Model-based Image Reconstruction Algorithm Research Articles

A machine learning decision criterion for reducing scan time for hyperspectral neutron computed tomography systems

We present the first machine learning-based autonomous hyperspectral neutron computed tomography experiment performed at the Spallation Neutron Source. Hyperspectral neutron computed tomography allows the characterization of samples by enabling the reconstruction of crystallographic information and elemental/isotopic composition of objects relevant to materials science. High quality reconstructions using traditional algorithms such as the filtered back projection require a high signal-to-noise ratio across a wide wavelength range combined with a large number of projections. This results in scan times of several days to acquire hundreds of hyperspectral projections, during which end users have minimal feedback. To address these challenges, a golden ratio scanning protocol combined with model-based image reconstruction algorithms have been proposed. This novel approach enables high quality real-time reconstructions from streaming experimental data, thus providing feedback to users, while requiring fewer yet a fixed number of projections compared to the filtered back projection method. In this paper, we propose a novel machine learning criterion that can terminate a streaming neutron tomography scan once sufficient information is obtained based on the current set of measurements. Our decision criterion uses a quality score which combines a reference-free image quality metric computed using a pre-trained deep neural network with a metric that measures differences between consecutive reconstructions. The results show that our method can reduce the measurement time by approximately a factor of five compared to a baseline method based on filtered back projection for the samples we studied while automatically terminating the scans.

Towards quantitative in vivo dosimetry using x-ray acoustic computed tomography.

Radiation dosimetry is essential for radiation therapy (RT) to ensure that radiation dose is accurately delivered to the tumor. Despite its wide use in clinical intervention, the delivered radiation dose can only be planned and verified via simulation. This makes precision radiotherapy challenging while in-line verification of the delivered dose is still absent in the clinic. X-ray-induced acoustic computed tomography (XACT) has recently been proposed as an imaging tool for in vivo dosimetry. Most of the XACT studies focus on localizing the radiation beam. However, it has not been studied for its potential for quantitative dosimetry. The aim of this study was to investigate the feasibility of using XACT for quantitative in vivo dose reconstruction during radiotherapy. Varian Eclipse system was used to generate simulated uniform and wedged 3D radiation field with a size of 4 cm 4 cm. In order to use XACT for quantitative dosimetry measurements, we have deconvoluted the effects of both the x-ray pulse shape and the finite frequency response of the ultrasound detector. We developed a model-based image reconstruction algorithm to quantify radiation dose in vivo using XACT imaging, and universal back-projection (UBP) reconstruction is used as comparison. The reconstructed dose was calibrated before comparing it to the percent depth dose (PDD) profile. Structural similarity index matrix (SSIM) and root mean squared error (RMSE) are used for numeric evaluation. Experimental signals were acquired from 4 cm 4 cm radiation field created by Linear Accelerator (LINAC) at depths of 6, 8, and 10 cm beneath the water surface. The acquired signals were processed before reconstruction to achieve accurate results. Applying model-based reconstruction algorithm with non-negative constraints successfully reconstructed accurate radiation dose in 3D simulation study. The reconstructed dose matches well with the PDD profile after calibration in experiments. The SSIMs between the model-based reconstructions and initial doses are over 85%, and the RMSEs of model-based reconstructions are eight times lower than the UBP reconstructions. We have also shown that XACT images can be displayed as pseudo-color maps of acoustic intensity, which correspond to different radiation doses in the clinic. Our results show that the XACT imaging by model-based reconstruction algorithm is considerably more accurate than the dose reconstructed by UBP algorithm. With proper calibration, XACT is potentially applicable to the clinic for quantitative in vivo dosimetry across a wide range of radiation modalities. In addition, XACT's capability of real-time, volumetric dose imaging seems well-suited for the emerging field of ultrahigh dose rate "FLASH" radiotherapy.

