Graphics processing unit accelerating compressed sensing photoacoustic computed tomography with total variation

Photoacoustic computed tomography with compressed sensing (CS-PACT) is a commonly used imaging strategy for sparse-sampling PACT. However, it is very time-consuming because of the iterative process involved in the image reconstruction. In this paper, we present a graphics processing unit (GPU)-based parallel computation framework for total-variation-based CS-PACT and adapted into a custom-made PACT system. Specifically, five compute-intensive operators are extracted from the iteration algorithm and are redesigned for parallel performance on a GPU. We achieved an image reconstruction speed 24–31 times faster than the CPU performance. We performed in vivo experiments on human hands to verify the feasibility of our developed method

A Multi-Grid Iterative Method for Photoacoustic Tomography

Inspired by the recent advances on minimizing nonsmooth or bound-constrained convex functions on models using varying degrees of fidelity, we propose a line search multigrid (MG) method for full-wave iterative image reconstruction in photoacoustic tomography (PAT) in heterogeneous media. To compute the search direction at each iteration, we decide between the gradient at the target level, or alternatively an approximate error correction at a coarser level, relying on some predefined criteria. To incorporate absorption and dispersion, we derive the analytical adjoint directly from the first-order acoustic wave system. The effectiveness of the proposed method is tested on a total-variation penalized Iterative Shrinkage Thresholding algorithm (ISTA) and its accelerated variant (FISTA), which have been used in many studies of image reconstruction in PAT. The results show the great potential of the proposed method in improving speed of iterative image reconstruction

Diluted maximum-likelihood algorithm for quantum tomography

We propose a refined iterative likelihood-maximization algorithm for reconstructing a quantum state from a set of tomographic measurements. The algorithm is characterized by a very high convergence rate and features a simple adaptive procedure that ensures likelihood increase in every iteration and convergence to the maximum-likelihood state. We apply the algorithm to homodyne tomography of optical states and quantum tomography of entangled spin states of trapped ions and investigate its convergence properties.Comment: v2: Convergence proof adde

On Iterative Algorithms for Quantitative Photoacoustic Tomography in the Radiative Transport Regime

In this paper, we describe the numerical reconstruction method for quantitative photoacoustic tomography (QPAT) based on the radiative transfer equation (RTE), which models light propagation more accurately than diffusion approximation (DA). We investigate the reconstruction of absorption coefficient and/or scattering coefficient of biological tissues. Given the scattering coefficient, an improved fixed-point iterative method is proposed to retrieve the absorption coefficient for its cheap computational cost. And we prove the convergence. To retrieve two coefficients simultaneously, Barzilai-Borwein (BB) method is applied. Since the reconstruction of optical coefficients involves the solution of original and adjoint RTEs in the framework of optimization, an efficient solver with high accuracy is improved from~\cite{Gao}. Simulation experiments illustrate that the improved fixed-point iterative method and the BB method are the comparative methods for QPAT in two cases.Comment: 21 pages, 44 figure

Maximum-likelihood coherent-state quantum process tomography

Coherent-state quantum process tomography (csQPT) is a method of completely characterizing a quantum-optical "black box" by probing it with coherent states and performing homodyne measurements on the output [M. Lobino et al, Science 322, 563 (2008)]. We present a technique for csQPT that is fully based on statistical inference, specifically, quantum expectation-maximization. The method relies on the Jamiolkowski isomorphism and iteratively reconstructs the process tensor in the Fock basis directly from the experimental data. This approach permits incorporation of a priori constraints into the reconstruction procedure, thereby guaranteeing that the resulting process tensor is physically consistent. Furthermore, our method is easier to implement and requires a narrower range of coherent states than its predecessors. We test its feasibility using simulations on several experimentally relevant processes.Comment: 17 pages, 4 figure