Image Reconstruction In Optical Tomography Research Articles

DOTnet 2.0: Deep learning network for diffuse optical tomography image reconstruction

Breast cancer is the most common cancer worldwide. The standard imaging modality for breast cancer screening is X-ray mammography, which suffers from low sensitivities in women with dense breasts and can potentially cause cancers despite a low radiation dosage. Diffuse Optical Tomography (DOT) is a noninvasive imaging technique that can potentially be employed to improve breast cancer early detection. However, conventional model-based algorithms for reconstructing DOT images usually produce low-quality images with limited resolution and low reconstruction accuracy. We propose to integrate deep neural networks (DNNs) with the conventional DOT reconstruction methods. This hybrid framework significantly enhances image quality. The DNNs have been trained and tested with sample data derived from clinically relevant breast models. The sample dataset contains blood vessel structures from breast structures and artificially created vessels using the Lindenmayer-system algorithm. By comparing the hybrid reconstruction with the ground truth image, we demonstrated a multi scale - structural similarity index measure (MS-SSIM) score of 0.80–0.90. Whereas using conventional reconstruction, MS-SSIM provided a much inferior score of 0.36–0.59. In terms of DOT image quality, both qualitative and quantitative assessments of the reconstructed images signify that the hybrid approach is superior to conventional methods. This improvement suggests that DOT can potentially become a viable alternative to breast cancer screening, providing a step towards the next-generation device for optical mammography.

Gauss-Seidel based spatially varying optimal regularization improves reconstruction in diffuse optical tomography

ABSTRACT The inverse problem associated with Diffuse optical tomography image reconstruction is known to be highly nonlinear, under-determined, and ill-posed. The Levenberg-Marquardt technique is employed in solving it and is known to produce low-resolution reconstructed images. To stabilize the inversion of the large matrix, a heuristically chosen regularization parameter is used. A novel methodology is developed using Gauss-Seidel, Modified Richardson, and Kaczmarz recursive methods to solve the inverse problem and to obtain spatially varying regularization parameters, which are optimally obtained for every node automatically, which is otherwise not possible. The proposed methods are thoroughly compared with the existing traditional methods in both 2-D and 3-D imaging domains using numerically simulated noisy data and also real-life phantom data. Of all the proposed methods, the Gauss-Seidel-based method provides a quantitatively accurate estimation of spatially varying regularization using the model-resolution-matrix-based method and hence improves the quality of the reconstructed images with better resolution characteristics.

Short-separation regression incorporated diffuse optical tomography image reconstruction modeling for high-density functional near-infrared spectroscopy.

Short-separation (SS) regression and diffuse optical tomography (DOT) image reconstruction, two widely adopted methods in functional near-infrared spectroscopy (fNIRS), were demonstrated to individually facilitate the separation of brain activation and physiological signals, with further improvement using both sequentially. We hypothesized that doing both simultaneously would further improve the performance. Motivated by the success of these two approaches, we propose a method, SS-DOT, which applies SS and DOT simultaneously. The method, which employs spatial and temporal basis functions to represent the hemoglobin concentration changes, enables us to incorporate SS regressors into the time series DOT model. To benchmark the performance of the SS-DOT model against conventional sequential models, we use fNIRS resting state data augmented with synthetic brain response as well as data acquired during a ball squeezing task. The conventional sequential models comprise performing SS regression and DOT. The results show that the SS-DOT model improves the image quality by increasing the contrast-to-background ratio by a threefold improvement. The benefits are marginal at small brain activation. The SS-DOT model improves the fNIRS image reconstruction quality.

Age-related changes in diffuse optical tomography sensitivity profiles in infancy.

