Diffuse Optical Tomography Reconstruction Research Articles

Randomized recursive techniques for image reconstruction in diffuse optical tomography

Randomized recursive techniques for image reconstruction in diffuse optical tomography

Enhanced model iteration algorithm with graph neural network for diffuse optical tomography.

Diffuse optical tomography (DOT) employs near-infrared light to reveal the optical parameters of biological tissues. Due to the strong scattering of photons in tissues and the limited surface measurements, DOT reconstruction is severely ill-posed. The Levenberg-Marquardt (LM) is a popular iteration method for DOT, however, it is computationally expensive and its reconstruction accuracy needs improvement. In this study, we propose a neural model based iteration algorithm which combines the graph neural network with Levenberg-Marquardt (GNNLM), which utilizes a graph data structure to represent the finite element mesh. In order to verify the performance of the graph neural network, two GNN variants, namely graph convolutional neural network (GCN) and graph attention neural network (GAT) were employed in the experiments. The results showed that GCNLM performs best in the simulation experiments within the training data distribution. However, GATLM exhibits superior performance in the simulation experiments outside the training data distribution and real experiments with breast-like phantoms. It demonstrated that the GATLM trained with simulation data can generalize well to situations outside the training data distribution without transfer training. This offers the possibility to provide more accurate absorption coefficient distributions in clinical practice.

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.

Automated pipeline for breast cancer diagnosis using US assisted diffuse optical tomography.

Ultrasound (US)-guided diffuse optical tomography (DOT) is a portable and non-invasive imaging modality for breast cancer diagnosis and treatment response monitoring. However, DOT data pre-processing and imaging reconstruction often require labor intensive manual processing which hampers real-time diagnosis. In this study, we aim at providing an automated US-assisted DOT pre-processing, imaging and diagnosis pipeline to achieve near real-time diagnosis. We have developed an automated DOT pre-processing method including motion detection, mismatch classification using deep-learning approach, and outlier removal. US-lesion information needed for DOT reconstruction was extracted by a semi-automated lesion segmentation approach combined with a US reading algorithm. A deep learning model was used to evaluate the quality of the reconstructed DOT images and a two-step deep-learning model developed earlier is implemented to provide final diagnosis based on US imaging features and DOT measurements and imaging results. The presented US-assisted DOT pipeline accurately processed the DOT measurements and reconstruction and reduced the procedure time to 2 to 3 minutes while maintained a comparable classification result with manually processed dataset.

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.

One-dimensional convolutional neural network for Jacobian in Diffuse Optical Tomography.

Non-linear least square minimization algorithms are often employed to solve Diffuse Optical Tomography (DOT) inverse problem. However, it is time-consuming to calculate the Jacobian matrix. This work has proposed a data-driven neural network method to improve computational efficiency. The singular value decomposition is employed to compute the updated Jacobian and a mapping from boundary measurements to the singular values based on a convolutional neural network (CNN) is learned to obtain the singular values. The method is validated with 3D numerical simulation data. We have demonstrated that the approach can save computation time compared to Adjoint method, and reconstructed absorption coefficient close to Adjoint method.Clinical Relevance- These results are not focused on clinical relevance currently, but in the future may be helpful to accelerant DOT reconstruction in clinic.

Diffuse optical tomography spatial prior for EEG source localization in human visual cortex

Electroencephalography (EEG) and diffuse optical tomography (DOT) are imaging methods which are widely used for neuroimaging. While the temporal resolution of EEG is high, the spatial resolution is typically limited. DOT, on the other hand, has high spatial resolution, but the temporal resolution is inherently limited by the slow hemodynamics it measures. In our previous work, we showed using computer simulations that when using the results of DOT reconstruction as the spatial prior for EEG source reconstruction, high spatio-temporal resolution could be achieved. In this work, we experimentally validate the algorithm by alternatingly flashing two visual stimuli at a speed that is faster than the temporal resolution of DOT. We show that the joint reconstruction using both EEG and DOT clearly resolves the two stimuli temporally, and the spatial confinement is drastically improved in comparison to reconstruction using EEG alone.

