A Penalized Linear and Nonlinear Combined Conjugate Gradient Method for the Reconstruction of Fluorescence Molecular Tomography

Conjugate gradient method is verified to be efficient for nonlinear optimization problems of large-dimension data. In this paper, a penalized linear and nonlinear combined conjugate gradient method for the reconstruction of fluorescence molecular tomography (FMT) is presented. The algorithm combines the linear conjugate gradient method and the nonlinear conjugate gradient method together based on a restart strategy, in order to take advantage of the two kinds of conjugate gradient methods and compensate for the disadvantages. A quadratic penalty method is adopted to gain a nonnegative constraint and reduce the illposedness of the problem. Simulation studies show that the presented algorithm is accurate, stable, and fast. It has a better performance than the conventional conjugate gradient-based reconstruction algorithms. It offers an effective approach to reconstruct fluorochrome information for FMT

Computational Modeling of Human Head Conductivity

Abstract. The computational environment for estimation of unknown regional electrical conductivities of the human head, based on realistic geometry from seg-mented MRI up to 2563 resolution, is described. A finite difference alternating di-rection implicit (ADI) algorithm, parallelized using OpenMP, is used to solve the forward problem describing the electrical field distribution throughout the head given known electrical sources. A simplex search in the multi-dimensional para-meter space of tissue conductivities is conducted in parallel using a distributed system of heterogeneous computational resources. The theoretical and computa-tional formulation of the problem is presented. Results from test studies are pro-vided, comparing retrieved conductivities to known solutions from simulation. Performance statistics are also given showing both the scaling of the forward problem and the performance dynamics of the distributed search.

Bioluminescence tomography using eigenvectors expansion and iterative solution for the optimized permissible source region

A reconstruction algorithm for bioluminescence tomography (BLT) has been developed. The algorithm numerically calculates the Green’s function at different wavelengths using the diffusion equation and finite element method. The optical properties used in calculating the Green’s function are reconstructed using diffuse optical tomography (DOT) and assuming anatomical information is provided by x-ray computed tomography or other methods. A symmetric system of equations is formed using the Green’s function and the measured light fluence rate and the resulting eigenvalue problem is solved to get the eigenvectors of this symmetric system of equations. A space can be formed from the eigenvectors obtained and the reconstructed source is written as an expansion of the eigenvectors corresponding to non-zero eigenvalues. The coefficients of the expansion are found to obtain the reconstructed BL source distribution. The problem is solved iteratively by using a permissible source region that is shrunk by removing nodes with low probability to contribute to the source. Throughout this process the permissible region shrinks from the entire object to just a few nodes. The best estimate of the reconstructed source is chosen that which minimizes the difference between the calculated and measured light fluence rates. 3D simulations presented here show that the reconstructed source is in good agreement with the actual source in terms of locations, magnitudes, sizes, and total powers for both localized multiple sources and large inhomogeneous source distributions

Fast and efficient image reconstruction for high density diffuse optical imaging of the human brain

Real-time imaging of human brain has become an important technique within neuroimaging. In this study, a fast and efficient sensitivity map generation based on Finite Element Models (FEM) is developed which utilises a reduced sensitivitys matrix taking advantage of sparsity and parallelisation processes. Time and memory efficiency of these processes are evaluated and compared with conventional method showing that for a range of mesh densities from 50000 to 320000 nodes, the required memory is reduced over tenfold and computational time fourfold allowing for near real-time image recovery

Algorithms for bioluminescence tomography incorporating anatomical information and reconstruction of tissue optical properties

Reconstruction algorithms are presented for a two-step solution of the bioluminescence tomography (BLT) problem. In the first step, a priori anatomical information provided by x-ray computed tomography or by other methods is used to solve the continuous wave (cw) diffuse optical tomography (DOT) problem. A Taylor series expansion approximates the light fluence rate dependence on the optical properties of each region where first and second order direct derivatives of the light fluence rate with respect to scattering and absorption coefficients are obtained and used for the reconstruction. In the second step, the reconstructed optical properties at different wavelengths are used to calculate the Green’s function of the system. Then an iterative minimization solution based on the L1 norm shrinks the permissible regions where the sources are allowed by selecting points with higher probability to contribute to the source distribution. This provides an efficient BLT reconstruction algorithm with the ability to determine relative source magnitudes and positions in the presence of noise

