Fast tomographic reconstruction strategy for diffuse optical tomography

A simple algorithm for diffuse optical tomography without Jacobian inversion

A computationally simpler algorithm to reconstruct the optical property distribution of turbid media using diffuse optical tomographic principles is presented. The proposed algorithm eliminates the requirement of large Jacobian matrix inversion which otherwise is essential for tomographic imaging. The most significant Jacobians are identified based on proper thresholding of the measurement and the intersection of these Jacobians gives the approximate spatial location of the inhomogeneity. The algorithm is tested and optimized using simulations and further validated using tissue-mimicking phantom-based experiments andin-vivosmall-animal experiments.

Comparison of source localization techniques in diffuse optical tomography for fNIRS application using a realistic head model

Functional near-infrared spectroscopy (fNIRS) is a non-invasive imaging technique that elicits growing interest for research and clinical applications. In the last decade, efforts have been made to develop a mathematical framework in order to image the effective sources of hemoglobin variations in brain tissues. Different approaches can be used to impose additional information or constraints when reconstructing the cerebral images of an ill-posed problem. The goal of this study is to compare the performance and limitations of several source localization techniques in the context of fNIRS tomography using individual anatomical magnetic resonance imaging (MRI) to model light propagation. The forward problem is solved using a Monte Carlo simulation of light propagation in the tissues. The inverse problem has been linearized using the Rytov approximation. Then, Tikhonov regularization applied to least squares, truncated singular value decomposition, back-projection, L1-norm regularization, minimum norm estimates, low resolution electromagnetic tomography and Bayesian model averaging techniques are compared using a receiver operating characteristic analysis, blurring and localization error measures. Using realistic simulations (n = 450) and data acquired from a human participant, this study depicts how these source localization techniques behave in a human head fNIRS tomography. When compared to other methods, Bayesian model averaging is proposed as a promising method in DOT and shows great potential to improve specificity, accuracy, as well as to reduce blurring and localization error even in presence of noise and deep sources. Classical reconstruction methods, such as regularized least squares, offer better sensitivity but higher blurring; while more novel L1-based method provides sparse solutions with small blurring and high specificity but lower sensitivity. The application of these methods is also demonstrated experimentally using visual fNIRS experiment with adult participant.

A Tensor B-Spline Approach for Solving the Diffusion PDE With Application to Optical Diffusion Tomography

Optical Diffusion Tomography (ODT) is a modern non-invasive medical imaging modality which requires mathematical modelling of near-infrared light propagation in tissue. Solving the ODT forward problem equation accurately and efficiently is crucial. Typically, the forward problem is represented by a Diffusion PDE and is solved using the Finite Element Method (FEM) on a mesh, which is often unstructured. Tensor B-spline signal processing has the attractive features of excellent interpolation and approximation properties, multiscale properties, fast algorithms and does not require meshing. This paper introduces Tensor B-spline methodology with arbitrary spline degree tailored to solve the ODT forward problem in an accurate and efficient manner. We show that our Tensor B-spline formulation induces efficient and highly parallelizable computational algorithms. Exploitation of B-spline properties for integration over irregular domains proved valuable. The Tensor B-spline solver was tested on standard problems and on synthetic medical data and compared to FEM, including state-of-the art ODT forward solvers. Results show that 1) a significantly higher accuracy can be achieved with the same number of nodes, 2) fewer nodes are required to achieve a prespecified accuracy, 3) the algorithm converges in significantly fewer iterations to a given error. These findings support the value of Tensor B-spline methodology for high-performance ODT implementations. This may translate into advances in ODT imaging for biomedical research and clinical application.

A reconstruction approach in wavelet domain for fluorescent molecular tomography via rotated sources illumination

Background

Fluorescent molecular tomography (FMT) aims at reconstructing the spatial map of optical and fluorescence parameters from fluence measurements. Basically, solving large-scale matrix equations is computationally expensive for image reconstruction of FMT. Despite the reconstruction quality can be improved with more sources, it may result in higher computational costs for reconstruction. This article presents a novel method in the wavelet domain with rotated sources illumination.