Fusion deep learning approach combining diffuse optical tomography and ultrasound for improving breast cancer classification.

Diffuse optical tomography (DOT) is a promising technique that provides functional information related to tumor angiogenesis. However, reconstructing the DOT function map of a breast lesion is an ill-posed and underdetermined inverse process. A co-registered ultrasound (US) system that provides structural information about the breast lesion can improve the localization and accuracy of DOT reconstruction. Additionally, the well-known US characteristics of benign and malignant breast lesions can further improve cancer diagnosis based on DOT alone. Inspired by a fusion model deep learning approach, we combined US features extracted by a modified VGG-11 network with images reconstructed from a DOT deep learning auto-encoder-based model to form a new neural network for breast cancer diagnosis. The combined neural network model was trained with simulation data and fine-tuned with clinical data: it achieved an AUC of 0.931 (95% CI: 0.919-0.943), superior to those achieved using US images alone (0.860) or DOT images alone (0.842).

Tikhonov regularization-based extended Kalman filter technique for robust and accurate reconstruction in diffuse optical tomography.

Diffuse optical tomography (DOT) is a non-invasive imaging modality that uses near-infrared light to probe the optical properties of tissue. In conventionally used deterministic methods for DOT inversion, the measurement errors were not taken into account, resulting in unsatisfactory noise robustness and, consequently, affecting the DOT image reconstruction quality. In order to overcome this defect, an extended Kalman filter (EKF)-based DOT reconstruction algorithm was introduced first, which improved the reconstruction results by incorporating a priori information and measurement errors to the model. Further, to mitigate the instability caused by the ill-condition of the observation matrix in the tomographic imaging problem, a new, to the best of our knowledge, estimation algorithm was derived by incorporating Tikhonov regularization to the EKF method. To verify the effectiveness of the EKF algorithm and Tikhonov regularization-based EKF algorithm for DOT imaging, a series of numerical simulations and phantom experiments were conducted, and the experimental results were quantitatively evaluated and compared with two conventionally used deterministic methods involving the algebraic reconstruction technique and Levenberg-Marquardt algorithm. The results show that the two EKF-based algorithms can accurately estimate the location and size of the target, and the imaging accuracy and noise robustness are obviously improved. Furthermore, the Tikhonov regularization-based EKF obtained optimal parameter estimations, especially under the circumstance of low absorption contrast (1.2) and high noise level (10%).

Diffusion optical tomography reconstruction based on convex–nonconvex graph total variation regularization

Graph total variation (GTV) is a powerful regularization tool for diffuse optical tomography (DOT) reconstruction since it combines the powerful representation ability of graph and the edge‐preserving ability of total variation (TV) regularization. However, as everyone knows, the classical TV regularization trend underestimates the large edge values. In this paper, we propose a convex–nonconvex graph total variation (CNC‐GTV) regularization for DOT reconstruction. In particular, we construct a nonconvex regularization by subtracting the generalized Huber function from the GTV regularization. We show that the global convexity of the objective function can be guaranteed by adjusting the nonconvex control parameters. Moreover, we present an alternating direction multiplier method (ADMM) to solve the proposed DOT reconstruction model. Numerical experiments show that the proposed model outperforms existing models in visual and numerical results.

A Rapid, Low-Cost, and High-Precision Multifrequency Electrical Impedance Tomography Data Acquisition System for Plant Phenotyping

