Conjugate gradient preconditioning methods with symmetric algebraic reconstruction technique in photoacoustic imaging

Photoacoustic imaging (PAI) is a fast-developing biomedical imaging technology suitable for noninvasive structural and functional imaging. Image reconstruction of PAI requires the solution of an inverse source problem, where the source represents the optical energy absorption distribution in the object. PAI in spherical or circular geometry gives good image resolution yet is slow in signal acquisition and image formation. Reducing the number of detection angles can ameliorate such issues. Besides, it is almost impossible to cover the entire surface of tissue. This will restrict it in the medical application with incomplete projection data. To resolve such limiting factors, in this thesis, a preconditioned conjugate gradient method is applied to the normal equations (PCCGNR method) for reconstructing the absorption distribution. Under the common assumption, a zero-mean Gaussian noise is added to the projection signals and a computer simulated has been used for the evaluation. This algorithm works well in rectification of the measurement and converges quickly onto an accurate estimate of the distribution of absolute absorption. It not only runs much faster than the FBP algorithm, but also shows stronger robustness in that it provides better image quality with detection data. We observed that diagonal preconditioners offer some improvement in convergence rate for image reconstruction, and reconstructed image preconditioning with ω=0 (diagonal scaling) is closer to the true image than with ω > 0. In addition, a physical experiment that will be done with our experiment equipment system further demonstrates the potential of the proposed algorithm in practical applications.