Diffuse optical tomography uses near-infrared light spectroscopy to measure changes in cerebral hemoglobin concentration. Anatomical interpretations of the location that generates the hemodynamic signal requires accurate descriptions of diffuse optical tomography sensitivity to the underlying cortical structures. Such information is limited for pediatric populations because they undergo rapid head and brain development. The present study used photon propagation simulation methods to examine diffuse optical tomography sensitivity profiles in realistic head models among infants ranging from 2 weeks to 24 months with narrow age bins, children (4 and 12 years) and adults (20 to 24 years). The sensitivity profiles changed systematically with the source-detector separation distance. The peak of the sensitivity function in the head was largest at the smallest separation distance and decreased as separation distance increased. The fluence value dissipated more quickly with sampling depth at the shorter source-detector separations than the longer separation distances. There were age-related differences in the shape and variance of sensitivity profiles across a wide range of source-detector separation distances. Our findings have important implications in the design of sensor placement and diffuse optical tomography image reconstruction in (functional) near-infrared light spectroscopy research. Age-appropriate realistic head models should be used to provide anatomical guidance for standalone near-infrared light spectroscopy data in infants.

SIMBA: Scalable Inversion in Optical Tomography Using Deep Denoising Priors

Two features desired in a three-dimensional (3D) optical tomographic image reconstruction algorithm are the ability to reduce imaging artifacts and to do fast processing of large data volumes. Traditional iterative inversion algorithms are impractical in this context due to their heavy computational and memory requirements. We propose and experimentally validate a novel scalable iterative mini-batch algorithm (SIMBA) for fast and high-quality optical tomographic imaging. SIMBA enables high-quality imaging by combining two complementary information sources: the physics of the imaging system characterized by its forward model and the imaging prior characterized by a denoising deep neural net. SIMBA easily scales to very large 3D tomographic datasets by processing only a small subset of measurements at each iteration. We establish the theoretical fixed-point convergence of SIMBA under nonexpansive denoisers for convex data-fidelity terms. We validate SIMBA on both simulated and experimentally collected intensity diffraction tomography (IDT) datasets. Our results show that SIMBA can significantly reduce the computational burden of 3D image formation without sacrificing the imaging quality.

Point spread function based image reconstruction in optical projection tomography

As a result of the shallow depth of focus of the optical imaging system, the use of standard filtered back projection in optical projection tomography causes space-variant tangential blurring that increases with the distance to the rotation axis. We present a novel optical tomographic image reconstruction technique that incorporates the point spread function of the imaging lens in an iterative reconstruction. The technique is demonstrated using numerical simulations, tested on experimental optical projection tomography data of single fluorescent beads, and applied to high-resolution emission optical projection tomography imaging of an entire zebrafish larva. Compared to filtered back projection our results show greatly reduced radial and tangential blurring over the entire mm2 field of view, and a significantly improved signal to noise ratio.

Frequency-domain optical tomographic image reconstruction algorithm with the simplified spherical harmonics (SP3) light propagation model

We introduce here the finite volume formulation of the frequency-domain simplified spherical harmonics model with n-th order absorption coefficients (FD-SPN) that approximates the frequency-domain equation of radiative transfer (FD-ERT). We then present the FD-SPN based reconstruction algorithm that recovers absorption and scattering coefficients in biological tissue. The FD-SPN model with 3rd order absorption coefficient (i.e., FD-SP3) is used as a forward model to solve the inverse problem. The FD-SP3 is discretized with a node-centered finite volume scheme and solved with a restarted generalized minimum residual (GMRES) algorithm. The absorption and scattering coefficients are retrieved using a limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm. Finally, the forward and inverse algorithms are evaluated using numerical phantoms with optical properties and size that mimic small-volume tissue such as finger joints and small animals.The forward results show that the FD-SP3 model approximates the FD-ERT (S12) solution within high accuracy; the average errors in the phase (<3.7%) and the amplitude (<7.1%) of the partial current at the boundary are reported. From the inverse results we find that the absorption and scattering coefficient maps are more accurately reconstructed with the SP3 model than those with the SP1 model. Therefore, this work shows that the FD-SP3 is an efficient model for optical tomographic imaging of small-volume media with non-diffuse properties both in terms of computational time and accuracy as it requires significantly lower CPU time than the FD-ERT (S12) and also it is more accurate than the FD-SP1.