Methods

We use the finite element method for the computation of the forward model. The global inverse problem is solved based on wavelet in conjunction with principal component analysis. The iterative reconstruction is implemented with sources rotated in a certain angle. The original excitation light sources are used to reconstruct the image in the first iteration. Then, upon the sources are rotated by a certain angle, they are employed for the next iteration of reconstruction.

Results

Simulation results demonstrate that our method can considerably reduce the time taken for the computation of inverse problem in FMT. Furthermore, the approach proposed is also shown to largely outperform the traditional method in terms of the precision of inverse solutions.

Conclusions

Our method has the capability to locate the inclusions. The proposed method can significantly speed up the reconstruction process with the high reconstruction quality.

Analytical model of optical fluence inside multiple cylindrical inhomogeneities embedded in an otherwise homogeneous turbid medium for quantitative photoacoustic imaging

We present an analytical model of optical fluence for multiple cylindrical inhomogeneities embedded in an otherwise homogeneous turbid medium. The model is based on the diffusion equation and represents the optical fluence distribution inside and outside inhomogeneities as a series of modified Bessel functions. We take into account the interplay between cylindrical inhomogeneities by introducing new boundary conditions on the surface of inhomogeneities. The model is compared with the numerical solution of the diffusion equation with NIRFAST software. The fluences inside the inhomogeneities obtained by the two methods are in close agreement. This permits the use of the model as a forward model for quantitative photoacoustic imaging.

Compressed-sensing-based fluorescence molecular tomographic image reconstruction with grouped sources

BACKGROUND

Although the quality of reconstructed results can be improved with the increment of the number of measurements, the scale of the matrices involved in the reconstruction of fluorescence molecular tomography (FMT) will become larger, which leads to the poor efficiency of the process of tomographic image reconstruction. In this paper, we proposed a new method for image reconstruction of FMT based on compressed sensing, in which a scheme of grouped sources is incorporated.

METHODS

The forward equations are implemented using the finite element method (FEM). The reconstruction model is formulated under the framework of compressed sensing theory. The regularization term and the total variation penalty are incorporated in the objective function. During the reconstruction of FMT, the sources are divided into two groups for iteration in turn. One group of sources is employed in the first iteration of inverse problem, and the other group is employed in the next iteration.

RESULTS

Simulation results demonstrate that the computation time and mean square error (MSE) of the reconstruction with our algorithm are less than those with the traditional method. The proposed algorithm can reconstruct the target with enhanced contrast and more accurate shape.

CONCLUSIONS

The proposed algorithm can significantly improve the speed and accuracy of the reconstruction of FMT. Furthermore, our compressed-sensing-based method can reduce the number of measurements.

Full domain-decomposition scheme for diffuse optical tomography of large-sized tissues with a combined CPU and GPU parallelization

The common approach to diffuse optical tomography is to solve a nonlinear and ill-posed inverse problem using a linearized iteration process that involves repeated use of the forward and inverse solvers on an appropriately discretized domain of interest. This scheme normally brings severe computation and storage burdens to its applications on large-sized tissues, such as breast tumor diagnosis and brain functional imaging, and prevents from using the matrix-fashioned linear inversions for improved image quality. To cope with the difficulties, we propose in this paper a parallelized full domain-decomposition scheme, which divides the whole domain into several overlapped subdomains and solves the corresponding subinversions independently within the framework of the Schwarz-type iterations, with the support of a combined multicore CPU and multithread graphics processing unit (GPU) parallelization strategy. The numerical and phantom experiments both demonstrate that the proposed method can effectively reduce the computation time and memory occupation for the large-sized problem and improve the quantitative performance of the reconstruction.

Image reconstruction of fluorescent molecular tomography based on the simplified matrix system

Fluorescent molecular tomographic image reconstruction usually involves repeatedly solving large-scale matrix equations, which are computationally expensive. In this paper, a method is proposed to reduce the scale of the matrix system. The Jacobian matrix is simplified by deleting the columns or the rows whose values are smaller than a threshold. Furthermore, the measurement data are divided into two groups and are used for iteration of image reconstruction in turn. The simplified system is then solved in the wavelet domain to further accelerate the process of solving the inverse problem. Simulation results demonstrate that the proposed method can significantly speed up the reconstruction process.

