A continuous adjoint for photo-acoustic tomography of the brain
A continuous adjoint for photo-acoustic tomography of the brain
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DOI：
10.1088/1361-6420/aac530
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发表时间：
2018-08-01
期刊：
影响因子：
2.1
通讯作者：
Holman, Sean
中科院分区：
文献类型：
--
作者：
Javaherian, Ashkan;Holman, Sean
我们提出了一个基于耦合方程系统的大脑光声断层扫描优化框架，该系统描述了声波在线性各向同性非均匀和有损耗弹性介质中的传播，具有吸收和物理色散，遵循频率幂律，使用分数阶拉普拉斯算子。导出了相关连续正演算子的伴随算子，并给出了基于k空间伪谱法计算伴随算子的数值框架。我们解析地证明了所导出的连续伴随与相关的离散正算子的伴随相匹配。我们在一阶正约束优化算法中包含这个伴随，该算法通过总变差最小化进行正则化，并表明迭代单调收敛于目标函数的最小值，即使在估计介质的物理参数时存在一些误差。
We present an optimisation framework for photo-acoustic tomography of the brain based on a system of coupled equations that describe the propagation of sound waves in linear isotropic inhomogeneous and lossy elastic media with absorption and physical dispersion following a frequency power law using fractional Laplacian operators. The adjoint of the associated continuous forward operator is derived, and a numerical framework for computing this adjoint based on a k-space pseudo-spectral method is presented. We analytically show that the derived continuous adjoint matches the adjoint of an associated discretised forward operator. We include this adjoint in a first-order positivity constrained optimisation algorithm that is regularised by total variation minimisation, and show that the iterates monotonically converge to a minimiser of an objective function, even in the presence of some error in estimating the physical parameters of the medium.