The contour of each region will be processed piecewise...

A first inversion of the backscatter profile and extinction-to-backscatter ratio from pulsed elastic-backscatter lidar returns is treated by means of an extended Kalman filter (EKF). The EKF approach enables one to overcome the intrinsic limitations of standard straightforward nonmemory procedures such as the slope method, exponential curve fitting, and the backward inversion algorithm. Whereas...

Many different techniques to reduce the dimensions of a model have been proposed in the near past. Krylov subspace methods are relatively cheap, but generate non-optimal models. In this paper a combination of Krylov subspace methods and Orthonormal Vector Fitting is proposed. In that way an optimal model for a large model can be generated. In the first step, a Krylov subspace method reduces the...

Introduction 2 Signal arithmetic 3 Signals and noise 6 Smoothing 11 Differentiation 17 Resolution enhancement 26 Harmonic analysis 28 Convolution 31 Deconvolution 32 Fourier filter 34 Integration and peak area measurement 35 Linear least-squares curve fitting 37 Multicomponent spectroscopy 49 Non-linear iterative curve fitting 54 Accuracy and precision of peak parameter measurement 58 SPECTRUM ...

Introduction 2 Signal arithmetic 3 Signals and noise 6 Smoothing 11 Differentiation 17 Resolution enhancement 26 Harmonic analysis 28 Convolution 31 Deconvolution 32 Fourier filter 34 Integration and peak area measurement 35 Linear least-squares curve fitting 37 Multicomponent spectroscopy 49 Non-linear iterative curve fitting 54 Accuracy and precision of peak parameter measurement 58 SPECTRUM ...