Spatial-frequency-compression scheme for diffuse optical tomography with dense sampling dataset

Dense sampling of illumination and detection offers an effective way of improving the image-reconstruction performance of near-infrared diffuse optical tomography (DOT) at a cost of lengthy computation times. In this paper, we describe a fast DOT scheme for reconstructing the absorption coefficient image of a slab medium from dense sampling of both illumination and detection in the noncontact DOT. The proposed method is carried out with spatial-frequency encoding in both the source and detection spaces, and involves a spatial-frequency-compression (SFC) strategy for selecting the useful spatial frequency based on the tissue transfer function. The method is expected to considerably reduce the calculation time for reconstruction while improving the quality of the reconstructed images. Results from the simulated data show that the speed for absorption reconstruction with the proposed SFC method is more than 400 times faster than that with the conventional one. A noncontact DOT system for dense sampling of both illumination and detection is developed by using laser raster scanning and CCD-based data acquisition. Experimental measurements on several solid phantoms demonstrate that a high quantitativeness ratio can be obtained from the proposed method thanks to reduction of the ill-posedness of the inverse calculation. It takes less than 20 s for the proposed method to experimentally reconstruct one absorption image from a 256×256-sized dataset, which would take a few hours with the conventional method.

Accelerated gradient based diffuse optical tomographic image reconstruction

PURPOSE

Fast reconstruction of interior optical parameter distribution using a new approach called Broyden-based model iterative image reconstruction (BMOBIIR) and adjoint Broyden-based MOBIIR (ABMOBIIR) of a tissue and a tissue mimicking phantom from boundary measurement data in diffuse optical tomography (DOT).

METHODS

DOT is a nonlinear and ill-posed inverse problem. Newton-based MOBIIR algorithm, which is generally used, requires repeated evaluation of the Jacobian which consumes bulk of the computation time for reconstruction. In this study, we propose a Broyden approach-based accelerated scheme for Jacobian computation and it is combined with conjugate gradient scheme (CGS) for fast reconstruction. The method makes explicit use of secant and adjoint information that can be obtained from forward solution of the diffusion equation. This approach reduces the computational time many fold by approximating the system Jacobian successively through low-rank updates.

RESULTS

Simulation studies have been carried out with single as well as multiple inhomogeneities. Algorithms are validated using an experimental study carried out on a pork tissue with fat acting as an inhomogeneity. The results obtained through the proposed BMOBIIR and ABMOBIIR approaches are compared with those of Newton-based MOBIIR algorithm. The mean squared error and execution time are used as metrics for comparing the results of reconstruction.

CONCLUSIONS

We have shown through experimental and simulation studies that Broyden-based MOBIIR and adjoint Broyden-based methods are capable of reconstructing single as well as multiple inhomogeneities in tissue and a tissue-mimicking phantom. Broyden MOBIIR and adjoint Broyden MOBIIR methods are computationally simple and they result in much faster implementations because they avoid direct evaluation of Jacobian. The image reconstructions have been carried out with different initial values using Newton, Broyden, and adjoint Broyden approaches. These algorithms work well when the initial guess is close to the true solution. However, when initial guess is far away from true solution, Newton-based MOBIIR gives better reconstructed images. The proposed methods are found to be stable with noisy measurement data.

Region-based reconstruction method for fluorescent molecular tomography

A common difficulty for the traditional methods of fluorescent molecular tomographic (FMT) reconstruction is that only a small amount of measurements can be used to recover the image comprised of a large number of pixels. This difficulty not only leads to expensive computational cost but also likely results in an unstable solution prone to be affected by the noise in the measurement data. In this paper, we propose a region-based method for reducing the unknowns, where the target areas are determined by searching for the nearest neighbor nodes. In this method, the Hessian matrix of the second-order derivatives is incorporated to speed up the optimization process. An iteration strategy of multi-wavelength measurement is introduced to further improve the accuracy of inverse solutions. Simulation results demonstrate that the proposed approach can significantly speed up the reconstruction process and improve the image quality of FMT.