Optical Tomographic Image Reconstruction Based on Beam Propagation and Sparse Regularization

Optical tomographic imaging requires an accurate forward model as well as regularization to mitigate missing-data artifacts and to suppress noise. Nonlinear forward models can provide more accurate interpretation of the measured data than their linear counterparts, but they generally result in computationally prohibitive reconstruction algorithms. Although sparsity-driven regularizers significantly improve the quality of reconstructed image, they further increase the computational burden of imaging. In this paper, we present a novel iterative imaging method for optical tomography that combines a nonlinear forward model based on the beam propagation method (BPM) with an edge-preserving three-dimensional (3-D) total variation (TV) regularizer. The central element of our approach is a time-reversal scheme, which allows for an efficient computation of the derivative of the transmitted wave-field with respect to the distribution of the refractive index. This time-reversal scheme together with our stochastic proximal-gradient algorithm makes it possible to optimize under a nonlinear forward model in a computationally tractable way, thus enabling a high-quality imaging of the refractive index throughout the object. We demonstrate the effectiveness of our method through several experiments on simulated and experimentally measured data.

Performance evaluation of typical approximation algorithms for nonconvex ℓ_p-minimization in diffuse optical tomography

The sparse estimation methods that utilize the ℓp-norm, with p being between 0 and 1, have shown better utility in providing optimal solutions to the inverse problem in diffuse optical tomography. These ℓp-norm-based regularizations make the optimization function nonconvex, and algorithms that implement ℓp-norm minimization utilize approximations to the original ℓp-norm function. In this work, three such typical methods for implementing the ℓp-norm were considered, namely, iteratively reweighted ℓ1-minimization (IRL1), iteratively reweighted least squares (IRLS), and the iteratively thresholding method (ITM). These methods were deployed for performing diffuse optical tomographic image reconstruction, and a systematic comparison with the help of three numerical and gelatin phantom cases was executed. The results indicate that these three methods in the implementation of ℓp-minimization yields similar results, with IRL1 fairing marginally in cases considered here in terms of shape recovery and quantitative accuracy of the reconstructed diffuse optical tomographic images.

Sparse Recovery Methods Hold Promise for Diffuse Optical Tomographic Image Reconstruction

The sparse recovery methods utilize the ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> -norm-based regularization in the estimation problem with 0 ≤ p ≤ 1. These methods have a better utility when the number of independent measurements are limited in nature, which is a typical case for diffuse optical tomographic image reconstruction problem. These sparse recovery methods, along with an approximation to utilize the ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> -norm, have been deployed for the reconstruction of diffuse optical images. Their performance was compared systematically using both numerical and gelatin phantom cases to show that these methods hold promise in improving the reconstructed image quality.

Diffuse optical tomography: image reconstruction and verification.

In this study, we intend to use diffuse optical Tomography (DOT) as a noninvasive, safe and low cost technique that can be considered as a functional imaging method and mention the importance of image reconstruction in accuracy and procession of image. One of the most important and fastest methods in image reconstruction is the boundary element method (BEM). This method is introduced and employed in our works. Generally, to image a biological tissue we must obtain its optical properties. In order to reach this goal we benefit from diffusion equation because tissue is highly scattering medium. Diffusion equation is solved by boundary element equation (BEM) in our research. First, we assume a double layer phantom with different scattering and absorption coefficients to simulate and verify precession and accuracy of image reconstruction by BEM. Light absorption can be affected by volume fraction of blood in skin. For a specific skin species the volume fraction is calculated and then the results are compared with the reconstructed values obtained by BEM. Since the depth of tissue is important in light absorption a two layer phantom with known values is made and the depths of layers are reconstructed by BEM then they are compared with the expected values. A homogenous phantom with known scattering and absorption coefficients was made and then these coefficients were reconstructed by BEM. Finally, an inhomogeneous phantom (phantom with defect) whose defect was in a known position was made and the absorption and scattering coefficients were reconstructed and compared with real values. Comparison between real or simulated values and reconstructed values of scattering and absorption coefficients, volume fraction of blood and thickness of phantom layers by BEM shows maximum errors of 24%, 7% and 35%, respectively. Comparison between BEM data and real or simulated values shows an acceptabl eagreement. Consequently, we can rely on BEM as a beneficial method in diffuse optical tomography image reconstruction.