Plant phenotyping plays an important role for the thorough assessment of plant traits such as growth, development, and physiological processes with the target of achieving higher crop yields by the proper crop management. The assessment can be done by utilizing two- and three-dimensional image reconstructions of the inhomogeneities. The quality of the reconstructed image is required to maintain a high accuracy and a good resolution, and it is desirable to reconstruct the images with the lowest possible noise. In this work, an electrical impedance tomography (EIT) data acquisition system is developed for the reconstruction and evaluation of the inhomogeneities by utilizing a non-destructive method. A high-precision EIT system is developed by designing an electrode array sensor using a cylindrical domain for the measurements in different planes. Different edible plant slices along with multiple plant roots are taken in the EIT domain to assess and calibrate the system, and their reconstructed results are evaluated by utilizing an impedance imaging technique. A non-invasive imaging is carried out in multiple frequencies by utilizing a difference method of reconstruction. The performance and accuracy of the EIT system are evaluated by measuring impedances between 1 and 100 kHz using a low-cost and rapid electrical impedance spectroscopy (EIS) tool connected to the sensor. A finite element method (FEM) modeling is utilized for image reconstruction, which is carried out using electrical impedance and diffuse optical tomography reconstruction software (EIDORS). The reconstruction is made successfully with the optimized results obtained using Gauss–Newton (GN) algorithms.

An In Situ Electrical Impedance Tomography Sensor System for Biomass Estimation of Tap Roots.

Root biomass is one of the most relevant root parameters for studies of plant response to environmental change. In this work, a dynamic and adjustable electrode array sensor system is designed for developing a cost-effective, high-speed data acquisition system based on electrical impedance tomography (EIT). The developed EIT system is found to be suitable for in situ measurements and capable of monitoring the changes in root growth and development with three-dimensional imaging by measuring impedances in multiple frequencies with the help of an EIT sensor. The designed EIT sensor system is assessed and calibrated by the inhomogeneities in both water and soil media. The impedances are measured for multiple tap roots using an electrical impedance spectroscopy (EIS) tool connected to the sensor at frequencies ranging from 1 kHz to 100 kHz. The changes in conductivity are calculated by obtaining the boundary voltages from the measured impedances for a given stimulation current. A non-invasive imaging method is utilized, and the spectral changes are observed accordingly to evaluate the growth of the roots. A further root analysis helps us estimate the root biomass non-destructively in real-time. The root size (such as, weight, length) is correlated with the measured impedances. A regression analysis is performed using the least square method, and more than 97% correlation is found for the biomass estimation of carrot roots with an RMSE of 4.516. The obtained models are later validated using a new and separate set of carrot root samples and the accuracy of the predicted models is found to be 93% or above. A complete electrode model is utilized, and the reconstruction analysis is performed and optimized by utilizing the impedance imaging technique in difference method. The tomography of the root is reconstructed with finite element method (FEM) modeling considering one-step Gauss–Newton (GN) algorithm which is carried out using an open source software known as electrical impedance and diffuse optical tomography reconstruction software (EIDORS).

Evaluation of a pipeline for simulation, reconstruction, and classification in ultrasound-aided diffuse optical tomography of breast tumors.

.SignificanceDiffuse optical tomography is an ill-posed problem. Combination with ultrasound can improve the results of diffuse optical tomography applied to the diagnosis of breast cancer and allow for classification of lesions.AimTo provide a simulation pipeline for the assessment of reconstruction and classification methods for diffuse optical tomography with concurrent ultrasound information.ApproachA set of breast digital phantoms with benign and malignant lesions was simulated building on the software VICTRE. Acoustic and optical properties were assigned to the phantoms for the generation of B-mode images and optical data. A reconstruction algorithm based on a two-region nonlinear fitting and incorporating the ultrasound information was tested. Machine learning classification methods were applied to the reconstructed values to discriminate lesions into benign and malignant after reconstruction.ResultsThe approach allowed us to generate realistic US and optical data and to test a two-region reconstruction method for a large number of realistic simulations. When information is extracted from ultrasound images, at least 75% of lesions are correctly classified. With ideal two-region separation, the accuracy is higher than 80%.ConclusionsA pipeline for the generation of realistic ultrasound and diffuse optics data was implemented. Machine learning methods applied to a optical reconstruction with a nonlinear optical model and morphological information permit to discriminate malignant lesions from benign ones.

Regression-based neural network for improving image reconstruction in diffuse optical tomography.

