On the adjoint operator in photoacoustic tomography
On the adjoint operator in photoacoustic tomography
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DOI：
10.1088/0266-5611/32/11/115012
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发表时间：
2016-11-01
期刊：
影响因子：
2.1
通讯作者：
Treeby, Brad E.
中科院分区：
文献类型：
--
作者：
Arridge, Simon R.;Betcke, Marta M.;Treeby, Brad E.
光声层析成像(PAT)是从耦合物理技术发展而来的一种新兴的生物医学成像技术，它的成像对比度是由光吸收引起的，但信息是以超声脉冲的形式传递到组织表面的。在已有完整数据集的情况下，已经提出了许多重建PAT图像的算法和公式。然而，在许多实际成像场景中，不可能获得完整的数据，或者可能对数据进行二次采样以获得更快的数据采集。在这种情况下，需要能够结合先验知识来改善数据丢失的图像重建算法。因此，最近人们对使用变分图像重建的兴趣越来越大。应用这些技术的一个关键因素是PAT向前算子的伴随，本文将从物理、理论和数值角度对其进行描述。首先，给出了连续框架中PAT前向算子的伴随的一个简单的数学推导。然后，在变分PAT图像重建的背景下，描述了一种使用k-空间时间域波传播模型的伴随的有效的数值实现，包括二维和三维例子，包括非均匀声速。这种解析伴随相对于代数伴随(通过采用特定数值正演格式的直接伴随而获得)的主要优点是它可以使用目前可用的快速波传播解算器来实现。
Photoacoustic tomography (PAT) is an emerging biomedical imaging from coupled physics technique, in which the image contrast is due to optical absorption, but the information is carried to the surface of the tissue as ultrasound pulses. Many algorithms and formulae for PAT image reconstruction have been proposed for the case when a complete data set is available. In many practical imaging scenarios, however, it is not possible to obtain the full data, or the data may be sub-sampled for faster data acquisition. In such cases, image reconstruction algorithms that can incorporate prior knowledge to ameliorate the loss of data are required. Hence, recently there has been an increased interest in using variational image reconstruction. A crucial ingredient for the application of these techniques is the adjoint of the PAT forward operator, which is described in this article from physical, theoretical and numerical perspectives. First, a simple mathematical derivation of the adjoint of the PAT forward operator in the continuous framework is presented. Then, an efficient numerical implementation of the adjoint using a k-space time domain wave propagation model is described and illustrated in the context of variational PAT image reconstruction, on both 2D and 3D examples including inhomogeneous sound speed. The principal advantage of this analytical adjoint over an algebraic adjoint (obtained by taking the direct adjoint of the particular numerical forward scheme used) is that it can be implemented using currently available fast wave propagation solvers.