A model-based image reconstruction algorithm for near real-time transcranial photoacoustic imaging

Photoacoustic imaging is a promising hybrid imaging modality that can visualize both microscopic and macroscopic structures and oxygenation changes in brain function. Phase aberration caused by the skull is a major barrier for high-quality photoacoustic imaging of the brain. Time-reversal methods have been used to address this issue, though they rely on solving the full-wave equation, and is therefore computationally heavy and slow. Herein, a near real-time model-based image reconstruction algorithm is proposed. The acoustic forward model is mathematically described as a model matrix and image reconstructions are performed by employing the pseudoinverse of the model matrix and calculating the initial pressure distribution. The pseudoinverse matrix only needs to be computed once for the same experimental setup and acoustic medium and is obtained offline prior to imaging. The proposed algorithm shows equivalent image quality but considerably faster reconstruction time (>40 times faster), compared to the time-reversal method and therefore could potentially enable near real-time photoacoustic imaging.

Joint Demosaicing and Fusion of Multiresolution Coded Acquisitions: A Unified Image Formation and Reconstruction Method

Novel optical imaging devices allow for hybrid acquisition modalities such as compressed acquisitions with locally different spatial and spectral resolutions captured by the same focal plane array. In this work, we propose to model a multiresolution coded acquisition (MRCA) in a generic framework, which natively includes acquisitions by conventional systems such as those based on spectral/color filter arrays, compressed coded apertures, and multiresolution sensing. We propose a model-based image reconstruction algorithm performing a joint demosaicing and fusion (JoDeFu) of any acquisition modeled in the MRCA framework. The JoDeFu reconstruction algorithm solves an inverse problem with a proximal splitting technique and is able to reconstruct an uncompressed image datacube at the highest available spatial and spectral resolution. An implementation of the code is available at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/danaroth83/jodefu</uri> .

Algorithm-Driven Advances for Scientific CT Instruments: From model-based to deep learning-based approaches

Multi-scale 3D characterization is widely used by materials scientists to further their understanding of the relationships between microscopic structure and macroscopic function. Scientific computed tomography (CT) instruments are one of the most popular choices for 3D non-destructive characterization of materials at length scales ranging from the angstrom-scale to the micron-scale. These instruments typically have a source of radiation that interacts with the sample to be studied and a detector assembly to capture the result of this interaction. A collection of such high-resolution measurements are made by re-orienting the sample which is mounted on a specially designed stage/holder after which reconstruction algorithms are used to produce the final 3D volume of interest. The end goal of scientific CT scans include determining the morphology,chemical composition or dynamic behavior of materials when subjected to external stimuli. In this article, we will present an overview of recent advances in reconstruction algorithms that have enabled significant improvements in the performance of scientific CT instruments - enabling faster, more accurate and novel imaging capabilities. In the first part, we will focus on model-based image reconstruction algorithms that formulate the inversion as solving a high-dimensional optimization problem involving a data-fidelity term and a regularization term. In the last part of the article, we will present an overview of recent approaches using deep-learning based algorithms for improving scientific CT instruments.

Model-based reconstruction for enhanced x-ray CT of dense tri-structural isotropic particles.

Tri-structural isotropic (TRISO) fuel particles are a key component of next generation nuclear fuels. Using x-ray computed tomography (CT) to characterize TRISO particles is challenging because of the strong attenuation of the x-ray beam by the uranium core, leading to severe photon starvation in a substantial fraction of the measurements. Furthermore, the overall acquisition time for a high-resolution CT scan can be very long when using conventional laboratory-based x-ray systems and reconstruction algorithms. Specifically, when analytic methods such as the Feldkamp-Davis-Kress (FDK) algorithm are used for reconstruction, it results in severe streak artifacts and noise in the corresponding 3D volume, which makes subsequent analysis of the particles challenging. In this paper, we develop and apply model-based image reconstruction (MBIR) algorithms to improve the quality of CT reconstructions for TRISO particles to facilitate better characterization. We demonstrate that the proposed MBIR algorithms can significantly suppress artifacts with minimal pre-processing compared to conventional approaches. We also demonstrate that the proposed MBIR approach can obtain high-quality reconstruction compared to the FDK approach even when using a fraction of the typically acquired measurements, thereby enabling dramatically faster measurement times for TRISO particles.

Improved Acquisition and Reconstruction for Wavelength-Resolved Neutron Tomography.

