Computational Compensation for Model Imperfections in Photoacoustic Computed Tomography

Citation

Hu, Peng (2023) Computational Compensation for Model Imperfections in Photoacoustic Computed Tomography. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/6hdm-ar41. https://resolver.caltech.edu/CaltechTHESIS:06022023-051815823

Abstract

Photoacoustic computed tomography (PACT) images biological tissues’ optical absorption through detection of photon-absorption-induced ultrasonic waves. Various systems have been proposed for PACT and they are described by different mathematical models to reconstruct from detected ultrasonic signals the photon-absorption-induced initial pressure, the main contrast in PACT. Accurate image reconstruction has high requirements for the system and the mathematical model, which is often imperfect in practice due to multiple factors, e.g., limited transducer bandwidth, finite transducer element size, sparse spatial sampling, partial-view detection, and tissue motion. The focus of this dissertation is on using computational methods to compensate for these model imperfections.

First, for a human breast imaging system based on a full-ring transducer array, we incorporate the limited transducer bandwidth into the model for spatiotemporal analysis to clarify the aliasing due to sparse spatial sampling and propose (1) two methods (radius-dependent spatiotemporal antialiasing and location-dependent spatiotemporal antialiasing) to mitigate these artifacts. Second, for an isotropic-resolution 3D PACT system formed by four arc arrays, we consider both the limited transducer bandwidth and the finite transducer element size and (2) compress the system matrix through singular value decomposition and fast Fourier transform for its efficient explicit expression. Enabled by this expression, we then propose (3) fast sparsely sampling functional imaging by incorporating a densely sampled prior image into the system matrix, which maintains the critical linearity while mitigating artifacts, and (4) intra-image nonrigid motion correction by incorporating the motion as subdomain translations into the system matrix and reconstructing the translations together with the image iteratively. Finally, for a single-shot 3D PACT system based on a single ultrasonic transducer, we propose (5) a fast implementation of the forward model by connecting traditional PACT with virtual detector responses through fast Fourier transform, and we iteratively reconstruct the image from signals with extremely compressed sensing and partial-view detection.

All these proposed methods enable image reconstruction or significantly improve image quality in numerical simulations, phantom experiments, and in vivo experiments. Although they are demonstrated only for certain PACT systems, they are directly applicable to other systems and can be extended to other tomographic imaging modalities such as X-ray computed tomography (X-ray CT) and magnetic resonance imaging (MRI).

Thesis Files