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Remote sensing images are often contaminated by varying degrees of stripes, which severely affects the visual quality and subsequent application of the data. Unlike with conventional methods, we achieve the destriping by separating the stripe component based on a full analysis of the various stripe properties. Under an optimization framework, an \ell^0-norm-based regularization is used to characterize the global sparse distribution of the stripes. In addition, difference-based constraints are adopted to describe the local smoothness and discontinuity in the along-stripe and across-stripe directions, respectively. The alternating direction method of multipliers is applied to solve and accelerate the model optimization. Experiments with both simulated and real data demonstrate the effectiveness of the proposed model, in terms of both qualitative and quantitative perspectives. [ABSTRACT FROM AUTHOR]

In this paper we consider the computation of approximate solutions for inverse problems in Hilbert spaces. In order to capture the special feature of solutions, non-smooth convex functions are introduced as penalty terms. By exploiting the Hilbert space structure of the underlying problems, we propose a fast iterative regularization method which reduces to the classical nonstationary iterated Tikhonov regularization when the penalty term is chosen to be the square of norm. Each iteration of the method consists of two steps: the first step involves only the operator from the problem while the second step involves only the penalty term. This splitting character has the advantage of making the computation efficient. In case the data is corrupted by noise, a stopping rule is proposed to terminate the method and the corresponding regularization property is established. Finally, we test the performance of the method by reporting various numerical simulations, including the image deblurring, the determination of source term in Poisson equation, and the de-autoconvolution problem. [ABSTRACT FROM AUTHOR]

Optimal control for an elliptic system with pointwise Euclidean norm constraints on the control variables is investigated. First order optimality conditions are derived in a manner that is amenable for numerical realisation. An efficient semismooth Newton algorithm is proposed based on this optimality system. Numerical examples are given to validate the superlinear convergence of the semismooth Newton algorithm. [ABSTRACT FROM AUTHOR]

The semismooth Newton method for optimal control problems for systems of partial differential equations with polygonal constraints on the controls is developed. The Newton derivatives are characterized for the case of systems of dimension two, superlinear convergence is verified and a simple proof-of-concept numerical example is provided. [ABSTRACT FROM AUTHOR]

Abstract: The topological structure of a dynamical network plays a pivotal part in its properties, dynamics and control. Thus, understanding and modeling the structure of a network will lead to a better knowledge of its evolutionary mechanisms and to a better cottoning on its dynamical and functional behaviors. However, in many practical situations, the topological structure of a dynamical network is usually unknown or uncertain. Thus, exploring the underlying topological structure of a dynamical network is of great value. In recent years, there has been a growing interest in structure identification of dynamical networks. As a result, various methods for identifying the network structure have been proposed. However, in most of the previous work, few of them were discussed in the perspective of optimization. In this paper, an optimization algorithm based on the projected conjugate gradient method is proposed to identify a network structure. It is straightforward and applicable to networks with or without observation noise. Furthermore, the proposed algorithm is applicable to dynamical networks with partially observed component variables for each multidimensional node, as well as small-scale networks with time-varying structures. Numerical experiments are conducted to illustrate the good performance and universality of the new algorithm. [Copyright &y& Elsevier]

Abstract: Optimal control for a system consistent of the viscosity dependent Stokes equations coupled with a transport equation for the viscosity is studied. Motivated by a lack of sufficient regularity of the adjoint equations, artificial diffusion is introduced to the transport equation. The asymptotic behavior of the regularized system is investigated. Optimality conditions for the regularized optimal control problems are obtained and again the asymptotic behavior is analyzed. The lack of uniqueness of solutions to the underlying system is another source of difficulties for the problem under investigation. [Copyright &y& Elsevier]

In this paper, we consider the sparse phase retrieval problem, recovering an s -sparse signal x ♮ ∈ R n from m phaseless samples y i = | 〈 x ♮ , a i 〉 | for i = 1 , ... , m. Existing sparse phase retrieval algorithms are usually first-order and hence converge at most linearly. Inspired by the hard thresholding pursuit (HTP) algorithm in compressed sensing, we propose an efficient second-order algorithm for sparse phase retrieval. Our proposed algorithm is theoretically guaranteed to give an exact sparse signal recovery in finite (in particular, at most O (log ⁡ m + log ⁡ (‖ x ♮ ‖ 2 / | x min ♮ |)) steps, when { a i } i = 1 m are i.i.d. standard Gaussian random vector with m ∼ O (s log ⁡ (n / s)) and the initialization is in a neighborhood of the underlying sparse signal. Together with a spectral initialization, our algorithm is guaranteed to have an exact recovery from O (s 2 log ⁡ n) samples. Since the computational cost per iteration of our proposed algorithm is the same order as popular first-order algorithms, our algorithm is extremely efficient. Experimental results show that our algorithm can be several times faster than existing sparse phase retrieval algorithms. [ABSTRACT FROM AUTHOR]