Nonquadratic penalization improves near-infrared diffuse optical tomography

A new approach that can easily incorporate any generic penalty function into the diffuse optical tomographic image reconstruction is introduced to show the utility of nonquadratic penalty functions. The penalty functions that were used include quadratic (ℓ2), absolute (ℓ1), Cauchy, and Geman-McClure. The regularization parameter in each of these cases was obtained automatically by using the generalized cross-validation method. The reconstruction results were systematically compared with each other via utilization of quantitative metrics, such as relative error and Pearson correlation. The reconstruction results indicate that, while the quadratic penalty may be able to provide better separation between two closely spaced targets, its contrast recovery capability is limited, and the sparseness promoting penalties, such as ℓ1, Cauchy, and Geman-McClure have better utility in reconstructing high-contrast and complex-shaped targets, with the Geman-McClure penalty being the most optimal one.

Efficient gradient-free simplex method for estimation of optical properties in image-guided diffuse optical tomography

Typical image-guided diffuse optical tomographic image reconstruction procedures involve reduction of the number of optical parameters to be reconstructed equal to the number of distinct regions identified in the structural information provided by the traditional imaging modality. This makes the image reconstruction problem less ill-posed compared to traditional underdetermined cases. Still, the methods that are deployed in this case are same as those used for traditional diffuse optical image reconstruction, which involves a regularization term as well as computation of the Jacobian. A gradient-free Nelder-Mead simplex method is proposed here to perform the image reconstruction procedure and is shown to provide solutions that closely match ones obtained using established methods, even in highly noisy data. The proposed method also has the distinct advantage of being more efficient owing to being regularization free, involving only repeated forward calculations.

Convergence rate calculation of simultaneous iterative reconstruction technique algorithm for diffuse optical tomography image reconstruction: A feasibility study

Diffuse optical tomography (DOT) is an emerging technique for functional biological imaging. The imaging quality of DOT depends on the imaging reconstruction algorithm. The SIRT has been widely used for DOT image reconstruction but there is no criterion to truncate based on any kind of residual parameter. The iteration loops will always be decided by experimental rule. This work presents the CR calculation that can be great help for SIRT optimization. In this paper, four inhomogeneities with various shapes of absorption distributions are simulated as imaging targets. The images are reconstructed and analyzed based on the simultaneous iterative reconstruction technique (SIRT) method. For optimization between time consumption and imaging accuracy in reconstruction process, the numbers of iteration loop needed to be optimized with a criterion in algorithm, that is, the root mean square error (RMSE) should be minimized in limited iterations. For clinical applications of DOT, the RMSE cannot be obtained because the measured targets are unknown. Thus, the correlations between the RMSE and the convergence rate (CR) in SIRT algorithm are analyzed in this paper. From the simulation results, the parameter CR reveals the related RMSE value of reconstructed images. The CR calculation offers an optimized criterion of iteration process in SIRT algorithm for DOT imaging. Based on the result, the SIRT can be modified with CR calculation for self-optimization. CR reveals an indicator of SIRT image reconstruction in clinical DOT measurement. Based on the comparison result between RMSE and CR, a threshold value of CR (CRT) can offer an optimized number of iteration steps for DOT image reconstruction. This paper shows the feasibility study by utilizing CR criterion for SIRT in simulation and the clinical application of DOT measurement relies on further investigation.

Accelerated gradient based diffuse optical tomographic image reconstruction

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). 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. 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. 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.

