An iterative algorithm for solving ill-conditioned linear least squares problems

Linear Least Squares（LLS） problems are particularly difficult to solve because they are frequently ill-conditioned, and involve large quantities of data. Ill-conditioned LLS problems are commonly seen in mathematics and geosciences, where regularization algorithms are employed to seek optimal solutions. For many problems, even with the use of regularization algorithms it may be impossible to obtain an accurate solution. Riley and Golub suggested an iterative scheme for solving LLS problems. For the early iteration algorithm, it is difficult to improve the well-conditioned perturbed matrix and accelerate the convergence at the same time. Aiming at this problem, self-adaptive iteration algorithm（SAIA） is proposed in this paper for solving severe ill-conditioned LLS problems. The algorithm is different from other popular algorithms proposed in recent references. It avoids matrix inverse by using Cholesky decomposition, and tunes the perturbation parameter according to the rate of residual error decline in the iterative process. Example shows that the algorithm can greatly reduce iteration times, accelerate the convergence,and also greatly enhance the computation accuracy.

A Novel Method to Enhance the Inversion Speed and Precision of the NMR T_(2) Spectrum by the TSVD Based Linearized Bregman Iteration

The low-field nuclear magnetic resonance(NMR)technique has been used to probe the pore size distribution and the fluid composition in geophysical prospecting and related fields.However,the speed and accuracy of the existing numerical inversion methods are still challenging due to the ill-posed nature of the first kind Fredholm integral equation and the contamination of the noises.This paper proposes a novel inversion algorithmto accelerate the convergence and enhance the precision using empirical truncated singular value decompositions(TSVD)and the linearized Bregman iteration.The L1 penalty term is applied to construct the objective function,and then the linearized Bregman iteration is utilized to obtain fast convergence.To reduce the complexity of the computation,empirical TSVD is proposed to compress the kernel matrix and determine the appropriate truncated position.This novel inversion method is validated using numerical simulations.The results indicate that the proposed novel method is significantly efficient and can achieve quick and effective data solutions with low signal-to-noise ratios.

Copy Move Forgery Detection Using Novel Quadsort Moth Flame Light Gradient Boosting Machine

A severe problem in modern information systems is Digital media tampering along with fake information.Even though there is an enhancement in image development,image forgery,either by the photographer or via image manipulations,is also done in parallel.Numerous researches have been concentrated on how to identify such manipulated media or information manually along with automatically;thus conquering the complicated forgery methodologies with effortlessly obtainable technologically enhanced instruments.However,high complexity affects the developed methods.Presently,it is complicated to resolve the issue of the speed-accuracy trade-off.For tackling these challenges,this article put forward a quick and effective Copy-Move Forgery Detection(CMFD)system utilizing a novel Quad-sort Moth Flame(QMF)Light Gradient Boosting Machine(QMF-Light GBM).Utilizing Borel Transform(BT)-based Wiener Filter(BWF)and resizing,the input images are initially pre-processed by eliminating the noise in the proposed system.After that,by utilizing the Orientation Preserving Simple Linear Iterative Clustering(OPSLIC),the pre-processed images,partitioned into a number of grids,are segmented.Next,as of the segmented images,the significant features are extracted along with the feature’s distance is calculated and matched with the input images.Next,utilizing the Union Topological Measure of Pattern Diversity(UTMOPD)method,the false positive matches that took place throughout the matching process are eliminated.After that,utilizing the QMF-Light GBM visualization,the visualization of forged in conjunction with non-forged images is performed.The extensive experiments revealed that concerning detection accuracy,the proposed system could be extremely precise when contrasted to some top-notch approaches.

An iterative linear quadratic regulator based trajectory tracking controller for wheeled mobile robot

We present an iterative linear quadratic regulator(ILQR) method for trajectory tracking control of a wheeled mobile robot system.The proposed scheme involves a kinematic model linearization technique,a global trajectory generation algorithm,and trajectory tracking controller design.A lattice planner,which searches over a 3D(x,y,θ) configuration space,is adopted to generate the global trajectory.The ILQR method is used to design a local trajectory tracking controller.The effectiveness of the proposed method is demonstrated in simulation and experiment with a significantly asymmetric differential drive robot.The performance of the local controller is analyzed and compared with that of the existing linear quadratic regulator(LQR) method.According to the experiments,the new controller improves the control sequences(v,ω) iteratively and produces slightly better results.Specifically,two trajectories,'S' and '8' courses,are followed with sufficient accuracy using the proposed controller.

Stability analysis for discrete linear systems with state saturation by a saturation-dependent Lyapunov functional

This paper concerns the stability analysis problem of discrete linear systems with state saturation using a saturation-dependent Lyapunov functional. We introduce a free matrix characterized by the sum of the absolute value of each elements for each row less than 1, which makes the state with saturation constraint reside in a convex polyhedron. A saturation-dependent Lyapunov functional is then designed to obtain a sufficient condition for such systems to be globally asymptotically stable. Based on this stability criterion, the state feedback control law synthesis problem is also studied. The obtained results are formulated in terms of bilinear matrix inequalities that can be solved by the presented iterative linear matrix ineoualitv algorithm. Two numerical examoles are used to demonstrate the effectiveness of the nronosed method_

New Estimates for the Rate of Convergence of the Method of Subspace Corrections

We discuss estimates for the rate of convergence of the method of successive subspace corrections in terms of condition number estimate for the method of parallel subspace corrections.We provide upper bounds and in a special case,a lower bound for preconditioners defined via the method of successive subspace corrections.

