The Research On Photoacoustic Image Reconstruction Algorithm Based On Finite Element Method

As a new kind of nondestructive medical imaging technology, photoacoustic imaging attracted much attention recently. In this imaging modality, a laser is used as light source to excite the tissue and produce the photoacoustic signal. Upon detecting the photoacoustic signal, the photoacoustic image with regard to the optical absorption can be obtained with a proper reconstruction algorithm. The photoacoustic imaging technique not only owns the advantage of high contrast for optical imaging modalities but also owns the advantage of high resolution for ultrasound imaging ones. In this thesis, we focus on the study of reconstruction algorithms, the purpose of which is to accelerate the implementation of the reconstruction algorithms and to reduce the impact of the modeling error on the reconstruction results. The main work and contributions are as follows:Firstly, we derived the discretized version of the forward model of the photoacoustic imaging modality in the framework of the finite element method, based on which the inverse reconstruction scheme was presented based on the Marquardt- Tikhonov regularization strategy. In order to alleviate the problem of excessively intensive computational requirements resulted from the repeated computation of the matrix inversion, a novel matrix manipulation strategy was proposed for reducing the size of it. With this strategy, we can significantly speed up the inverse reconstruction process without any sacrifice of the reconstruction accuracy.Secondly, the modeling error of the diffusion approximation(DA) employed for describing the optical transportation in the quantitative photoacoustic tomography(QPAT) was studied. It was found that the DA model results in large approximation error especially in near field positions and also for the weak scattering media. Such error inevitably affects the reconstruction results significantly. To tackle such a problem, a novel method was proposed for compensating the modeling error of DA in the framework of Bayesian inference. Different from the traditional two-step reconstruction algorithm, our method can not only compensate the modeling error but also reconstruct the optical absorption coefficients directly from the photoacoustic measurements in only one step. Experimental results show that our one-step reconstruction algorithm can significantly improve the reconstructed results of the QPAT.