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1.
This paper considers a variational model for restoring images from blurry and speckled observations. This model utilizes the favorable properties of framelet regularization (e.g., the sparsity and multiresolution properties of the framelet) that are well suited for speckle noise reduction. For solving the model, we first propose an approximation model that is motivated by the well-known variable-splitting and penalty techniques in optimization. We then develop an alternating minimization algorithm to solve the approximation model. We also show that the sequence generated by the algorithm converges to the solution of the proposed model. The numerical results on simulated data and real utrasound images demonstrate that our approach outperforms several state-of-the-art algorithms.  相似文献   

2.
Motivated by the Cayley–Hamilton theorem, a novel adaptive procedure, called a Power Sparse Approximate Inverse (PSAI) procedure, is proposed that uses a different adaptive sparsity pattern selection approach to constructing a right preconditioner M for the large sparse linear system Ax=b. It determines the sparsity pattern of M dynamically and computes the n independent columns of M that is optimal in the Frobenius norm minimization, subject to the sparsity pattern of M. The PSAI procedure needs a matrix–vector product at each step and updates the solution of a small least squares problem cheaply. To control the sparsity of M and develop a practical PSAI algorithm, two dropping strategies are proposed. The PSAI algorithm can capture an effective approximate sparsity pattern of A?1 and compute a good sparse approximate inverse M efficiently. Numerical experiments are reported to verify the effectiveness of the PSAI algorithm. Numerical comparisons are made for the PSAI algorithm and the adaptive SPAI algorithm proposed by Grote and Huckle as well as for the PSAI algorithm and three static Sparse Approximate Inverse (SAI) algorithms. The results indicate that the PSAI algorithm is at least comparable to and can be much more effective than the adaptive SPAI algorithm and it often outperforms the static SAI algorithms very considerably and is more robust and practical than the static ones for general problems. Copyright © 2008 John Wiley & Sons, Ltd.  相似文献   

3.
Image recovery problems can be solved using optimization techniques. They lead often to the solution of either a large-scale convex quadratic program or equivalently a nondifferentiable minimization problem. To solve the quadratic program, we use an infeasible predictor-corrector interior-point method, presented in the more general framework of monotone LCP. The algorithm has polynomial complexity and it converges with asymptotic quadratic rate. When implementing the method to recover images, we take advantage of the underlying sparsity of the problem. We obtain good performances, that we assess by comparing the method with a variable-metric proximal bundle algorithm applied to the solution of equivalent nonsmooth problem.  相似文献   

4.
A method is presented to update a special finite element (FE) analytical model, based on matrix approximation theory with spectral constraint. At first, the model updating problem is treated as a matrix approximation problem dependent on the spectrum data from vibration test and modal parameter identification. The optimal approximation is the first modified solution of FE model. An algorithm is given to preserve the sparsity of the model by multiple correction. The convergence of the algorithm is investigated and perturbation of the modified solution is analyzed. Finally, a numerical example is provided to confirm the convergence of the algorithm and perturbation theory.  相似文献   

5.
We propose an iterative algorithm for the minimization of a ? 1-norm penalized least squares functional, under additional linear constraints. The algorithm is fully explicit: it uses only matrix multiplications with the three matrices present in the problem (in the linear constraint, in the data misfit part and in the penalty term of the functional). None of the three matrices must be invertible. Convergence is proven in a finite-dimensional setting. We apply the algorithm to a synthetic problem in magneto-encephalography where it is used for the reconstruction of divergence-free current densities subject to a sparsity promoting penalty on the wavelet coefficients of the current densities. We discuss the effects of imposing zero divergence and of imposing joint sparsity (of the vector components of the current density) on the current density reconstruction.  相似文献   

6.