Wavelength-resolved neutron tomography (WRNT) is an emerging technique for characterizing samples relevant to the materials sciences in 3D. WRNT studies can be carried out at beam lines in spallation neutron or reactor-based user facilities. Because of the limited availability of experimental time, potential imperfections in the neutron source, or constraints placed on the acquisition time by the type of sample, the data can be extremely noisy resulting in tomographic reconstructions with significant artifacts when standard reconstruction algorithms are used. Furthermore, making a full tomographic measurement even with a low signal-to-noise ratio can take several days, resulting in a long wait time before the user can receive feedback from the experiment when traditional acquisition protocols are used. In this paper, we propose an interlaced scanning technique and combine it with a model-based image reconstruction algorithm to produce high-quality WRNT reconstructions concurrent with the measurements being made. The interlaced scan is designed to acquire data so that successive measurements are more diverse in contrast to typical sequential scanning protocols. The model-based reconstruction algorithm combines a data-fidelity term with a regularization term to formulate the wavelength-resolved reconstruction as minimizing a high-dimensional cost-function. Using an experimental dataset of a magnetite sample acquired over a span of about two days, we demonstrate that our technique can produce high-quality reconstructions even during the experiment compared to traditional acquisition and reconstruction techniques. In summary, the combination of the proposed acquisition strategy with an advanced reconstruction algorithm provides a novel guideline for designing WRNT systems at user facilities.

Momentum-Net: Fast and Convergent Iterative Neural Network for Inverse Problems.

Iterative neural networks (INN) are rapidly gaining attention for solving inverse problems in imaging, image processing, and computer vision. INNs combine regression NNs and an iterative model-based image reconstruction (MBIR) algorithm, often leading to both good generalization capability and outperforming reconstruction quality over existing MBIR optimization models. This paper proposes the first fast and convergent INN architecture, Momentum-Net, by generalizing a block-wise MBIR algorithm that uses momentum and majorizers with regression NNs. For fast MBIR, Momentum-Net uses momentum terms in extrapolation modules, and noniterative MBIR modules at each iteration by using majorizers, where each iteration of Momentum-Net consists of three core modules: image refining, extrapolation, and MBIR. Momentum-Net guarantees convergence to a fixed-point for general differentiable (non)convex MBIR functions (or data-fit terms) and convex feasible sets, under two asymptomatic conditions. To consider data-fit variations across training and testing samples, we also propose a regularization parameter selection scheme based on the "spectral spread" of majorization matrices. Numerical experiments for light-field photography using a focal stack and sparse-view computational tomography demonstrate that, given identical regression NN architectures, Momentum-Net significantly improves MBIR speed and accuracy over several existing INNs; it significantly improves reconstruction quality compared to a state-of-the-art MBIR method in each application.

Validation and Comparison of Monte Carlo and Finite Element Method in Forward Modeling for Near Infrared Optical Tomography.

Near infrared optical tomography (NIROT) is a non-invasive imaging technique to provide physiological information e.g. the oxygenation of tissue. For image reconstruction in clinical and preclinical scenarios, models to accurately describe light propagation are needed. This work aims to assess the accuracy and efficiency of different models, which paves the way for an optimal design of model-based image reconstruction algorithms in NIROT for realistic tissue geometries and heterogeneities. Two popular simulators were evaluated: the Monte Carlo (MC) method based MCX and the finite element method (FEM) based Toast++. We compared simulated results with experimental data measured on a homogeneous silicone phantom with well-calibrated parameters. The laser light was focused on the center of the phantom surface and images were captured by a CCD camera in both reflection and transmission modes. For transmittance measurements, the two models showed good agreement. Both achieve a cosine similarity of ~99%. In contrast, for reflectance measurements, FEM results deviated more from the measured values than MC, yielding similarity values of 86% and 94%, respectively. This study recommends the use of MC for NIROT in reflection mode and both MC and FEM yield excellent results for transmission mode.

High-density functional diffuse optical tomography based on frequency-domain measurements improves image quality and spatial resolution.