To take full advantage of FLASH dose rate (40 Gy/s) and high-dose conformity, we introduce a novel optimization and delivery technique, the spot-scanning proton arc therapy (SP Arc) + FLASH (SPLASH). SPLASH framework was implemented in an open-source proton planning platform (MatRad, Department of Medical Physics in Radiation Oncology, German Cancer Research Center). It optimizes with the clinical dose-volume constraint based on dose distribution and the dose-average dose rate by minimizing the monitor unit constraint on spot weight and accelerator beam current sequentially, enabling the first dynamic arc therapy with voxel-based FLASH dose rate. This new optimization framework minimizes the overall cost function value combined with plan quality and voxel-based dose-rate constraints. Three representative cases (brain, liver, and prostate cancer) were used for testing purposes. Dose-volume histogram, dose-rate-volume histogram, and dose-rate map were compared among intensity modulated proton radiation therapy (IMPT), SPArc, and SPLASH. SPLASH/SPArc could offer superior plan quality over IMPT in terms of dose conformity. The dose-rate-volume histogram results indicated SPLASH could significantly improve V 40 Gy/s in the target and region of interest for all tested cases compared with SPArc and IMPT. The optimal beam current per spot is simultaneously generated, which is within the existing proton machine specifications in the research version (<200 nA). SPLASH offers the first voxel-based ultradose-rate and high-dose conformity treatment using proton beam therapy. Such a technique has the potential to fit the needs of a broad range of disease sites and simplify clinical workflow without applying a patient-specific ridge filter, which has never before been demonstrated. [ABSTRACT FROM AUTHOR]

We consider the variational regularization for inverse problems in a general form. Based on the discrepancy principle, we propose a heuristic parameter choice rule for choosing the regularization parameter which does not require the information on the noise level and is therefore purely data driven. Under variational source conditions, we obtain a posteriori error estimates. According to the Bakushinskii veto, convergence in the worst case scenario cannot be expected in general. However, by imposing certain conditions on the noisy data, we establish a convergence result for the heuristic rule. Applications of the results are addressed and numerical simulations are reported. [ABSTRACT FROM AUTHOR]

In this paper, a stabilized finite element method for optimal control problems governed by a convection dominated diffusion equation is investigated. The state and the adjoint variables are approximated by piecewise linear continuous functions with bubble functions. The control variable either is approximated by piecewise linear functions (called the standard method) or is not discretized directly (called the variational discretization method). The stabilization term only depends on bubble functions, and the projection operator can be replaced by the difference of two local Gauss integrations. A priori error estimates for both methods are given and numerical examples are presented to illustrate the theoretical results. [ABSTRACT FROM PUBLISHER]

The article reports that the spot-scanning proton arc therapy was introduced in 2016 offering superior target conformity and simplify the proton therapy treatment workflow. Topics include examines it is considered an advanced intensity modulated proton therapy (IMPT) technique through arc trajectory optimization.

We consider a boundary value problem involving a Riemann–Liouville fractional derivative of order α ∈ ( 3 / 2 , 2 ) on the unit interval ( 0 , 1 ) . The standard Galerkin finite element approximation converges slowly due to the presence of singularity term x α − 1 in the solution representation. In this work, we develop a simple technique, by transforming it into a second-order two-point boundary value problem with nonlocal low order terms, whose solution can reconstruct directly the solution to the original problem. The stability of the variational formulation, and the optimal regularity pickup of the solution are analyzed. A novel Galerkin finite element method with piecewise linear or quadratic finite elements is developed, and L 2 ( D ) error estimates are provided. The approach is then applied to the corresponding fractional Sturm–Liouville problem, and error estimates of the eigenvalue approximations are given. Extensive numerical results fully confirm our theoretical study. [ABSTRACT FROM AUTHOR]