Discretization Error Analysis and Adaptive Meshing Algorithms for Fluorescence Diffuse Optical Tomography in the Presence of Measurement Noise

Quantitatively accurate fluorescence diffuse optical tomographic (FDOT) image reconstruction is a computationally demanding problem that requires repeated numerical solutions of two coupled partial differential equations and an associated inverse problem. Recently, adaptive finite element methods have been explored to reduce the computation requirements of the FDOT image reconstruction. However, existing approaches ignore the ubiquitous presence of noise in boundary measurements. In this paper, we analyze the effect of finite element discretization on the FDOT forward and inverse problems in the presence of measurement noise and develop novel adaptive meshing algorithms for FDOT that take into account noise statistics. We formulate the FDOT inverse problem as an optimization problem in the maximum a posteriori framework to estimate the fluorophore concentration in a bounded domain. We use the mean-square-error (MSE) between the exact solution and the discretized solution as a figure of merit to evaluate the image reconstruction accuracy, and derive an upper bound on the MSE which depends upon the forward and inverse problem discretization parameters, noise statistics, a priori information of fluorophore concentration, source and detector geometry, as well as background optical properties. Next, we use this error bound to develop adaptive meshing algorithms for the FDOT forward and inverse problems to reduce the MSE due to discretization in the reconstructed images. Finally, we present a set of numerical simulations to illustrate the practical advantages of our adaptive meshing algorithms for FDOT image reconstruction.

Accelerating frequency-domain diffuse optical tomographic image reconstruction using graphics processing units

Diffuse optical tomographic image reconstruction uses advanced numerical models that are computationally costly to be implemented in the real time. The graphics processing units (GPUs) offer desktop massive parallelization that can accelerate these computations. An open-source GPU-accelerated linear algebra library package is used to compute the most intensive matrix-matrix calculations and matrix decompositions that are used in solving the system of linear equations. These open-source functions were integrated into the existing frequency-domain diffuse optical image reconstruction algorithms to evaluate the acceleration capability of the GPUs (NVIDIA Tesla C 1060) with increasing reconstruction problem sizes. These studies indicate that single precision computations are sufficient for diffuse optical tomographic image reconstruction. The acceleration per iteration can be up to 40, using GPUs compared to traditional CPUs in case of three-dimensional reconstruction, where the reconstruction problem is more underdetermined, making the GPUs more attractive in the clinical settings. The current limitation of these GPUs in the available onboard memory (4 GB) that restricts the reconstruction of a large set of optical parameters, more than 13,377.

A higher order diffusion model for three-dimensional photon migration and image reconstruction in optical tomography

In this work, we derived three-dimensional simplified spherical harmonics approximated higher order diffusion equations. We also solved the higher order diffusion equations using a finite element method and compared the solutions from the first-order diffusion equation and Monte Carlo simulations. We found that the conducted model is able to improve the first-order diffusion solution in a transport-like homogeneous or heterogeneous medium. Reconstructed images based on the higher order diffusion model are also presented. We conclude that the developed higher order diffusion model is able to accurately describe light propagation in biological tissues and to offer improved image reconstruction.

Optical tomography with the equation of radiative transfer

PurposeThis paper sets out to give an overview about state‐of‐the‐art optical tomographic image reconstruction algorithms that are based on the equation of radiative transfer (ERT).Design/methodology/approachAn objective function, which describes the discrepancy between measured and numerically predicted light intensity data on the tissue surface, is iteratively minimized to find the unknown spatial distribution of the optical parameters or sources. At each iteration step, the predicted partial current is calculated by a forward model for light propagation based on the ERT. The equation of radiative is solved with either finite difference or finite volume methods.FindingsTomographic reconstruction algorithms based on the ERT accurately recover the spatial distribution of optical tissue properties and light sources in biological tissue. These tissues either can have small geometries/large absorption coefficients, or can contain void‐like inclusions.Originality/valueThese image reconstruction methods can be employed in small animal imaging for monitoring blood oxygenation, in imaging of tumor growth, in molecular imaging of fluorescent and bioluminescent probes, in imaging of human finger joints for early diagnosis of rheumatoid arthritis, and in functional brain imaging.

Differences between Fluorescent and Bioluminescent Measurement for Optical Tomography Image Reconstruction in a Simultaneous PET and Optical CT Imaging System

Differences between Fluorescent and Bioluminescent Measurement for Optical Tomography Image Reconstruction in a Simultaneous PET and Optical CT Imaging System