The alternating direction method of multipliers （ADMM for short） is efficient for linearly constrained convex optimization problem. The practicM computationM cost of ADMM depends on the sub-problem solvers. The prox...The alternating direction method of multipliers （ADMM for short） is efficient for linearly constrained convex optimization problem. The practicM computationM cost of ADMM depends on the sub-problem solvers. The proximal point algorithm is a common sub-problem-solver. However, the proximal parameter is sensitive in the proximM ADMM. In this paper, we propose a homotopy-based proximal linearized ADMM, in which a homotopy method is used to soNe the sub-problems at each iteration. Under some suitable conditions, the global convergence and the convergence rate of O（1/k） in the worst case of the proposed method are proven. Some preliminary numerical results indicate the validity of the proposed method.展开更多
为了实现快速成像,磁共振指纹(Magnetic Resonance Fingerprinting,MRF)技术通常使用非笛卡尔稀疏采样模板对K空间进行高度欠采样,从而获得稀疏K空间信号.然而,从稀疏的K空间信号重建像空间数据是一个病态不适定问题,重建出的MRF像空间...为了实现快速成像,磁共振指纹(Magnetic Resonance Fingerprinting,MRF)技术通常使用非笛卡尔稀疏采样模板对K空间进行高度欠采样,从而获得稀疏K空间信号.然而,从稀疏的K空间信号重建像空间数据是一个病态不适定问题,重建出的MRF像空间数据存在大量的混叠伪影,直接影响到组织生理参数的重建准确度.为此需要将各种先验知识引入重建模型之中,以缓解MRF重建问题的不适定性.针对上述问题,本文提出一种融合局部低秩先验与Bloch流形约束的MRF重建模型,并使用交替方向乘子法(Alternating Direction Method of Multipliers,ADMM)求解模型中的非凸MRF重建问题.本文算法在引入MRF像空间数据的局部低秩先验的同时,使用预先构建的字典为重建指纹提供流形约束.一方面通过空域局部低秩约束有效抑制混叠伪影的产生,另一方面利用字典先验避免指纹的时域流形特征在迭代重建过程中丢失.仿真实验结果表明,相较于引入了全局低秩先验与Bloch流形约束的其他同类算法,本文算法可以提供更高的组织参数重建准确度.展开更多
A practical image reconstruction method for multi-source quantitative photoacoustic tomography （QPAT） is proposed in this work with the consideration of detector response function and limited-view scanning. First, t...A practical image reconstruction method for multi-source quantitative photoacoustic tomography （QPAT） is proposed in this work with the consideration of detector response function and limited-view scanning. First, the correct detector response function, i.e., spa- tim impulse response （SIR） and acousto-electric impulse response （EIR）, is considered for the ultrasonic transducer to accurately model the acoustic measurement; second, acoustic data is only measured near optical sources with meaningful signal-to-noise ratio （SNR）, i.e., the limited-view scanning, which also reduces the data acquisition time for point trans- ducer. However, due to the incomplete limited-view data, a two-step image reconstruction method （i.e., to first reconstruct initial acoustic pressure and then reconstruct optical coef- ficients） no longer applies, since it is neither possible nor necessary to robustly reconstruct initial acoustic pressure with limited-view data. Therefore, here we propose a direct image reconstruction method that incorporates SIR, EIR and limited-view scanning in a coupled opto-acoustic forward model, regularizes the framelet sparsity, and then solves the QPAT alternating direction method of multipliers. nonlinear QPAT data fidelity with tensor problem with Quasi-Newton method based展开更多
基金supported by the National Natural Science Foundation of China(11571074,61170308)the Natural Science Foundation of Fujian Province(2015J01010)the Major Science Foundation of Fujian Provincial Department of Education(JA14037)
文摘The alternating direction method of multipliers （ADMM for short） is efficient for linearly constrained convex optimization problem. The practicM computationM cost of ADMM depends on the sub-problem solvers. The proximal point algorithm is a common sub-problem-solver. However, the proximal parameter is sensitive in the proximM ADMM. In this paper, we propose a homotopy-based proximal linearized ADMM, in which a homotopy method is used to soNe the sub-problems at each iteration. Under some suitable conditions, the global convergence and the convergence rate of O（1/k） in the worst case of the proposed method are proven. Some preliminary numerical results indicate the validity of the proposed method.
文摘为了实现快速成像,磁共振指纹(Magnetic Resonance Fingerprinting,MRF)技术通常使用非笛卡尔稀疏采样模板对K空间进行高度欠采样,从而获得稀疏K空间信号.然而,从稀疏的K空间信号重建像空间数据是一个病态不适定问题,重建出的MRF像空间数据存在大量的混叠伪影,直接影响到组织生理参数的重建准确度.为此需要将各种先验知识引入重建模型之中,以缓解MRF重建问题的不适定性.针对上述问题,本文提出一种融合局部低秩先验与Bloch流形约束的MRF重建模型,并使用交替方向乘子法(Alternating Direction Method of Multipliers,ADMM)求解模型中的非凸MRF重建问题.本文算法在引入MRF像空间数据的局部低秩先验的同时,使用预先构建的字典为重建指纹提供流形约束.一方面通过空域局部低秩约束有效抑制混叠伪影的产生,另一方面利用字典先验避免指纹的时域流形特征在迭代重建过程中丢失.仿真实验结果表明,相较于引入了全局低秩先验与Bloch流形约束的其他同类算法,本文算法可以提供更高的组织参数重建准确度.
文摘A practical image reconstruction method for multi-source quantitative photoacoustic tomography （QPAT） is proposed in this work with the consideration of detector response function and limited-view scanning. First, the correct detector response function, i.e., spa- tim impulse response （SIR） and acousto-electric impulse response （EIR）, is considered for the ultrasonic transducer to accurately model the acoustic measurement; second, acoustic data is only measured near optical sources with meaningful signal-to-noise ratio （SNR）, i.e., the limited-view scanning, which also reduces the data acquisition time for point trans- ducer. However, due to the incomplete limited-view data, a two-step image reconstruction method （i.e., to first reconstruct initial acoustic pressure and then reconstruct optical coef- ficients） no longer applies, since it is neither possible nor necessary to robustly reconstruct initial acoustic pressure with limited-view data. Therefore, here we propose a direct image reconstruction method that incorporates SIR, EIR and limited-view scanning in a coupled opto-acoustic forward model, regularizes the framelet sparsity, and then solves the QPAT alternating direction method of multipliers. nonlinear QPAT data fidelity with tensor problem with Quasi-Newton method based