In this paper, an inverse Robin problem for an elliptic equation is investigated. The Robin coefficient is assumed to be a small perturbation from a reference coefficient, hence a sparse structure is a priori known. An Lq-regularized output least square formulation is considered with q ∈ (0,1). The existence of the minimizer is proved. The convergence of the finite element discretization with respect to mesh size is shown. A modified Newton algorithm is applied to solve the smoothing first order optimality system. Two-dimensional and three-dimensional numerical examples demonstrate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

A two-grid variational multiscale (VMS) method based on two local Gauss integrations for the convection dominated nonlinear convection diffusion equation is investigated. This method combines the two-grid strategy with the variational multiscale method which chooses polynomial bubble functions as subgrid scale. Two local Gauss integrations are applied to replace the projection operator without adding any extra storage. Moreover, the error estimates for the algorithms of the two-grid method are obtained. Numerical examples validate the theoretical results of the presented methods. [ABSTRACT FROM AUTHOR]

We develop a primal dual active set with continuation algorithm for solving the ℓ 0 -regularized least-squares problem that frequently arises in compressed sensing. The algorithm couples the primal dual active set method with a continuation strategy on the regularization parameter. At each inner iteration, it first identifies the active set from both primal and dual variables, and then updates the primal variable by solving a (typically small) least-squares problem defined on the active set, from which the dual variable can be updated explicitly. Under certain conditions on the sensing matrix, i.e., mutual incoherence property or restricted isometry property, and the noise level, a finite step global convergence of the overall algorithm is established. Extensive numerical examples are presented to illustrate the efficiency and accuracy of the algorithm and its convergence behavior. [ABSTRACT FROM AUTHOR]

• Highlights of revision of "PSNA: A pathwise semismooth Newton algorithm for sparse recovery with optimal local convergence and oracle properties" (SIGPRO-D-20-01795) • In this paper, we propose a pathwise semismooth Newton algorithm (PSNA) for sparse recovery in high-dimensional linear models. PSNA is derived from a formulation of the KKT conditions for Lasso and Enet based on Newton derivatives. It solves the semismooth KKT equations efficiently by actively and continuously seeking the support of the regression coefficients along the solution path with warm start. At each knot in the path, PSNA converges locally superlinearly for the Enet criterion and achieves the best possible convergence rate for the Lasso criterion, i.e., PSNA converges in just one step at the cost of two matrixvector multiplication per iteration. Under certain regularity conditions on the design matrix and the minimum magnitude of the nonzero elements of the target regression coefficients, we show that PSNA hits a solution with the same signs as the regression coefficients and achieves a sharp estimation error bound in finite steps with high probability. Extensive simulation studies support our theoretical results and indicate that PSNA is competitive with or outperforms state-of-the-art Lasso solvers in terms of efficiency and accuracy. • We thank the editor and reviewers for their thorough review of our manuscript and for your careful reading and constructive comments. We have revised our manuscript by incorporating all of your suggestions. Our point-by-point responses to the editor and reviewer comments are included in separate flles. We propose a pathwise semismooth Newton algorithm (PSNA) for sparse recovery in high-dimensional linear models. PSNA is derived from a formulation of the KKT conditions for Lasso and Enet based on Newton derivatives. It solves the semismooth KKT equations efficiently by actively and continuously seeking the support of the regression coefficients along the solution path with warm start. At each knot in the path, PSNA converges locally superlinearly for the Enet criterion and achieves the best possible convergence rate for the Lasso criterion, i.e., PSNA converges in just one step at the cost of two matrix-vector multiplication per iteration. Under certain regularity conditions on the design matrix and the minimum magnitude of the nonzero elements of the target regression coefficients, we show that PSNA hits a solution with the same signs as the regression coefficients and achieves a sharp estimation error bound in finite steps with high probability. Extensive simulation studies support our theoretical results and indicate that PSNA is competitive with or outperforms state-of-the-art Lasso solvers in terms of efficiency and accuracy. [ABSTRACT FROM AUTHOR]

In this article, theP2−P2-stabilized finite element method based on two local Gaussian quadratures is applied to discretize the Stokes eigenvalue problem, and the corresponding convergence analysis is given. Furthermore, a two-level scheme, which solves the Stokes eigenvalue problem on a coarser grid and a Stokes problem on the fine grid, is employed to reduce the computational cost. Numerical examples are given to confirm the theoretical results. [ABSTRACT FROM PUBLISHER]