Measurements of dynamic near-infrared (NIR) light attenuation across the human head together with model-based image reconstruction algorithms allow the recovery of three-dimensional spatial brain activation maps. Previous studies using high-density diffuse optical tomography (HD-DOT) systems have reported improved image quality over sparse arrays. These HD-DOT systems incorporated multidistance overlapping continuous wave measurements that only recover differential intensity attenuation. We investigate the potential improvement in reconstructed image quality due to the additional incorporation of phase shift measurements, which reflect the time-of-flight of the measured NIR light, within the tomographic reconstruction from high-density measurements. To evaluate image reconstruction with and without the additional phase information, we simulated point spread functions across a whole-scalp field of view in 24 subject-specific anatomical models using an experimentally derived noise model. The addition of phase information improves the image quality by reducing localization error by up to 59% and effective resolution by up to 21% as compared to using the intensity attenuation measurements alone. Furthermore, we demonstrate that the phase data enable images to be resolved at deeper brain regions where intensity data fail, which is further supported by utilizing experimental data from a single subject measurement during a retinotopic experiment.

Image quality and dose characteristics for an O-arm intraoperative imaging system with model-based image reconstruction.

To assess the imaging performance and radiation dose characteristics of the O-arm CBCT imaging system (Medtronic Inc., Littleton MA) and demonstrate the potential for improved image quality and reduced dose via model-based image reconstruction (MBIR). Two main studies were performed to investigate previously unreported characteristics of the O-arm system. First is an investigation of dose and 3D image quality achieved with filtered back-projection (FBP) - including enhancements in geometric calibration, handling of lateral truncation and detector saturation, and incorporation of an isotropic apodization filter. Second is implementation of an MBIR algorithm based on Huber-penalized likelihood estimation (PLH) and investigation of image quality improvement at reduced dose. Each study involved measurements in quantitative phantoms as a basis for analysis of contrast-to-noise ratio and spatial resolution as well as imaging of a human cadaver to test the findings under realistic imaging conditions. View-dependent calibration of system geometry improved the accuracy of reconstruction as quantified by the full-width at half maximum of the point-spread function - from 0.80 to 0.65mm - and yielded subtle but perceptible improvement in high-contrast detail of bone (e.g., temporal bone). Standard technique protocols for the head and body imparted absorbed dose of 16 and 18mGy, respectively. For low-to-medium contrast (<100HU) imaging at fixed spatial resolution (1.3mm edge-spread function) and fixed dose (6.7mGy), PLH improved CNR over FBP by +48% in the head and +35% in the body. Evaluation at different dose levels demonstrated 30% increase in CNR at 62% of the dose in the head and 90% increase in CNR at 50% dose in the body. A variety of improvements in FBP implementation (geometric calibration, truncation and saturation effects, and isotropic apodization) offer the potential for improved image quality and reduced radiation dose on the O-arm system. Further gains are possible with MBIR, including improved soft-tissue visualization, low-dose imaging protocols, and extension to methods that naturally incorporate prior information of patient anatomy and/or surgical instrumentation.

Comparison Between Pre-Log and Post-Log Statistical Models in Ultra-Low-Dose CT Reconstruction

X-ray detectors in clinical computed tomography (CT) usually operate in current-integrating mode. Their complicated signal statistics often lead to intractable likelihood functions for practical use in model-based image reconstruction (MBIR). It is therefore desirable to design simplified statistical models without losing the essential factors. Depending on whether the CT transmission data are logarithmically transformed, pre-log and post-log models are two major categories of choices in CT MBIR. Both being approximations, it remains an open question whether one model can notably improve image quality over the other on real scanners. In this study, we develop and compare several pre-log and post-log MBIR algorithms under a unified framework. Their reconstruction accuracy based on simulation and clinical datasets are evaluated. The results show that pre-log MBIR can achieve notably better quantitative accuracy than post-log MBIR in ultra-low-dose CT, although in less extreme cases, post-log MBIR with handcrafted pre-processing remains a competitive alternative. Pre-log MBIR could play a growing role in emerging ultra-low-dose CT applications.

A linear, separable two-parameter model for dual energy CT imaging of proton stopping power computation.

