A Gradient Regularization Method in Crosswell Seismic Tomography

Crosswell seismic tomography can be used to study the lateral variation of reservoirs, reservoir properties and the dynamic movement of fluids. In view of the instability of crosswell seismic tomography, the gradient method was improved by introducing regularization, and a gradient regularization method is presented in this paper. This method was verified by processing numerical simulation data and physical model data.

A multi-source image fusion algorithm based on gradient regularized convolution sparse representation

Image fusion based on the sparse representation(SR)has become the primary research direction of the transform domain method.However,the SR-based image fusion algorithm has the characteristics of high computational complexity and neglecting the local features of an image,resulting in limited image detail retention and a high registration misalignment sensitivity.In order to overcome these shortcomings and the noise existing in the image of the fusion process,this paper proposes a new signal decomposition model,namely the multi-source image fusion algorithm of the gradient regularization convolution SR(CSR).The main innovation of this work is using the sparse optimization function to perform two-scale decomposition of the source image to obtain high-frequency components and low-frequency components.The sparse coefficient is obtained by the gradient regularization CSR model,and the sparse coefficient is taken as the maximum value to get the optimal high frequency component of the fused image.The best low frequency component is obtained by using the fusion strategy of the extreme or the average value.The final fused image is obtained by adding two optimal components.Experimental results demonstrate that this method greatly improves the ability to maintain image details and reduces image registration sensitivity.

Preconditioned Iterative Methods for Algebraic Systems from Multiplicative Half-Quadratic Regularization Image Restorations

Image restoration is often solved by minimizing an energy function consisting of a data-fidelity term and a regularization term.A regularized convex term can usually preserve the image edges well in the restored image.In this paper,we consider a class of convex and edge-preserving regularization functions,i.e.,multiplicative half-quadratic regularizations,and we use the Newton method to solve the correspondingly reduced systems of nonlinear equations.At each Newton iterate,the preconditioned conjugate gradient method,incorporated with a constraint preconditioner,is employed to solve the structured Newton equation that has a symmetric positive definite coefficient matrix. The eigenvalue bounds of the preconditioned matrix are deliberately derived,which can be used to estimate the convergence speed of the preconditioned conjugate gradient method.We use experimental results to demonstrate that this new approach is efficient, and the effect of image restoration is reasonably well.

Three-dimensional inversion of borehole-surface electrical data based on quasi-analytical approximation

3D inversion of borehole-surface electrical data for complex geo-electrical models is still a challenging problem in geophysical exploration. We have developed a program for 3D inversion to borehole-surface electrical data based on the quasi-analytical approximation （QA） and re-weighted regularized conjugate gradient method （RRCG） algorithms using Visual Fortran 6.5. Application of the QA approximation to forward modeling and Frechet derivative computations speeds up the calculation dramatically. The trial calculation for synthetic data of theoretical model showed that the program is fast and highly precise.