The development of fast and accurate image reconstruction algorithms is a central aspect of computed tomography. In this paper we address this issue for photoacoustic computed tomography in circular geometry. We investigate the Galerkin least squares method for that purpose. For approximating the function to be recovered we use subspaces of translation invariant spaces generated by a single Funktion. This includes many systems that have previously been employed in PAT such as generalized Kaiser-Bessel basis functions or the natural pixel basis. By exploiting an isometry property of the forward problem we are able to efficiently set up the Galerkin equation for a wide class of generating functions and Devise efficient algorithms for its solution. We establish a convergence analysis and present numerical simulations that demonstrate the efficiency and accuracy of the derived algorithm.
Performing a large number of spatial measurements enables high-resolution photoacoustic imaging without specific prior information. However, the acquisition of spatial measurements is time-consuming, costly, and technically challenging. By exploiting nonlinear prior information, compressed sensing techniques in combination with sophisticated reconstruction algorithms allow reducing the number of measurements while maintaining high spatial resolution. To this end, in this work we propose a multiscale factorization for the wave equation that decomposes the measured data into a low-frequency fact…
Photoacoustic tomography (PAT) is a hybrid imaging modality that intends to construct high-resolution images of optical properties of heterogeneous media from measured acoustic data generated by the photoacoustic effect. To date, most of the model-based quantitative image reconstructions in PAT are performed with either the radiative transport equation or its classical diffusion approximation as the model of light propagation. In this work, we study quantitative image reconstructions in PAT using the simplified $P_2$ equations as the light propagation model. We provide numerical evidences on t…
The majority of the solvers for the acoustic problem in Photoacoustic Tomography (PAT) rely on full solution of the wave equation which makes them less suitable for real-time and dynamic applications where only partial data is available. This is in contrast to other tomographic modalities, e.g. X-ray tomography, where partial data implies partial cost for the application of the forward and adjoint operators. In this work we present a novel solver for the forward and adjoint wave equations for the acoustic problem in PAT. We term the proposed solver Hamilton-Green as it approximates the fundame…
University of Vienna（维也纳大学）；Christian Doppler Laboratory for Mathematical Modeling and Simulation of Next Generations of Ultrasound Devices (MaMSi)（下一代超声设备数学建模与模拟克里斯蒂安·多普勒实验室）；Johann Radon Institute for Computational and Applied Mathematics (RICAM)（约翰·拉登计算与应用数学研究所）；Medical University of Vienna（维也纳医科大学）
In this article, we are concerned with a nonlinear inverse problem with a forward operator involving an unknown function. The problem arises in diverse applications and is challenging in the presence of an unknown function, which makes it ill-posed. Additionally, the nonlinear nature of the problem makes it difficult to use traditional methods, and thus, the study addresses a simplified version of the problem by either linearizing it or assuming knowledge of the unknown function. Here, we propose self-supervised learning to directly tackle a nonlinear inverse problem involving an unknown funct…
Photoacoustic computed tomography (PACT), also known as optoacoustic tomography, is an emerging imaging technique that holds great promise for biomedical imaging. PACT is a hybrid imaging method that can exploit the strong endogenous contrast of optical methods along with the high spatial resolution of ultrasound methods. In its canonical form that is addressed in this article, PACT seeks to estimate the photoacoustically-induced initial pressure distribution within the object. Image reconstruction methods are employed to solve the acoustic inverse problem associated with the image formation p…
Photoacoustic tomography (PAT) is an emerging imaging modality that aims at measuring the high-contrast optical properties of tissues by means of high-resolution ultrasonic measurements. The interaction between these two types of waves is based on the thermoacoustic effect. In recent years, many works have investigated the applicability of compressed sensing to PAT, in order to reduce measuring times while maintaining a high reconstruction quality. However, in most cases, theoretical guarantees are missing. In this work, we show that in many measurement setups of practical interest, compressed…
A New Sparsification and Reconstruction Strategy for Compressed Sensing Photoacoustic Tomography
Christian Doppler Laboratory for Photoacoustic Imaging and Laser Ultrasonics（光声成像和激光超声学 Christian Doppler 实验室）；Research Center for Non-Destructive Testing (RECENDT)（无损检测研究中心 (RECENDT)）；Department of Mathematics, University of Idaho（爱达荷大学数学系）
A Novel Compressed Sensing Scheme for Photoacoustic Tomography
University of Innsbruck（因斯布鲁克大学）；University of Göttingen（哥廷根大学）；Christian Doppler Laboratory for Photoacoustic Imaging and Laser Ultrasonics（光声成像与激光超声克劳斯·多普勒实验室）；Research Center for Non-Destructive Testing (RECENDT)（无损检测研究中心）
3D Uncertainty Quantification for Photoacoustic Tomography
University of Oulu（奥卢大学）；King Fahd University of Petroleum and Minerals（法赫德国王石油与矿产大学）；Technical University of Denmark（丹麦技术大学）；University of Eastern Finland（芬兰东部大学）
Fast algorithms enabling optimization and deep learning for photoacoustic tomography in a circular detection geometry
Research Unit of Mathematical Sciences, University of Oulu（奥卢大学数学科学研究所）；Department of Computer Science, University College London（伦敦大学学院计算机科学系）；Department of Mathematics, University of Arizona（亚利桑那大学数学系）；Department of Technical Physics, University of Eastern Finland（东部芬兰大学技术物理系）