We investigate an inverse problem of identifying a Robin coefficient with a sparse structure in the Laplace equation from noisy boundary measurements. The sparse structure of the Robin coefficient γ is understood as a small perturbation of a reference profile γ in the sense that their difference γ− γ has a small support. This problem is formulated as an optimal control problem with an L-regularization term. An iteratively reweighted least-squares algorithm with an inner semismooth Newton iteration is employed to solve the resulting optimization problem, and the convergence of the iteratively weighted least-squares algorithm is established. Numerical results for two-dimensional problems are presented to illustrate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

The success of compressed sensing relies essentially on the ability to efficiently find an approximately sparse solution to an under-determined linear system. In this paper, we developed an efficient algorithm for the sparsity promoting \ell^1-regularized least squares problem by coupling the primal dual active set strategy with a continuation technique (on the regularization parameter). In the active set strategy, we first determine the active set from primal and dual variables, and then update the primal and dual variables by solving a low-dimensional least square problem on the active set, which makes the algorithm very efficient. The continuation technique globalizes the convergence of the algorithm, with provable global convergence under restricted isometry property (RIP). Further, we adopt two alternative methods, i.e., a modified discrepancy principle and a Bayesian information criterion, to choose the regularization parameter automatically. Numerical experiments indicate that our algorithm is very competitive with state-of-the-art algorithms in terms of accuracy and efficiency, without a priori information about the regularization parameter. [ABSTRACT FROM AUTHOR]

We propose a fast Newton algorithm for ℓ 0 regularized high-dimensional generalized linear models based on support detection and root finding. We refer to the proposed method as GSDAR. GSDAR is developed based on the KKT conditions for ℓ 0 -penalized maximum likelihood estimators and generates a sequence of solutions of the KKT system iteratively. We show that GSDAR can be equivalently formulated as a generalized Newton algorithm. Under a restricted invertibility condition on the likelihood function and a sparsity condition on the regression coefficient, we establish an explicit upper bound on the estimation errors of the solution sequence generated by GSDAR in supremum norm and show that it achieves the optimal order in finite iterations with high probability. Moreover, we show that the oracle estimator can be recovered with high probability if the target signal is above the detectable level. These results directly concern the solution sequence generated from the GSDAR algorithm, instead of a theoretically defined global solution. We conduct simulations and real data analysis to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

We present a finite element analysis of electrical impedance tomography for reconstructing the conductivity distribution from electrode voltage measurements by means of Tikhonov regularization. Two popular choices of the penalty term, i.e., the H1(Ω)-norm smoothness penalty and total variation seminorm penalty, are considered. A piecewise linear finite element method is employed for discretizing the forward model, i.e., the complete electrode model, the conductivity, and the penalty functional. The convergence of the finite element approximations for the Tikhonov model on both polyhedral and smooth curved domains is established. This provides rigorous justifications for the ad hoc discretization procedures. Numerical experiments confirm the convergence analysis. [ABSTRACT FROM AUTHOR]

Accurate extracted ion chromatograms (XIC or EIC) is of great importance for Liquid chromatography - mass spectrometry (LC-MS) based quantitative proteomics. However, current preprocessing methods for XIC mainly focus on removing the peaks of low quality. Such operations are helpful for quantitation, but also contain two potential disadvantages: one is that some valuable information may be lost after the peak removal, and the other is that the retained peak lists are still contain noise. Both of the potential disadvantages may bias the final quantitative results. To solve these problems, we proposed an Alternating Direction Minimization (ADM) based denoising framework for XIC. This framework splits the observed XIC signal into baseline (background), noise and true signal, and the true signal is extracted for further analysis. The advantage of this framework is that the inner relationships over each XIC are considered, for which means that the XIC data is handled in a global way. Also, this framework is not sensitive to the noise type, so that it can be applied to wider applications. We adopted the framework for some sample data for quantitation. The quantitative results are employed to show the performance of XIC denoising. Experimental results confirm that the proposed method provides better and more reliable quantitations. • The noise over time inside the extracted ion chromatograms has been investigated. • A noise reduction method is proposed for such kind of noise. • This method considers the inner relationships of all scans in extracted ion chromatograms; it processes the data in a global way. [ABSTRACT FROM AUTHOR]