scholarly journals Fast and Robust Reconstruction for Fluorescence Molecular Tomography viaL1-2Regularization

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Haibo Zhang ◽  
Guohua Geng ◽  
Xiaodong Wang ◽  
Xuan Qu ◽  
Yuqing Hou ◽  
...  
Keyword(s):  
Simulated Data ◽  
Alternating Direction Method ◽  
Reconstruction Method ◽  
System Matrix ◽  
Fluorescence Molecular Tomography ◽  
Alternating Direction ◽  
Adaptive Penalty ◽  
Difference Of Convex ◽  
The Difference

Sparse reconstruction inspired by compressed sensing has attracted considerable attention in fluorescence molecular tomography (FMT). However, the columns of system matrix used for FMT reconstruction tend to be highly coherent, which meansL1minimization may not produce the sparsest solution. In this paper, we propose a novel reconstruction method by minimization of the difference ofL1andL2norms. To solve the nonconvexL1-2minimization problem, an iterative method based on the difference of convex algorithm (DCA) is presented. In each DCA iteration, the update of solution involves anL1minimization subproblem, which is solved by the alternating direction method of multipliers with an adaptive penalty. We investigated the performance of the proposed method with both simulated data andin vivoexperimental data. The results demonstrate that the DCA forL1-2minimization outperforms the representative algorithms forL1,L2,L1/2, andL0when the system matrix is highly coherent.

Fluorescence Molecular Tomography Using a Stochastic Variant of Alternating Direction Method of Multipliers

2017 ◽  
Vol 37 (7) ◽  
pp. 0717001
Author(s):  
侯榆青 Hou Yuqing ◽  
金明阳 Jin Mingyang ◽  
贺小伟 He Xiaowei ◽  
张 旭 Zhang Xu
Keyword(s):  
Alternating Direction Method ◽  
Method Of Multipliers ◽  
Fluorescence Molecular Tomography ◽  
Alternating Direction

Alternating Primal-Dual Algorithm for Minimizing Multiple-Summed Separable Problems with Application to Image Restoration

2020 ◽  
pp. 2154018
Author(s):  
Peng Wang ◽  
Shengwu Xiong
Keyword(s):  
Image Restoration ◽  
Alternating Direction Method ◽  
Dual Algorithm ◽  
Alternating Direction ◽  
Primal Dual ◽  
Separable Problems ◽  
The Difference ◽  
Primal Space ◽  
Speed And Accuracy ◽  
Better Than

In order to discover the difference among dual strategies, we propose an alternating primal-dual algorithm (APDA) that can be considered as a general version for minimizing problem which is multiple-summed separable convex but not necessarily smooth. First, the original multiple-summed problem is transformed into two subproblems. Second, one subproblem is solved in the primal space and the other is solved in the dual space. Finally, the alternating direction method is executed between the primal and the dual part. Furthermore, the classical alternating direction method of multipliers (ADMM) is extended to solve the primal subproblem which is also multiple summed, therefore, the extended ADMM can be seen as a parallel method for the original problem. Thanks to the flexibility of APDA, different dual strategies for image restoration are analyzed. Numerical experiments show that the proposed method performs better than some existing algorithms in terms of both speed and accuracy.

scholarly journals Compressed Sensing MRI Reconstruction Algorithm Based on Contourlet Transform and Alternating Direction Method

2015 ◽  
Vol 2015 ◽  
pp. 1-5
Author(s):  
Zhenyu Hu ◽  
Qiuye Wang ◽  
Congcong Ming ◽  
Lai Wang ◽  
Yuanqing Hu ◽  
...  
Keyword(s):  
Compressed Sensing ◽  
Computation Time ◽  
Reconstruction Algorithm ◽  
Alternating Direction Method ◽  
Contourlet Transform ◽  
Superior Performance ◽  
Reconstruction Method ◽  
Mr Images ◽  
Alternating Direction ◽  
Mri Reconstruction

Compressed sensing (CS) based methods have recently been used to reconstruct magnetic resonance (MR) images from undersampled measurements, which is known as CS-MRI. In traditional CS-MRI, wavelet transform can hardly capture the information of image curves and edges. In this paper, we present a new CS-MRI reconstruction algorithm based on contourlet transform and alternating direction method (ADM). The MR images are firstly represented by contourlet transform, which can describe the images’ curves and edges fully and accurately. Then the MR images are reconstructed by ADM, which is an effective CS reconstruction method. Numerical results validate the superior performance of the proposed algorithm in terms of reconstruction accuracy and computation time.

scholarly journals A Sparsity-Constrained Preconditioned Kaczmarz Reconstruction Method for Fluorescence Molecular Tomography

2016 ◽  
Vol 2016 ◽  
pp. 1-15
Author(s):  
Duofan Chen ◽  
Jimin Liang ◽  
Yao Li ◽  
Guanghui Qiu
Keyword(s):  
Low Cost ◽  
Biological Tissues ◽  
Reconstruction Method ◽  
Fluorescence Molecular Tomography ◽  
In Vivo Experiments ◽  
Fluorescent Markers ◽  
Ill Posed ◽  
Kaczmarz Method ◽  
Memory Efficient

Fluorescence molecular tomography (FMT) is an imaging technique that can localize and quantify fluorescent markers to resolve biological processes at molecular and cellular levels. Owing to a limited number of measurements and a large number of unknowns as well as the diffusive transport of photons in biological tissues, the inverse problem in FMT is usually highly ill-posed. In this work, a sparsity-constrained preconditioned Kaczmarz (SCP-Kaczmarz) method is proposed to reconstruct the fluorescent target for FMT. The SCP-Kaczmarz method uses the preconditioning strategy to minimize the correlation between the rows of the forward matrix and constrains the Kaczmarz iteration results to be sparse. Numerical simulation and phantom and in vivo experiments were performed to test the efficiency of the proposed method. The results demonstrate that both the convergence and accuracy of the proposed method are improved compared with the classical memory-efficient low-cost Kaczmarz method.

scholarly journals Normalized Born Approximation-Based Two-Stage Reconstruction Algorithm for Quantitative Fluorescence Molecular Tomography

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Huangjian Yi ◽  
Duofang Chen ◽  
Wei Li ◽  
Shuang Zhou ◽  
Miao Ning ◽  
...  
Keyword(s):  
Born Approximation ◽  
Small Animal Imaging ◽  
Small Animal ◽  
Reconstruction Algorithm ◽  
Reconstruction Technique ◽  
Reconstruction Method ◽  
Fluorescence Molecular Tomography ◽  
Two Stage ◽  
Quantitative Reconstruction

Fluorescence molecular tomography (FMT) is a promising technique forin vivosmall animal imaging. In this paper, a two-stage reconstruction method based on normalized Born approximation is developed for FMT, which includes two steps for quantitative reconstruction. First, the localization of fluorescent fluorophore is determined byl1-norm regularization method. Then, in the location region of fluorophore, which is provided by the first stage, algebraic reconstruction technique (ART) is utilized for the fluorophore concentration reconstruction. The validity of the two-stage quantitative reconstruction algorithm is testified by simulation experiments on a 3D digital mouse atlas and physical experiments on a phantom. The results suggest that we are able to recover the fluorophore location and concentration.

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