In this study, we consider identification of parameters in a non-linear continuum-mechanical model of arteries by fitting the models response to clinical data. The fitting of the model is formulated as a constrained non-linear, non-convex least-squares minimization problem. The model parameters are directly related to the underlying physiology of arteries, and correctly identified they can be of great clinical value. The non-convexity of the minimization problem implies that incorrect parameter values, corresponding to local minima or stationary points may be found, however. Therefore, we investigate the feasibility of using a branch-and-bound algorithm to identify the parameters to global optimality. The algorithm is tested on three clinical data sets, in each case using four increasingly larger regions around a candidate global solution in the parameter space. In all cases, the candidate global solution is found already in the initialization phase when solving the original non-convex minimization problem from multiple starting points, and the remaining time is spent on increasing the lower bound on the optimal value. Although the branch-and-bound algorithm is parallelized, the overall procedure is in general very time-consuming.

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7.
We consider the problem of experimental design for linear ill-posed inverse problems. The minimization of the objective function in the classic A-optimal design is generalized to a Bayes risk minimization with a sparsity constraint. We present efficient algorithms for applications of such designs to large-scale problems. This is done by employing Krylov subspace methods for the solution of a subproblem required to obtain the experiment weights. The performance of the designs and algorithms is illustrated with a one-dimensional magnetotelluric example and an application to two-dimensional super-resolution reconstruction with MRI data.  相似文献   

8.
A computational arrangement of Gauss elimination is presented for solving sparse, nonsymmetric linear systems arising from partial differential equation problems. It is particularly targeted for use on distributed memory message passing multiprocessor computers and it is presented and analyzed in this context. The objective of the algorithm is to exploit the sparsity (i.e., reducing computation, communication, and memory requirements) and to optimize the data structure manipulation overhead. The algorithm is based on the nested dissection approach, which starts with a large set of very sparse, completely independent subsystems and progresses in stages to a single, nearly dense system at the last stage. The computational efforts of each stage are roughly equal (almost exactly equal for model problems), yet the data structures appropriate for the first and last stages are quite different. Thus we use different types of data structures and algorithm components at different stages of the solution. The new organization is a combination of previous techniques including nested dissection, implicit block factorization, domain decomposition, fan-in, fan-out, up-looking, down-looking, and dynamic data structures. © 1993 John Wiley & Sons, Inc.  相似文献   

9.
We present an alternating direction dual augmented Lagrangian method for solving semidefinite programming (SDP) problems in standard form. At each iteration, our basic algorithm minimizes the augmented Lagrangian function for the dual SDP problem sequentially, first with respect to the dual variables corresponding to the linear constraints, and then with respect to the dual slack variables, while in each minimization keeping the other variables fixed, and then finally it updates the Lagrange multipliers (i.e., primal variables). Convergence is proved by using a fixed-point argument. For SDPs with inequality constraints and positivity constraints, our algorithm is extended to separately minimize the dual augmented Lagrangian function over four sets of variables. Numerical results for frequency assignment, maximum stable set and binary integer quadratic programming problems demonstrate that our algorithms are robust and very efficient due to their ability or exploit special structures, such as sparsity and constraint orthogonality in these problems.  相似文献   

10.
Sorensen (Ref. 1) has proposed a class of algorithms for sparse unconstrained minimization where the sparsity pattern of the Cholesky factors of the Hessian is known. His updates at each iteration depend on the choice of a vector, and in Ref. 1 the question of choosing this vector is essentially left open. In this note, we propose a variational problem whose solution may be used to choose this vector. The major part of the computation of a solution to this variational problem is similar to the computation of a trust-region step in unconstrained minimization. Therefore, well-developed techniques available for the latter problem can be used to compute this vector and to perform the updating.This research was supported by NSF Grant DMS-8414460 and by DOE Grant DE-FG06-85ER25007, awarded to Washington State University, and by the Applied Mathematical Sciences Subprogram of the US Department of Energy under Contract W-31-109-Eng-38 while the first author was visiting the Mathematics and Computer Science Division of Argonne National Laboratory.  相似文献   

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