The effect of Laplacian filter in adaptive unsharp masking for infrared image enhancement

Image processing, in particular image enhancement techniques have been the focal point of considerable research activity in the last decade. With the aid of an existing image enhancement technique, adaptive unsharp masking (AUM), we propose a novel kernel to be used in AUM filtering in order to enhance discontinuities which occur on the edges of targets of interest in infrared (IR) images. The proposed method uses an adaptive filter approach where an objective function is minimized by using descent algorithms. The output IR image has better sharpness and contrast adjustment for the detection of targets in terms of objective quality metrics. Hence, the proposed method ensures that the edges of the targets in IR images are sharper and that the quality of contrast adjustment has its optimum level in terms of peak signal-to-noise ratios.     

An efficient reproducing kernel method for solving the Allen–Cahn equation

In this paper, an efficient reproducing kernel method combined with the finite difference method and the Quasi-Newton method is proposed to solve the Allen–Cahn equation. Based on the Legendre polynomials, we construct a new reproducing kernel function with polynomial form. We prove that the semi-scheme can preserve the energy dissipation property unconditionally. Numerical experiments are given to show the efficiency and validity of the proposed scheme.     

Using eigenstructure of the Hessian to reduce the dimension of the intensity modulated radiation therapy optimization problem

Optimization is of vital importance when performing intensity modulated radiation therapy to treat cancer tumors. The optimization problem is typically large-scale with a nonlinear objective function and bounds on the variables, and we solve it using a quasi-Newton sequential quadratic programming method. This study investigates the effect on the optimal solution, and hence treatment outcome, when solving an approximate optimization problem of lower dimension. Through a spectral decompostion, eigenvectors and eigenvalues of an approximation to the Hessian are computed. An approximate optimization problem of reduced dimension is formulated by introducing eigenvector weights as optimization parameters, where only eigenvectors corresponding to large eigenvalues are included. The approach is evaluated on a clinical prostate case. Compared to bixel weight optimization, eigenvector weight optimization with few parameters results in faster initial decline in the objective function, but with inferior final solution. Another approach, which combines eigenvector weights and bixel weights as variables, gives lower final objective values than what bixel weight optimization does. However, this advantage comes at the expense of the pre-computational time for the spectral decomposition. A preliminary version of this paper was presented at the AAPM 46th annual meeting, held July 25–29, 2004 in Pittsburgh, PA.     

Multi-step quasi-Newton methods for optimization

Quasi-Newton methods update, at each iteration, the existing Hessian approximation (or its inverse) by means of data deriving from the step just completed. We show how “multi-step” methods (employing, in addition, data from previous iterations) may be constructed by means of interpolating polynomials, leading to a generalization of the “secant” (or “quasi-Newton”) equation. The issue of positive-definiteness in the Hessian approximation is addressed and shown to depend on a generalized version of the condition which is required to hold in the original “single-step” methods. The results of extensive numerical experimentation indicate strongly that computational advantages can accrue from such an approach (by comparison with “single-step” methods), particularly as the dimension of the problem increases.     

Convergence of the DFP Algorithm Without Exact Line Search

In this paper, we consider the DFP algorithm without exact line search. We strengthen the conditions on the line search and prove that, under the new line search conditions, the DFP algorithm is globally convergent, Q-superlinearly convergent, and n-step quadratically convergent.     

Large-scale linearly constrained optimization

An algorithm for solving large-scale nonlinear programs with linear constraints is presented. The method combines efficient sparse-matrix techniques as in the revised simplex method with stable quasi-Newton methods for handling the nonlinearities. A general-purpose production code (MINOS) is described, along with computational experience on a wide variety of problems.This research was supported by the U.S. Office of Naval Research (Contract N00014-75-C-0267), the National Science Foundation (Grants MCS71-03341 A04, DCR75-04544), the U.S. Energy Research and Development Administration (Contract E(04-3)-326 PA #18), the Victoria University of Wellington, New Zealand, and the Department of Scientific and Industrial Research Wellington, New Zealand.     

Combined lp and quasi-Newton methods for minimax optimization

We present an algorithm for minimax optimization that combines LP methods and quasi-Newton methods. The quasi-Newton algorithm is used only if an irregular solution is detected, in which case second-order derivative information is needed in order to obtain a fast final rate of convergence. We prove that the algorithm can converge only to a stationary point and that normally the final rate of convergence will be either quadratic or superlinear. The performance is illustrated through some numerical examples.     

Modeling Time-Varying Effects With Large-Scale Survival Data: An Efficient Quasi-Newton Approach

Nonproportional hazards models often arise in biomedical studies, as evidenced by a recent national kidney transplant study. During the follow-up, the effects of baseline risk factors, such as patients’ comorbidity conditions collected at transplantation, may vary over time. To model such dynamic changes of covariate effects, time-varying survival models have emerged as powerful tools. However, traditional methods of fitting time-varying effects survival model rely on an expansion of the original dataset in a repeated measurement format, which, even with a moderate sample size, leads to an extremely large working dataset. Consequently, the computational burden increases quickly as the sample size grows, and analyses of a large dataset such as our motivating example defy any existing statistical methods and software. We propose a novel application of quasi-Newton iteration method to model time-varying effects in survival analysis. We show that the algorithm converges superlinearly and is computationally efficient for large-scale datasets. We apply the proposed methods, via a stratified procedure, to analyze the national kidney transplant data and study the impact of potential risk factors on post-transplant survival. Supplementary materials for this article are available online.     

A QP-FREE AND SUPERLINEARLY CONVERGENT ALGORITHM FOR INEQUALITY CONSTRAINED OPTIMIZATIONS

1 IntroductionConsider tl1e optimizatioll problemndn{f(x): gj(x) 5 0, j e I, x E R"}, j1)where f(x), gj(x): R" - R, j E I = {l,2,...,m}.We know tl1e quasi-Newton meth.d[1]'[9]1[5]1[1O1 is one of the most effective methods to solveproblenl (1) due to its property of superlinear convergence and is still all hot topic at presenttime, which attracts a Iot of authors to make iInprovemellt both in theory a1ld app1ication.Fechinei and Lucidi[3] in 1995 proposed a locally superlinearly convergell…     

Nonmonotone BFGS-trained recurrent neural networks for temporal sequence processing

In this paper we propose a nonmonotone approach to recurrent neural networks training for temporal sequence processing applications. This approach allows learning performance to deteriorate in some iterations, nevertheless the network’s performance is improved over time. A self-scaling BFGS is equipped with an adaptive nonmonotone technique that employs approximations of the Lipschitz constant and is tested on a set of sequence processing problems. Simulation results show that the proposed algorithm outperforms the BFGS as well as other methods previously applied to these sequences, providing an effective modification that is capable of training recurrent networks of various architectures.