Diffuse optical tomography (DOT) is a non-invasive imaging technique utilizing multi-scattered light at visible and infrared wavelengths to detect anomalies in tissues. However, the DOT image reconstruction is based on solving the inverse problem, which requires massive calculations and time. In this article, for the first time, to the best of our knowledge, a simple, regression-based cascaded feed-forward deep learning neural network is derived to solve the inverse problem of DOT in compressed breast geometry. The predicted data is subsequently utilized to visualize the breast tissues and their anomalies. The dataset in this study is created using a Monte-Carlo algorithm, which simulates the light propagation in the compressed breast placed inside a parallel plate source-detector geometry (forward process). The simulated DL-DOT system's performance is evaluated using the Pearson correlation coefficient (R) and the Mean squared error (MSE) metrics. Although a comparatively smaller dataset (50 nos.) is used, our simulation results show that the developed feed-forward network algorithm to solve the inverse problem delivers an increment of ∼30% over the analytical solution approach, in terms of R. Furthermore, the proposed network's MSE outperforms that of the analytical solution's MSE by a large margin revealing the robustness of the network and the adaptability of the system for potential applications in medical settings.

Diffuse optical reconstructions of functional near infrared spectroscopy data using maximum entropy on the mean

Functional near-infrared spectroscopy (fNIRS) measures the hemoglobin concentration changes associated with neuronal activity. Diffuse optical tomography (DOT) consists of reconstructing the optical density changes measured from scalp channels to the oxy-/deoxy-hemoglobin concentration changes within the cortical regions. In the present study, we adapted a nonlinear source localization method developed and validated in the context of Electro- and Magneto-Encephalography (EEG/MEG): the Maximum Entropy on the Mean (MEM), to solve the inverse problem of DOT reconstruction. We first introduced depth weighting strategy within the MEM framework for DOT reconstruction to avoid biasing the reconstruction results of DOT towards superficial regions. We also proposed a new initialization of the MEM model improving the temporal accuracy of the original MEM framework. To evaluate MEM performance and compare with widely used depth weighted Minimum Norm Estimate (MNE) inverse solution, we applied a realistic simulation scheme which contained 4000 simulations generated by 250 different seeds at different locations and 4 spatial extents ranging from 3 to 40text {cm}^2 along the cortical surface. Our results showed that overall MEM provided more accurate DOT reconstructions than MNE. Moreover, we found that MEM was remained particularly robust in low signal-to-noise ratio (SNR) conditions. The proposed method was further illustrated by comparing to functional Magnetic Resonance Imaging (fMRI) activation maps, on real data involving finger tapping tasks with two different montages. The results showed that MEM provided more accurate HbO and HbR reconstructions in spatial agreement with the main fMRI cluster, when compared to MNE.

A low-cost, portable, two-dimensional bioimpedance distribution estimation system based on the AD5933 impedance converter

This study proposes a low-cost, portable, eight-channel electrical impedance tomograph based on the AD5933 impedance converter. The patterns for current injection and voltage measurement are managed by an Arduino Mega 2560 board and four 74HC4067 Texas Instruments multiplexers. Regarding the experimental results, the errors in the impedance estimates of an electrical circuit that represents a Cole model were less than 1.14% for the magnitude and 4.15% for the phase. Furthermore, the signal-to-noise ratio measured in a resistive phantom was 55.23 dB. Additional experiments consisted of placing five spheres of different size and conductivity in a saline tank, measuring their impedance through eight electrodes, and then generating impedance maps using the Electrical Impedance Tomography and Diffuse Optical Tomography Reconstruction Software (EIDORS). These maps were different for each sphere, suggesting the proposed prototype as a promising alternative for medical applications.

