In this paper, we formulate the reconstruction problem in diffuse optical tomography (DOT) in a statistical setting for determining the optical parameters, scattering and absorption, from boundary photon density measurements. A special kind of adaptive Metropolis algorithm for the reconstruction procedure using sparsity and total variation prior is presented. Finally, a simulation study of this technique with different regularization functions and its comparison to the deterministic Iteratively Regularized Gauss Newton method shows the effectiveness and stability of the method.
Diffuse Optical Tomography (DOT) is an emerging technology in medical imaging which employs light in the NIR spectrum to estimate the distribution of optical coefficients in biological tissues for diagnostic and monitoring purposes. DOT reconstruction implies the solution of a severely ill-posed inverse problem, for which regularization techniques are mandatory in order to achieve reasonable results. Traditionally, regularization techniques put a variance prior on the desired solution/gradient via regularization parameters, whose choice requires a fine tuning, specific for each case. In this w…
Diffuse optical tomography (DOT) is an imaging modality which uses near-infrared light. Although iterative numerical schemes are commonly used for its inverse problem, correct solutions are not obtained unless good initial guesses are chosen. We propose a numerical scheme of DOT which works even when good initial guesses of optical parameters are not available. We use simulated annealing (SA) which is a method of the Markov-chain Monte Carlo. To implement SA for DOT, a spin Hamiltonian is introduced in the cost function, and the Metropolis algorithm or single-component Metropolis-Hastings algo…
In this paper we investigate the non-linear and ill-posed inverse problem of simultaneously identifying the conductivity and the reaction in diffuse optical tomography with noisy measurement data available on an accessible part of the boundary. We propose an energy functional method and the total variational regularization combining with the quadratic stabilizing term to formulate the identification problem to a PDEs constrained optimization problem. We show the stability of the proposed regularization method and the convergence of the finite element regularized solutions to the identification…
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…
Limited Tomography Reconstruction via Tight Frame and Sinogram Extrapolation
Institute of Natural Sciences, Shanghai Jiao Tong University（上海交通大学自然科学研究院）；Beijing International Center for Mathematical Research Peking University（北京大学北京国际数学研究中心）；Institute of Natural Sciences, School of Mathematical Sciences, and MOE-LSC, Shanghai Jiao Tong University（上海交通大学自然科学研究院、数学科学学院和教育部科学计算与工程应用重点实验室）
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）
Solving or resolving global tomographic models with spherical wavelets, and the scale and sparsity of seismic heterogeneity
Princeton University（普林斯顿大学）；Université Libre de Bruxelles（布鲁塞尔自由大学）；GéoAzur Université de Nice（尼斯大学地理与地球物理实验室）；Program in Applied and Computational Mathematics Princeton University（普林斯顿大学应用与计算数学项目）
Disjoint sparsity for signal separation and applications to hybrid inverse problems in medical imaging
Department of Mathematics and Applications, École Normale Supérieure（巴黎高等师范学院数学与应用系）；Department of Mathematics and et Applications, École Normale Supérieure（巴黎高等师范学院数学与应用系）