Piecewise Linear Weighted Iterative Algorithm for Beam Alignment in Scanning Beam Interference Lithography

To obtain a good interference fringe contrast and high fidelity,an automated beam iterative alignment is achieved in scanning beam interference lithography(SBIL).To solve the problem of alignment failure caused by a large beam angle(or position)overshoot exceeding the detector range while also speeding up the convergence,a weighted iterative algorithm using a weight parameter that is changed linearly piecewise is proposed.The changes in the beam angle and position deviation during the alignment process based on different iterative algorithms are compared by experiment and simulation.The results show that the proposed iterative algorithm can be used to suppress the beam angle(or position)overshoot,avoiding alignment failure caused by over-ranging.In addition,the convergence speed can be effectively increased.The algorithm proposed can optimize the beam alignment process in SBIL.

A Novel Method for Automated Lung Region Segmentation in Chest X-Ray Images

Detecting and segmenting the lung regions in chest X-ray images is an important part in artificial intelligence-based computer-aided diagnosis/detection (AI-CAD) systems for chest radiography. However, if the chest X-ray images themselves are used as training data for the AI-CAD system, the system might learn the irrelevant image-based information resulting in the decrease of system’s performance. In this study, we propose a lung region segmentation method that can automatically remove the shoulder and scapula regions, mediastinum, and diaphragm regions in advance from various chest X-ray images to be used as learning data. The proposed method consists of three main steps. First, employ the simple linear iterative clustering algorithm, the lazy snapping technique and local entropy filter to generate an entropy map. Second, apply morphological operations to the entropy map to obtain a lung mask. Third, perform automated segmentation of the lung field using the obtained mask. A total of 30 images were used for the experiments. In order to verify the effectiveness of the proposed method, two other texture maps, namely, the maps created from the standard deviation filtering and the range filtering, were used for comparison. As a result, the proposed method using the entropy map was able to appropriately remove the unnecessary regions. In addition, this method was able to remove the markers present in the image, but the other two methods could not. The experimental results have revealed that our proposed method is a highly generalizable and useful algorithm. We believe that this method might act an important role to enhance the performance of AI-CAD systems for chest X-ray images.

Numerical Solution of Euler-Bernoulli Beam Equation by Using Barycentric Lagrange Interpolation Collocation Method

Euler-Bernoulli beam equation is very important that can be applied in the field of mechanics, science and technology. Some authors have put forward many different numerical methods, but the precision is not enough high. In this paper, we will illustrate the high-precision numerical method to solve Euler-Bernoulli beam equation. Three numerical examples are studied to demonstrate the accuracy of the present method. Results obtained by our method indicate new algorithm has the following advantages: small computational work, fast convergence speed and high precision.

Complex Traffic Scene Image Classification Based on Sparse Optimization Boundary Semantics Deep Learning

With the rapid development of intelligent traffic information monitoring technology,accurate identification of vehicles,pedestrians and other objects on the road has become particularly important.Therefore,in order to improve the recognition and classification accuracy of image objects in complex traffic scenes,this paper proposes a segmentation method of semantic redefine segmentation using image boundary region.First,we use the Seg Net semantic segmentation model to obtain the rough classification features of the vehicle road object,then use the simple linear iterative clustering(SLIC)algorithm to obtain the over segmented area of the image,which can determine the classification of each pixel in each super pixel area,and then optimize the target segmentation of the boundary and small areas in the vehicle road image.Finally,the edge recovery ability of condition random field(CRF)is used to refine the image boundary.The experimental results show that compared with FCN-8s and Seg Net,the pixel accuracy of the proposed algorithm in this paper improves by 2.33%and 0.57%,respectively.And compared with Unet,the algorithm in this paper performs better when dealing with multi-target segmentation.

A deep semantic segmentation-based algorithm to segment crops and weeds in agronomic color images

In precision agriculture,the accurate segmentation of crops and weeds in agronomic images has always been the center of attention.Many methods have been proposed but still the clean and sharp segmentation of crops and weeds is a challenging issue for the images with a high presence of weeds.This work proposes a segmentation method based on the combination of semantic segmentation and K-means algorithms for the segmenta-tion of crops and weeds in color images.Agronomic images of two different databases were used for the segmentation algorithms.Using the thresholding technique,everything except plants was removed from the images.Afterward,semantic segmentation was applied using U-net followed by the segmentation of crops and weeds using the K-means subtractive algorithm.The comparison of segmentation performance was made for the proposed method and K-Means clustering and superpixels algorithms.The proposed algorithm pro-vided more accurate segmentation in comparison to other methods with the maximum accuracy of equivalent to 99.19%.Based on the confusion matrix,the true-positive and true-negative values were 0.9952 and 0.8985 representing the true classification rate of crops and weeds,respectively.The results indicated that the proposed method successfully provided accurate and convincing results for the segmentation of crops and weeds in the images with a complex presence of weeds.