Shi Yan’s research while affiliated with Technical University of Denmark and other places

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Publications (4)


A fast method for simultaneous reconstruction and segmentation in X-ray CT application
  • Article

November 2021

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22 Reads

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2 Citations

Inverse Problems in Science and Engineering

Yiqiu Dong

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Chunlin Wu

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Shi Yan

In this paper, we propose a new method to solve the minimization problem in a simultaneous reconstruction and segmentation (SRS) model for X-ray computed tomography (CT). The SRS model uses Bayes' rule and the maximum a posteriori (MAP) estimate on the hidden Markov measure field model (HMMFM). The original method [Romanov M, Dahl AB, Dong Y, Hansen PC. Simultaneous tomographic reconstruction and segmentation with class priors. Inverse Problems Sci Eng. 2016;24(8):1432–1453] includes a subproblem with logarithmic-summation (log-sum) term, which is non-separable to the classification index. This subproblem was solved by Frank–Wolfe algorithm, which is very time consuming especially when dealing with large-scale CT problems. The starting point of this paper is the commutativity of log-sum operations, where the log-sum problem could be transformed into a sum-log problem by introducing an auxiliary variable. The corresponding sum-log problem for the SRS model is separable. By applying the primal-dual algorithm, the sum-log problem turns into several easy-to-solve convex subproblems. In addition, we introduce an improved model by adding Tikhonov regularization on the SRS model, and give some convergence results for the proposed methods. Experimental results demonstrate that the proposed methods produce comparable results compared with the original SRS method with much less CPU time.


GMM Based Simultaneous Reconstruction and Segmentation in X-Ray CT Application

April 2021

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4 Reads

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2 Citations

In this paper, we propose a new simultaneous reconstruction and segmentation (SRS) model in X-ray computed tomography (CT). The new SRS model is based on the Gaussian mixture model (GMM). In order to transform non-separable log-sum term in GMM into a form that can be easy solved, we introduce an auxiliary variable, which in fact plays a segmentation role. The new SRS model is much simpler comparing with the models derived from the hidden Markov measure field model (HMMFM). Numerical results show that the proposed model achieves improved results than other methods, and the CPU time is greatly reduced.


Comparison on a smooth phantom rec err seg err CPU Time (in second)
A fast method for simultaneous reconstruction and segmentation in X-ray CT application
  • Preprint
  • File available

January 2021

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29 Reads

In this paper, we propose a fast method for simultaneous reconstruction and segmentation (SRS) in X-ray computed tomography (CT). Our work is based on the SRS model where Bayes' rule and the maximum a posteriori (MAP) are used on hidden Markov measure field model (HMMFM). The original method leads to a logarithmic-summation (log-sum) term, which is non-separable to the classification index. The minimization problem in the model was solved by using constrained gradient descend method, Frank-Wolfe algorithm, which is very time-consuming especially when dealing with large-scale CT problems. The starting point of this paper is the commutativity of log-sum operations, where the log-sum problem could be transformed into a sum-log problem by introducing an auxiliary variable. The corresponding sum-log problem for the SRS model is separable. After applying alternating minimization method, this problem turns into several easy-to-solve convex sub-problems. In the paper, we also study an improved model by adding Tikhonov regularization, and give some convergence results. Experimental results demonstrate that the proposed algorithms could produce comparable results with the original SRS method with much less CPU time.

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The ℓ2, regularized group sparse optimization: Lower bound theory, recovery bound and algorithms

April 2020

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27 Reads

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14 Citations

Applied and Computational Harmonic Analysis

In this paper, we consider an unconstrained ℓ2,q minimization for group sparse signal recovery. For this nonconvex and non-Lipschitz problem, we mainly focus on its local minimizers. Firstly, a uniform lower bound for nonzero groups of the local minimizers is presented. Secondly, under group restricted isometry property (GRIP) assumptions, we provide a global recovery bound for points in a sublevel set of the objective function, as well as a local recovery bound for local minimizers. Thirdly, a sufficient condition for a stationary point to be a local minimizer is shown. Fourthly, inspired by the lower bound theory which indicates the sparsity of solutions, we propose a new efficient iteratively reweighted least square (IRLS) with thresholding algorithm, with nonexpansiveness of the group support set. Compared with the classical IRLS with smoothing algorithm, our algorithm performs better in both theoretical global convergence guarantee and numerical computation.

Citations (3)


... In order to suppress the noise and artifacts, regularization techniques based on image prior and deep learning (DL) methods are commonly used approaches in the literature nowadays. While deep learning methods have made significant advancements [3,17,18,24], variational methods based on image priors still play a reliable and crucial role in the practical applications of CT image reconstruction [19,21,33,53]. In this paper, we propose a segmentation-based method for CT image reconstruction, which can achieve image reconstruction and segmentation simultaneously. ...

Reference:

Superiorized iteration algorithm for CT image simultaneous reconstruction and segmentation
A fast method for simultaneous reconstruction and segmentation in X-ray CT application
  • Citing Article
  • November 2021

Inverse Problems in Science and Engineering

... In detail, the outlined identification strategy takes advantages of the flexibility and efficient modeling capabilities characterizing the Gaussian Mixture Models (GMMs). These statistical tools, indeed, allow to approximate any given probability density with high accuracy [11]; and, for this reason, they are exploited in a large variety of applications ranging from path planning [12] to object tracking [13], from image modeling and segmentation [14] to speech understanding [15]. Coping with the SM identification problem, a GMM is adopted for describing the VSN collected data, thus leading to the design of a learning based strategy, which involves the presence of an auto-encoder (AE) to deal with the emergence of possible dimensionality issues. ...

GMM Based Simultaneous Reconstruction and Segmentation in X-Ray CT Application
  • Citing Chapter
  • April 2021

... Under some group restricted eigenvalue conditions, the global and local recovery bounds for (1) were developed in [15]. Later, a general lower recovery bound for (1) with p = 2 was established in [19]. Recently, ℓ 1,0 -norm regularized optimization was built for multivariate regression [20]. ...

The ℓ2, regularized group sparse optimization: Lower bound theory, recovery bound and algorithms
  • Citing Article
  • April 2020

Applied and Computational Harmonic Analysis