Research On Photoacoustic Images Resolution Enhancement Using Sparse Optimization Based Reconstruction Method

Photoacoustic imaging(PAI) technique can provide accurate structure imaging and functional imaging for biological tissue in noninvasive ways. Recently, they have attracted great attention due to their virtues of high-contrast and high penetrability. PAI can be applied to early detection of tumour, functional brain imaging, angiography, etc.Typically, high-resolution photoacoustic images require full-view measurements from a number of ultrasonic transducers, which is challenging due to fast imaging, data storage and hardware requirements. Therefore, how to reconstruct high-resolution images from limited measurements under present implementation constraints is a critical problem, both theoretically and practically. This dissertation aims at utilizing limited measurements to obtain high-resolution photoacoustic images by leveraging sparse optimization methods.The main contributions and results of this dissertation can be summarized as follows:Edge expander based non-uniform sparse sampling and sparse signal reconstruction methods are proposed. Based on the assumption that the number of measurements should be prioritized by the importance of the components, I came up with an edge expander based model to simulate the non-uniform sampling process. The compressive measurements obtained from the non-uniform sparse sampling pattern are proved to be almost complete in theory. Moreover, matching reconstruction algorithms have also been proposed based on the characteristics of edge expanders. Simulation results from Gaussian random sparse signals with perceived support set demonstrate that non-uniform sparse sampling pattern with specifically designed algorithms can reconstruct the original signals quickly and effectively.The limited-view photoacoustic tomography(PAT) is studied. Limited-view problem is a common phenomenon in PAT, I propose to use an optical mask to realize multiple modulations of acoustic sources(from traditional multiple detectors and a single image source to few detectors but multiple modulations of image sources). Thus, one can obtain su?cient measurements from limited views. Moreover, the non-uniform sampling mask codes are designed by leveraging edge expanders, which can guarantee more completed acquisition. The proposed sampling pattern and sparsity regularization based algorithm have been validated by the vessel and breast cancer phantom studies, and is expected to promote the development of limited-view PAT.A directional total variation(DTV) based super-resolution(SR) method is studied.I propose to explore the high-level structure and to protect the edge reconstruction for the images with significant directional information by using DTV simultaneously, and an alternating direction method of multiplier(ADMM) based sparse optimization algorithm is also presented to solve the derived problem. I adopt Peak Signal to Noise Ratio(PSNR)and Structural Similarity(SSIM) for the objective evaluation. Results from images with some structured edge based simulations show the proposed method is an effective and simple SR method for texture images.A second-order directional total generalized variation(DTGV) based SR method for Photoacoustic Microscopy(PAM) images is studied. With the fact that many PAM images such as vessel images have significant directional information, I propose to use second-order DTGV to describe the higher-level underlying information based on firstorder DTV, and to remove the jagged artifacts produced by first-order DTV. I also present an ADMM based algorithm to solve the optimization problem. The novel results from vessel phantom, actual graphite image and thin bar copper image studies demonstrate the effectiveness of the proposed method to obtain the high-resolution PAM images.