This paper proposes an approach to measure the credibility of solutions of inverse problems with incomplete or missing data, encountered in some physical problems. In such problems, the same set of data can produce multiple solutions, depending on the constraints or assumptions used to compensate for the missing information. The actual “true” solution, against which the quality of a constrained solution can be measured, is not usually available. In this work, we propose to obtain a complete but coarse reference solution that reliably possesses attributes of the actual solution. This is done by solving an over-complete problem with the same set of data but with a coarser structure. A number of residual, composition and fidelity metrics are then used to quantitatively measure the quality of a solution obtained from incomplete data, against the coarse complete reference. The approach was tested with various degrees of incompleteness and different levels of uncertainty (noise) in data in the linear problem of image reconstruction in computed-tomography. The results show that the approach was successful in identifying credible solutions, as well as those that were not trustworthy.

Assessing the credibility of the solutions of incomplete-data inverse problems

The main objective of this paper is to provide a state-of-the-art review, analyze and discuss stochastic local search techniques used for solving hard combinatorial problems. It begins with a short introduction, motivation and some basic notation on combinatorial problems, search paradigms and other relevant features of searching techniques as needed for background. In the following a brief overview of the stochastic local search methods along with an analysis of the state-of-the-art stochastic local search algorithms is given. Finally, the last part of the paper present and discuss some of the most latest trends in application of stochastic local search algorithms in machine learning, data mining and some other areas of science and engineering. We conclude with a discussion on capabilities and limitations of stochastic local search algorithms.

/pdf/stochastic-local-search-a-state-of-the-art-review-53i0ew3yc2.pdf

Stochastic local search: a state-of-the-art review

The invention discloses a finite angle CT reconstruction method based on anisotropic total variation. According to the method, through an image reconstruction model using low-dose and sparse-view-angle CT images, a fast iterative reconstruction algorithm is combined with an anisotropic total variation method. The problems that in an existing finite angle CT reconstruction method, part of areas arefuzzy, the convergence speed is low, and accurate solving cannot be achieved are effectively solved. A slope filter in a filtering back projection reconstruction algorithm is introduced to preprocessan iterative equation in the solving process of a model, thereby solving the iterative equation by using an alternating projection approach method, and repeatedly iterating until a termination condition is met; Compared with an experiment of an existing reconstruction method, the method has the advantage that a good reconstruction effect can be achieved.

A finite angle CT reconstruction algorithm based on anisotropic total variation

The invention relates to a tomography image reconstruction method for an angle limitation and sparse sampling condition. The method comprises the following steps of: constructing an optimized objective function consisting of a projection error, an image first-order gradient and an L1 norm of an image gray scale on the basis of image non-zero pixel sparsity, image continuity and pixel gray scale non-negative constraints, and proposing a nonlinear tomography model; converting a nonlinear tomography reconstruction problem into an equivalent linear programming problem, and establishing a tomography model based on linear programming; and solving the linear programming problem by adopting a dual interior point method to obtain a tomographic reconstructed image. By means of the method, the problems of edge blurring, image deformation and the like of the reconstructed image caused by limited sampling angles and sparse sampling views can be solved, the high-quality tomographic reconstructed image is obtained, and the method has wide application prospects.

Tomography image reconstruction method for angle limitation and sparse sampling condition

The invention discloses a CT sparse projection image reconstruction method and a CT sparse projection image reconstruction device at a limited sampling angle. The method comprises the steps of obtaining a pseudo-inverse matrix of a projection equation according to projection data, generating a random solution set according to the pseudo-inverse matrix, reserving or replacing each solution in the current random solution set correspondingly, selecting an optimal solution from the current random solution set when the number of iterations reaches a preset maximum value, and adopting the selected optimal solution as a to-be-obtained reconstruction result. The device comprises a memory for storing at least one program and a processor for loading at least one program to execute the method of theinvention. According to the method, the pseudo-inverse of a discretized projection reconstruction equation is used as an initial solution of the algorithm, so that the quality of the initial solutionis guaranteed. A set of solutions are generated through random walk, and then the iterative optimization is carried out respectively. The diversity of optimization paths is guaranteed. Troubles causedby the defects of an initial solution and an iteration path of a traditional reconstruction method can be overcome. The method and the device are applied to the technical field of image processing.

CT sparse projection image reconstruction method and CT sparse projection image reconstruction device at limited sampling angle

Subject to data acquisition time, X-ray dose and geometric position of medical tomography system, only limited-angle or sparse projection data can be collected in many applications of medical computed tomography (CT). Lacking in completeness and symmetry of limited-angle sparse projection data leads to a huge search space for reconstruction algorithms. The conventional convex optimization methods typically suffer from poor convergence and unwanted local optima caused by the data insufficiency and the fixed descent path of iteration. To improve the reconstruction quality, a stochastic iterative evolution CT reconstruction algorithm is proposed, in which a population of solutions based on stochastic strategy is adopted to enhance the global search capability and the search direction is generated by combining gradient descent with fitness evaluation of stochastic population. Meanwhile, Markov Chain is introduced to predict the iterative evolution model and accelerate the proposed algorithm's convergence. Experiments results demonstrate the proposed algorithm's effectiveness and robustness in image reconstruction from limited-angle sparse projection data.

A stochastic iterative evolution CT reconstruction algorithm for limited-angle sparse projection data

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CT sparse projection image reconstruction method and CT sparse projection image reconstruction device at limited sampling angle

A stochastic iterative evolution CT reconstruction algorithm for limited-angle sparse projection data