Traditional Gradient Projection Research Articles

Rapid Gradient Projection Algorithm for Remote Sensing Image Reconstruction

Remote sensing reconstruction technology has become an important research topic due to the rapid development of aerospace,remote sensing,and communication technologies. In order to improve remote sensing reconstruction image quality, we design of a rapid Gradient Projection method. In the traditional Gradient Projection method, the searching direction changes each setp. Now we propose a rapid searching method by running with fix step. Experiment results show that the rapid Gradient Projection Algorithm get the better reconstruction image. The running results are shown by two remote sensing pictures. Further research is required in remote sensing edge intelligence technology to improve its depth and breadth of application.

Improved Gradient Projection Algorithm for Deblurred Image Application

For the purpose of reducing the noise of deblurred image, an improved Gradient Projection method by sparse coding Reconstruction (GPSR) algorithm is proposed. Different with the traditional Gradient Projection method for sparse reconstruction code (GPSR) method, the obvious distinctions between the original image and deblurred image are projected onto dimensional projection image value. Thus the picture noise are deleted. The classical Gradient Sparse Projection computing method, searching direction changes time by time. Now we propose the new method by running with fix step. The constraints of searching method is guarantee. We prove the new computing method in theory, and at the same time, we running the method by classical picture. We compare the running results of classic method and the fix step hunt method (FXHM), the running results of two methods are shown in the article, the performance of fix step hunt method (FXHM) is higher than the classic method as possible as it can.

Multi-source big data dynamic compressive sensing and optimization method for water resources based on IoT

Water resources data is usually featured by huge volume, multi-variable as well as multi-dimension, which leads to deficiency in terms of data integrity, rationality and efficacy in water resources management and allocation. In order to reduce the amount of data collected in the Internet of things, to improve the processing speed for water resources data, a constrained single objective optimization problem is transformed into a multi-objective optimization problem with sparse degree as the optimization objective in compressed sensing reconstruction, and then a sparse reconstruction method based on hybrid multi-objective optimization is proposed. The algorithm is designed based on the multi objective optimization problem, and the algorithm is easy to implement and adjust. Application results show that the proposed multi-objective particle swarm optimization-Genetic algorithm (MOPSOGA) is than traditional gradient projection sparse reconstruction algorithm (GPSR-BB) algorithm iterations decreased 43.9%. The success rate of reconstruction is higher than that of the traditional algorithm of 0.16; it's with a better reconstruction performance.

A Unified Framework for Low Autocorrelation Sequence Design via Majorization–Minimization

In this paper, we consider the low autocorrelation sequence design problem. We optimize a unified metric over a general constraint set. The unified metric includes the integrated sidelobe level (ISL) and the peak sidelobe level (PSL) as special cases, and the general constraint set contains the unimodular constraint, Peak-to-Average Ratio (PAR) constraint, and similarity constraint, to name a few. The optimization technique we employ is the majorization–minimization (MM) method, which is iterative and enjoys guaranteed convergence to a stationary solution. We carry out the MM method in two stages: in the majorization stage, we propose three majorizing functions: two for the unified metric and one for the ISL metric; in the minimization stage, we give closed-form solutions for algorithmic updates under different constraints. The update step can be implemented with a few Fast Fourier Transformations (FFTs) and/or Inverse FFTs (IFFTs). We also show the connections between the MM and gradient projection method under our algorithmic scheme. Numerical simulations have shown that the proposed MM-based algorithms can produce sequences with low autocorrelation and converge faster than the traditional gradient projection method and the state-of-the-art algorithms.

一种改进的稀疏信号重构的梯度投影算法

压缩感知理论作为一种全新的信号采集、编解码理论，已被广泛地应用于图像处理、模式识别、自动控制和生物传感等领域，并展现出强大的力量。为了更快速地求解压缩感知问题，在稀疏信号重构的Barzilai-Borwein (B-B)梯度投影(Barzilai-Borwein Gradient Projection for Sparse Reconstruction, GPSR-BB)算法的基础上，采用预测校正的技巧，提出了一种改进的梯度投影算法。该算法首先由常数步长的梯度投影产生一个预测点，再根据预测点及B-B方法计算步长得到新的迭代点。新算法单步迭代计算同样简单，且采用预测校正技巧可使迭代点更接近问题的解，从而可望减少算法的总的迭代次数。对随机生成的测试问题进行数值实验，数值结果表明新算法的运行时间要少于GPSR-BB算法。 As a novel sampling, coding and decoding theory, compressed sensing has been a powerful tool which was widely used to the fields of image processing, pattern recognition, automatic control, biological sensors and so on. Based on the Barzilai-Borwein (B-B) gradient projection for sparse reconstruction (GPSR-BB), this paper proposed a new algorithm by using predictor-corrector technique for solving compressed sensing problem fast. In the new algorithm, a predicted point was first generated by traditional gradient projection and then a new iteration point was obtained with B-B method according to the predicted point. In our algorithm, the calculation of a single iteration is also simple, and by using predictor-corrector technique, the iteration point may be closer to the solution of the problem, thereby the number of the iteration would be reduced. Numerical results show that the running time of the new algorithm is less than GPSR-BB for some randomly generated test problems.