Improved bioluminescence and fluorescence reconstruction algorithms using diffuse optical tomography, normalized data, and optimized selection of the permissible source region

Reconstruction algorithms are presented for two-step solutions of the bioluminescence tomography (BLT) and the fluorescence tomography (FT) problems. In the first step, a continuous wave (cw) diffuse optical tomography (DOT) algorithm is used to reconstruct the tissue optical properties assuming known anatomical information provided by x-ray computed tomography or other methods. Minimization problems are formed based on L1 norm objective functions, where normalized values for the light fluence rates and the corresponding Green’s functions are used. Then an iterative minimization solution shrinks the permissible regions where the sources are allowed by selecting points with higher probability to contribute to the source distribution. Throughout this process the permissible region shrinks from the entire object to just a few points. The optimum reconstructed bioluminescence and fluorescence distributions are chosen to be the results of the iteration corresponding to the permissible region where the objective function has its global minimum This provides efficient BLT and FT reconstruction algorithms without the need for a priori information about the bioluminescence sources or the fluorophore concentration. Multiple small sources and large distributed sources can be reconstructed with good accuracy for the location and the total source power for BLT and the total number of fluorophore molecules for the FT. For non-uniform distributed sources, the size and magnitude become degenerate due to the degrees of freedom available for possible solutions. However, increasing the number of data points by increasing the number of excitation sources can improve the accuracy of reconstruction for non-uniform fluorophore distributions

Xây dựng ảnh não ba chiều sử dụng phương pháp quang cận hồng ngoại

Kỹ thuật quang cận hồng ngoại fNIRS (functional near-infrared spectroscopy) là phương pháp không tiếp xúc được dùng để đo nồng độ hemoglobin của tín hiệu não. Độ phân giải về thời gian của của kỹ thuật này cao (xấp xỉ 1 ms). Tuy nhiên, độ phân giải về không gian thì bị hạn chế (xấp xỉ 10 mm) so với các kỹ thuật không tiếp xúc khác. Do đó trong nghiên cứu này, kỹ thuật fNIRS với 32 cặp thu phát cận hồng ngoại được dùng để đo đáp ứng động học não của 5 người đàn ông trưởng thành khi cho họ thực hiện các phép tính số học. Đặc biệt tọa độ của 256 điểm ảnh 3 chiều được tính toán dựa trên sự phân bố hình học của các cặp thu phát. Hệ số về chiều dài đường đi của các quang tử trong phương trình Beer-Lambert được ước lượng như một hàm của khoảng cách để tính toán độ hấp thụ của ánh sáng. Trị trung bình của nồng độ hemoglobin (Oxy-hemoglobin và deOxy-hemoglobin) được tính từ độ hấp thụ ánh sáng thì được dùng để dựng lại ảnh não 3 chiều. Kết quả đạt được cho thấy phương pháp đề nghị có thể phát hiện tính hoạt động của não với độ phân giải không gian cao hơn so với phương pháp truyền thống

Parallel Programming of gradient-based iterative image reconstruction schemes for optical tomography

Summary Optical tomography (OT) is a fast developing novel imaging modality that uses near-infrared (NIR) light to obtain cross-sectional views of optical properties inside the human body. A major challenge remains the time-consuming, computationalintensive image reconstruction problem that converts NIR transmission measurements into cross-sectional images. To increase the speed of iterative image reconstruction schemes that are commonly applied for OT, we have developed and implemented several parallel algorithms on a cluster of workstations. Static process distribution as well as dynamic load balancing schemes suitable for heterogeneous clusters and varying machine performances are introduced and tested. The resulting algorithms are shown to accelerate the reconstruction process to various degrees, substantially reducing the computation times for clinically relevant problems