脑部光电探测的连续伴随算子
A continuous adjoint for photo-acoustic tomography of the brain
AI总结：
本文提出基于耦合方程组的脑部光电探测优化框架，利用分数拉普拉斯算子描述声波传播，推导连续伴随算子并构建数值计算方法，证明其与离散算子伴随一致，结合正则化算法实现介质参数估计的鲁棒性。
摘要：
我们提出一个基于耦合方程组的优化框架，用于脑部光电探测，该方程组描述了线性各向同性非均匀且耗散的弹性介质中声波的传播，其中吸收和物理色散遵循频率幂律，并使用分数拉普拉斯算子。推导了所关联的连续正向算子的伴随算子，并展示了一个基于k空间伪谱方法计算该伴随算子的数值框架。我们分析证明所推导的连续伴随算子与关联离散算子的伴随算子一致。我们将该伴随算子纳入一个一阶正性约束优化算法中，该算法通过总变差最小化进行正则化，并证明即使在介质参数估计存在误差的情况下，迭代序列也单调收敛于目标函数的极小值。
英文摘要：
We present an optimization framework for photo-acoustic tomography of brain based on a system of coupled equations that describe the propagation of sound waves in linear isotropic inhomogeneous and lossy elastic media with the 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 pseudospectral method is presented. We analytically show that the derived continuous adjoint matches the adjoint of an associated discretised operator. We include this adjoint in a first-order positivity constrained optimization algorithm that is regularized by total variation minimization, and show that the iterates monotonically converge to a minimizer of an objective function, even in the presence of some error in estimating the physical parameters of the medium.
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