Medical Image Compressed Sensing Reconstruction

In order to improve the speed of compressed sensing image reconstruction algorithm, a two step rapid gradient projection for sparse reconstruction in medical image reconstruction is proposed. in traditional gradient projection for sparse reconstruction algorithm, the searching direction is alternate between the negative gradient direction when the direction is ill, the searching speed is slow. Now we search with two step gradient projection, the speed is increased when meets the ill-condition. Compared with the original GPSR algorithm, the TSGPSR algorithm not only accelerate the speed of operation, but also improves the accuracy of the reconstruction. and exhibits higher robustness under different noise intensities.

Improved Gradient Projection Algorithm for Compressed Sensing

In order to improve efficient of compressed sensing image reconstruction, an improved gradient projection algorithm of compressed sensing theory is proposed. In improved Gradient Projection algorithm, the pursuit direction is updated by search at negative gradient direction, thus the gradient direction is a single direction, because the traditional gradient projection algorithm searching at alternating searching method ,the efficient of gradient projection algorithm is higher than the traditional gradient projection algorithm, Experiment results show that, compared with the GPSR algorithm, the IGPSR algorithm improves the signals reconstruction accuracy, improves PSNR of reconstruction signals, and exhibits higher robustness under different noise intensities.

Rapid Gradient Projection Algorithm for Image Reconstruction

In order to improve the speed of compressed sensing image reconstruction algorithm, a rapid gradient projection algorithm for image reconstruction is proposed. In traditional Gradient Projection algorithm, the pursuit direction is alternating, in rapid gradient projection algorithm, we use the Newton's method to calculate the gradient descent direction, thus the constraints conditions of gradient projection is satisfied. And the target function is updated in each iteration computing. The effect of approximation matrix to target function is reduced. The iteration computing times is reduced, because the algorithm works in accurate search direction. Experiment results show that, compared with the GPSR algorithm, the RGPSR algorithm improves the signals reconstruction accuracy, improves PSNR of reconstruction signals, and exhibits higher robustness under different noise intensities.

A General Approximation Method for a Kind of Convex Optimization Problems in Hilbert Spaces

The constrained convex minimization problem is to find a pointx∗with the property thatx∗∈C, andh(x∗)=min h(x),∀x∈C, whereCis a nonempty, closed, and convex subset of a real Hilbert spaceH,h(x)is a real-valued convex function, andh(x)is not Fréchet differentiable, but lower semicontinuous. In this paper, we discuss an iterative algorithm which is different from traditional gradient-projection algorithms. We firstly construct a bifunctionF1(x,y)defined asF1(x,y)=h(y)−h(x). And we ensure the equilibrium problem forF1(x,y)equivalent to the above optimization problem. Then we use iterative methods for equilibrium problems to study the above optimization problem. Based on Jung’s method (2011), we propose a general approximation method and prove the strong convergence of our algorithm to a solution of the above optimization problem. In addition, we apply the proposed iterative algorithm for finding a solution of the split feasibility problem and establish the strong convergence theorem. The results of this paper extend and improve some existing results.

General-Weighted Least-Norm Control for Redundant Manipulators

This paper presents the general-weighted least-norm (GWLN) method for the control of redundant manipulators by a new concept of virtual joints, which consist of the performance function of subtasks. The GWLN method enables the redundant manipulator to perform multiple subtasks with the assumption that all the subtasks can be represented by the inequalities as the joint limits avoidance subtask. The number of subtasks to be coped with might be even larger than the number of joints if they do not happen simultaneously. The simulations in contrast to the traditional gradient projection method (GPM) and the recent directional GPM have been made to manifest the advantages of the proposed method. An experiment on the seven-degree-of-freedom redundant manipulator illustrates the good performance for tracking a given trajectory of end-effector position, while both guaranteeing the obstacle free and not violating the joint limits.

Motion Planning Algorithms of Redundant Manipulators Based on Self-motion Manifolds

The current motion planning approaches for redundant manipulators mainly includes two categories: improved gradient-projection method and some other efficiency numerical methods. The former is excessively sensitive to parameters, which makes adjustment difficult; and the latter treats the motion planning as general task by ignoring the particularity, which has good universal property but reduces the solving speed for on-line real-time planning. In this paper, a novel stepwise solution based on self-motion manifold is proposed for motion planning of redundant manipulators, namely, the chief tasks and secondary tasks are implemented step by step. Firstly, the posture tracking of end-effector is achieved accurately by employing the non-redundant joint. Secondly, the end-effector is set to keep stationary. Finally, self-motion of manipulator is realized via additional work on the gradient of redundant joint displacement. To verify this solution, experiments of round obstacle avoiding are carried out via the planar 3 degree-of-freedom manipulator. And the experimental results indicate that this motion planning algorithm can effectively achieve obstacle avoiding and posture tracking of the end-effector. Compared with traditional gradient projection method, this approach can accelerate the problem-solving process, and is more applicable to obstacle avoiding and other additional work in displacement level.

A Family of Supermemory Gradient Projection Methods for Constrained Optimization

A family of supermemory gradient projection methods for solving the convex constrained optimization problem is presented in this article. It is proven to have stronger convergence properties than the traditional gradient projection method. In particular, it is shown to be globally convergent if the objective function is convex.