To evaluate the accuracy and robustness of a simple, linear, separable, two-parameter model (basis vector model, BVM) in mapping proton stopping powers via dual energy computed tomography (DECT) imaging. The BVM assumes that photon cross sections (attenuation coefficients) of unknown materials are linear combinations of the corresponding radiological quantities of dissimilar basis substances (i.e., polystyrene, CaCl2 aqueous solution, and water). The authors have extended this approach to the estimation of electron density and mean excitation energy, which are required parameters for computing proton stopping powers via the Bethe-Bloch equation. The authors compared the stopping power estimation accuracy of the BVM with that of a nonlinear, nonseparable photon cross section Torikoshi parametric fit model (VCU tPFM) as implemented by the authors and by Yang et al. ["Theoretical variance analysis of single- and dual-energy computed tomography methods for calculating proton stopping power ratios of biological tissues," Phys. Med. Biol. 55, 1343-1362 (2010)]. Using an idealized monoenergetic DECT imaging model, proton ranges estimated by the BVM, VCU tPFM, and Yang tPFM were compared to International Commission on Radiation Units and Measurements (ICRU) published reference values. The robustness of the stopping power prediction accuracy of tissue composition variations was assessed for both of the BVM and VCU tPFM. The sensitivity of accuracy to CT image uncertainty was also evaluated. Based on the authors' idealized, error-free DECT imaging model, the root-mean-square error of BVM proton stopping power estimation for 175 MeV protons relative to ICRU reference values for 34 ICRU standard tissues is 0.20%, compared to 0.23% and 0.68% for the Yang and VCU tPFM models, respectively. The range estimation errors were less than 1 mm for the BVM and Yang tPFM models, respectively. The BVM estimation accuracy is not dependent on tissue type and proton energy range. The BVM is slightly more vulnerable to CT image intensity uncertainties than the tPFM models. Both the BVM and tPFM prediction accuracies were robust to uncertainties of tissue composition and independent of the choice of reference values. This reported accuracy does not include the impacts of I-value uncertainties and imaging artifacts and may not be achievable on current clinical CT scanners. The proton stopping power estimation accuracy of the proposed linear, separable BVM model is comparable to or better than that of the nonseparable tPFM models proposed by other groups. In contrast to the tPFM, the BVM does not require an iterative solving for effective atomic number and electron density at every voxel; this improves the computational efficiency of DECT imaging when iterative, model-based image reconstruction algorithms are used to minimize noise and systematic imaging artifacts of CT images.

5D respiratory motion model based image reconstruction algorithm for 4D cone-beam computed tomography

4D cone-beam computed tomography (4DCBCT) reconstructs a temporal sequence of CBCT images for the purpose of motion management or 4D treatment in radiotherapy. However the image reconstruction often involves the binning of projection data to each temporal phase, and therefore suffers from deteriorated image quality due to inaccurate or uneven binning in phase, e.g., under the non-periodic breathing. A 5D model has been developed as an accurate model of (periodic and non-periodic) respiratory motion. That is, given the measurements of breathing amplitude and its time derivative, the 5D model parametrizes the respiratory motion by three time-independent variables, i.e., one reference image and two vector fields. In this work we aim to develop a new 4DCBCT reconstruction method based on 5D model. Instead of reconstructing a temporal sequence of images after the projection binning, the new method reconstructs time-independent reference image and vector fields with no requirement of binning. The image reconstruction is formulated as a optimization problem with total-variation regularization on both reference image and vector fields, and the problem is solved by the proximal alternating minimization algorithm, during which the split Bregman method is used to reconstruct the reference image, and the Chambolle's duality-based algorithm is used to reconstruct the vector fields. The convergence analysis of the proposed algorithm is provided for this nonconvex problem. Validated by the simulation studies, the new method has significantly improved image reconstruction accuracy due to no binning and reduced number of unknowns via the use of the 5D model.

Multi-channel beam-scanning imaging at kHz frame rates by Lissajous trajectory microscopy.

A beam-scanning microscope based on Lissajous trajectory imaging is described for achieving streaming 2D imaging with continuous frame rates up to 1.4 kHz. The microscope utilizes two fast-scan resonant mirrors to direct the optical beam on a circuitous trajectory through the field of view. By separating the full Lissajous trajectory time-domain data into sub-trajectories (partial, undersampled trajectories) effective frame-rates much higher than the repeat time of the Lissajous trajectory are achieved with many unsampled pixels present. A model-based image reconstruction (MBIR) 3D in-painting algorithm is then used to interpolate the missing data for the unsampled pixels to recover full images. The MBIR algorithm uses a maximum a posteriori estimation with a generalized Gaussian Markov random field prior model for image interpolation. Because images are acquired using photomultiplier tubes or photodiodes, parallelization for multi-channel imaging is straightforward. Preliminary results show that when combined with the MBIR in-painting algorithm, this technique has the ability to generate kHz frame rate images across 6 total dimensions of space, time, and polarization for SHG, TPEF, and confocal reflective birefringence data on a multimodal imaging platform for biomedical imaging. The use of a multi-channel data acquisition card allows for multimodal imaging with perfect image overlay. Image blur due to sample motion was also reduced by using higher frame rates.