Reconstruction and Localization of Tumors in Breast Optical Imaging via Convolution Neural Network Based on Batch Normalization Layers

The Near-Infrared (NIR) Diffuse Optical Tomography (DOT) aims to reconstruct optical-property images of tissue and identify and localize breast tumors. This study has developed an efficient and fast DOT reconstruction method based on Deep Learning (DL) algorithm. The DL has already been applied in DOT application with limitations such as a limited dataset and the reconstruction of absorption coefficients only. We solve the problem of a limited dataset by generating a large dataset with multiple phantoms and inclusions at various positions. Moreover, a single Deep Neural Network (DNN) model has been designed to reconstruct absorption coefficients and scattering coefficients. For evaluation of the proposed DNN models, the phantom experimental dataset has been used where the results of the proposed DNN models outperform the results of the Tikhonov Regularization (TR) method and other Artificial Neural Networks (ANN). Moreover, it is shown that the DNN model with batch normalization layer results in improved spatial resolution, based on Contrast-and-Size Detail (CSD) analysis, as compared to DNN models without batch normalization layers.

A Data Self-Calibration Method Based on High-Density Parallel Plate Diffuse Optical Tomography for Breast Cancer Imaging.

When performing the diffuse optical tomography (DOT) of the breast, the mismatch between the forward model and the experimental conditions will significantly hinder the reconstruction accuracy. Therefore, the reference measurement is commonly used to calibrate the measured data before the reconstruction. However, it is complicated to customize corresponding reference phantoms based on the breast shape and background optical parameters of different subjects in clinical trials. Furthermore, although high-density (HD) DOT configuration has been proven to improve imaging quality, a large number of source-detector (SD) pairs also increase the difficulty of multi-channel correction. To enhance the applicability of the breast DOT, a data self-calibration method based on an HD parallel-plate DOT system is proposed in this paper to replace the conventional relative measurement on a reference phantom. The reference predicted data can be constructed directly from the measurement data with the support of the HD-DOT system, which has nearly a hundred sets of measurements at each SD distance. The proposed scheme has been validated by Monte Carlo (MC) simulation, breast-size phantom experiments, and clinical trials, exhibiting the feasibility in ensuring the quality of the DOT reconstruction while effectively reducing the complexity associated with relative measurements on reference phantoms.

Deep learning-based method to accurately estimate breast tissue optical properties in the presence of the chest wall.

.Significance: In general, image reconstruction methods used in diffuse optical tomography (DOT) are based on diffusion approximation, and they consider the breast tissue as a homogenous, semi-infinite medium. However, the semi-infinite medium assumption used in DOT reconstruction is not valid when the chest wall is underneath the breast tissue.Aim: We aim to reduce the chest wall’s effect on the estimated average optical properties of breast tissue and obtain accurate forward model for DOT reconstruction.Approach: We propose a deep learning-based neural network approach where a convolution neural network (CNN) is trained to simultaneously obtain accurate optical property values for both the breast tissue and the chest wall.Results: The CNN model shows great promise in reducing errors in estimating the optical properties of the breast tissue in the presence of a shallow chest wall. For patient data, the CNN model predicted the breast tissue optical absorption coefficient, which was independent of chest wall depth.Conclusions: Our proposed method can be readily used in DOT and diffuse spectroscopy measurements to improve the accuracy of estimated tissue optical properties.

Machine learning model with physical constraints for diffuse optical tomography.

A machine learning model with physical constraints (ML-PC) is introduced to perform diffuse optical tomography (DOT) reconstruction. DOT reconstruction is an ill-posed and under-determined problem, and its quality suffers by model mismatches, complex boundary conditions, tissue-probe contact, noise etc. Here, for the first time, we combine ultrasound-guided DOT with ML to facilitate DOT reconstruction. Our method has two key components: (i) a neural network based on auto-encoder is adopted for DOT reconstruction, and (ii) physical constraints are implemented to achieve accurate reconstruction. Both qualitative and quantitative results demonstrate that the accuracy of the proposed method surpasses that of existing models. In a phantom study, compared with the Born conjugate gradient descent (Born-CGD) reconstruction method, the ML-PC method decreases the mean percentage error of the reconstructed maximum absorption coefficient from 16.41% to 13.4% for high contrast phantoms and from 23.42% to 9.06% for low contrast phantoms, with improved depth distribution of the target absorption maps. In a clinical study, better contrast was obtained between malignant and benign breast lesions, with the ratio of the medians of the maximum absorption coefficient improved from 1.63 to 2.22.