Novel Regularized Image Reconstruction Methods for Sparse Photoacoustic Tomography

Abstract

Among all tissue imaging modalities, photo-acoustic tomography (PAT), has been getting increasing attention in the recent past due to the fact that it has high contrast, high penetrability, and has capability of retrieving high resolution. By using the combination of optical absorption and acoustic wave propagation, PAT has been able to image tissues at a relatively large depths with high resolution compared to purely optical modalities. Upon shining with a laser pulse, the substance under investigation absorbs optical energy and undergoes thermoelastic expansion; as a result, the spatial distribution of the concentration of the substance gets translated into the distribution of pressure-rise. This initial pressure rise travels outwards as ultrasound waves which are collected by ultrasound transducers placed at the boundary. From the ultrasound signal measured by the transducers as a function of time, a PAT reconstruction method recovers an estimate of the initial pressure-rise by solving the associated inverse problem. The inverse problem is however challenging. It is challenging because the image has to be recovered for the entire cross-sectional plane, whereas the samples of the acoustic pressure are available only from the points lying in the periphery of the imaging specimen where the transducers are located. In this thesis, we make contributions in two widely used types of reconstructions methods known as the time-reversal method, and the model based method. We summarize our contributions in three parts in the following. In the first part, we develop an improved model based method. Model-based reconstruction methods in PAT express the measured pressure samples as a linear transformation on the initial pressure-rise and perform a regularized reconstruction. Model based methods yield superior image quality even in the situation where measured data size is small. We propose a model-based image reconstruction method for PAT involving a novel form of regularization and demonstrate its ability to recover...