Gas/oil/water flow measurement by electrical capacitance tomography

In the oil industry, it is important to measure gas/oil/water flows produced from oil wells. To determine oil production, it is necessary to measure the water-in-liquid ratio (WLR), liquid fraction and some other parameters, which are related to multiphase flow rates. A research team from the University of Manchester and Schlumberger Gould Research have developed an experimental apparatus for gas/oil/water flow measurement based on a flow-conditioning device and electrical capacitance tomography (ECT) and microwave sensors. This paper presents the ECT part of the developed apparatus, including the re-engineering of an ECT sensor and a model-based image reconstruction algorithm, which is used to derive the WLR and the thickness of the liquid layer in oil-continuous annular flows formed by the flow-conditioning device. The ECT sensor was tested both at Schlumberger and on TUV-NEL's Multiphase Flow Facility. The experimental results are promising.

An efficient Jacobian reduction method for diffuse optical image reconstruction

Model based image reconstruction in Diffuse Optical Tomography relies on both the numerical accuracy of the forward model as well as the computational speed and efficiency of the inverse model. Most model based image reconstruction algorithms rely on Newton type inversion methods, whereby the inverse of a large Jacobian is approximated. In this work we present an efficient Jacobian reduction method which takes into account the total sensitivity of the imaging domain to the measured boundary data. It is shown using numerical and phantom data that by removing regions within the inverse model whose contribution to the measured data is less than 1%, it has no significant effect upon the estimated inverse problem, but does provide up to a 14 fold improvement in computational time.

Statistical analysis of nonlinearly reconstructed near-infrared tomographic images: Part I--Theory and simulations.

Near-infrared (NIR) diffuse tomography is an emerging method for imaging the interior of tissues to quantify concentrations of hemoglobin and exogenous chromophores non-invasively in vivo. It often exploits an optical diffusion model-based image reconstruction algorithm to estimate spatial property values from measurements of the light flux at the surface of the tissue. In this study, mean-squared error (MSE) over the image is used to evaluate methods for regularizing the ill-posed inverse image reconstruction problem in NIR tomography. Estimates of image bias and image standard deviation were calculated based upon 100 repeated reconstructions of a test image with randomly distributed noise added to the light flux measurements. It was observed that the bias error dominates at high regularization parameter values while variance dominates as the algorithm is allowed to approach the optimal solution. This optimum does not necessarily correspond to the minimum projection error solution, but typically requires further iteration with a decreasing regularization parameter to reach the lowest image error. Increasing measurement noise causes a need to constrain the minimum regularization parameter to higher values in order to achieve a minimum in the overall image MSE.

Microwave image reconstruction utilizing log-magnitude and unwrapped phase to improve high-contrast object recovery.

Reconstructing images of large high-contrast objects with microwave methods has proved difficult. Successful images have generally been obtained by using a priori information to constrain the image reconstruction to recover the correct electromagnetic property distribution. In these situations, the measured electric field phases as a function of receiver position around the periphery of the imaging field-of-view vary rapidly often undergoing changes of greater than pi radians especially when the object contrast and illumination frequency increase. In this paper, we introduce a modified form of a Maxwell equation model-based image reconstruction algorithm which directly incorporates log-magnitude and phase of the measured electric field data. By doing so, measured phase variation can be unwrapped and distributed over more than one Rieman sheet in the complex plane. Simulation studies and microwave imaging experiments demonstrate that significant image quality enhancements occur with this approach for large high-contrast objects. Simple strategies for visualizing and unwrapping phase values as a function of the transmitter and receiver positions within our microwave imaging array are described. Metrics of the degree of phase variation expressed in terms of the amount and extent of phase wrapping are defined and found to be figures-of-merit which estimate when it is critical to deploy the new image reconstruction approach. In these cases, the new algorithm recovers high-quality images without resorting to the use of a priori information on object contrast and/or size as previously required.