Accurate Forward Model Research Articles

Radiative transfer equation modeling by streamline diffusion modified continuous Galerkin method.

Optical tomography has a wide range of biomedical applications. Accurate prediction of photon transport in media is critical, as it directly affects the accuracy of the reconstructions. The radiative transfer equation (RTE) is the most accurate deterministic forward model, yet it has not been widely employed in practice due to the challenges in robust and efficient numerical implementations in high dimensions. Herein, we propose a method that combines the discrete ordinate method (DOM) with a streamline diffusion modified continuous Galerkin method to numerically solve RTE. Additionally, a phase function normalization technique was employed to dramatically reduce the instability of the DOM with fewer discrete angular points. To illustrate the accuracy and robustness of our method, the computed solutions to RTE were compared with Monte Carlo (MC) simulations when two types of sources (ideal pencil beam and Gaussian beam) and multiple optical properties were tested. Results show that with standard optical properties of human tissue, photon densities obtained using RTE are, on average, around 5% of those predicted by MC simulations in the entire/deeper region. These results suggest that this implementation of the finite element method-RTE is an accurate forward model for optical tomography in human tissues.

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.

Comprehensive simulation platform for a metamaterial imaging system.

Recently, a frequency-diverse, metamaterial-based aperture has been introduced in the context of microwave and millimeter wave imaging. The generic form of the aperture is that of a parallel plate waveguide, in which complementary metamaterial elements patterned into the upper plate couple energy from the waveguide mode to the scene. To reliably predict the imaging performance of such an aperture prior to fabrication and experiments, it is necessary to have an accurate forward model that predicts radiation from the aperture, a model for scattering from an arbitrary target in the scene, and a set of image reconstruction approaches that allow scene estimation from an arbitrary set of measurements. Here, we introduce a forward model in which the metamaterial elements are approximated as polarizable magnetic dipoles, excited by the fields propagating within the waveguide. The dipoles used in the model can have arbitrarily assigned polarizability characteristics. Alternatively, fields measured from actual metamaterial samples can be decomposed into a set of effective dipole radiators, allowing the performance of actual samples to be quantitatively modeled and compared with simulated apertures. To confirm the validity of our model, we simulate measurements and scene reconstructions with a virtual multiaperture imaging system operating in the K-band spectrum (18-26.5 GHz) and compare its performance with an experimental system.

A passive and active microwave-vector radiative transfer (PAM-VRT) model

A passive and active microwave vector radiative transfer (PAM-VRT) package has been developed. This fast and accurate forward microwave model, with flexible and versatile input and output components, self-consistently and realistically simulates measurements/radiation of passive and active microwave sensors. The core PAM-VRT, microwave radiative transfer model, consists of five modules: gas absorption (two line-by-line databases and four fast models); hydrometeor property of water droplets and ice (spherical and nonspherical) particles; surface emissivity (from Community Radiative Transfer Model (CRTM)); vector radiative transfer of successive order of scattering (VSOS); and passive and active microwave simulation. The PAM-VRT package has been validated against other existing models, demonstrating good accuracy. The PAM-VRT not only can be used to simulate or assimilate measurements of existing microwave sensors, but also can be used to simulate observation results at some new microwave sensors.

An accurate and fast forward model of three‐dimensional electromagnetic wave scattering in a layered structure with multilayer rough interfaces

AbstractWe develop an accurate and fast forward model for calculating the compact closed‐form high‐order perturbative solutions of the problem of three‐dimensional (3‐D) radiation and propagation electromagnetic fields in a layered structure with multilayer rough interfaces. The proposed method for the fast forward model is first demonstrated by strictly theoretical formulas derivation in the framework of classical small perturbation method (SPM) without other else approximation and equivalent process. The kernel functions of high order are proposed for calculating the radar cross sections with more efficiency and clear physical meanings for better use in practice. What is more, we give the clear physical interpretation of the first‐order fully polarimetric electromagnetic wave scattering mechanism in the layered structure with multilayer rough interfaces. The proposed forward model is necessary to insure a successful inversion process. Furthermore, the high‐order SPM solutions derived by employing the proposed method are validated with existing methods and numerical results. Finally, we study the performance of the high‐order fully polarimetric electromagnetic wave scattering according to the numerical results and analyze the scattering enhancement phenomena.

Adaptive SPECT imaging with crossed-slit apertures.

Preclinical single-photon emission computed tomography (SPECT) is an essential tool for studying the progression, response to treatment, and physiological changes in small animal models of human disease. The wide range of imaging applications is often limited by the static design of many preclinical SPECT systems. We have developed a prototype imaging system that replaces the standard static pinhole aperture with two sets of movable, keel-edged copper-tungsten blades configured as crossed (skewed) slits. These apertures can be positioned independently between the object and detector, producing a continuum of imaging configurations in which the axial and transaxial magnifications are not constrained to be equal. We incorporated a megapixel silicon double-sided strip detector to permit ultrahigh-resolution imaging. We describe the configuration of the adjustable slit aperture imaging system and discuss its application toward adaptive imaging, and reconstruction techniques using an accurate imaging forward model, a novel geometric calibration technique, and a GPU-based ultra-high-resolution reconstruction code.

TU‐A‐9A‐03: Development and Verification of a Forward Model That Assists in Iterative Post‐Processing Algorithms Used to Reduce Blur in Compton Backscatter Imaging Systems

Purpose:In Compton Backscatter Imaging (CBI), the source and detector reside on the same side of the patient. We previously demonstrated the applicability of CBI systems for medical purposes using an industrial system. To assist in post‐processing images from a CBI system, a forward model based on radiation absorption and scatter principles has been developed.Methods:The forward model was developed in C++ using raytracing to track particles. The algorithm accepts phantoms of any size and resolution to calculate the fraction of incident photons scattered back to the detector, and can perform these calculations for any detector geometry and source specification. To validate the model, results were compared to MCNP‐X, which is a Monte Carlo based simulation software, for various combinations of source specifications, detector geometries, and phantom compositions.Results:The model verified that the backscatter signal to the detector was based on three interaction probabilities: a) attenuation of photons going into the phantom, b) Compton scatter of photons toward the detector, and c) attenuation of photons coming out of the phantom. The results from the MCNP‐X simulations and the forward model varied from 1 to 5%. This difference was less than 1% for energies higher than 30 keV, but was up to 4% for lower energies. At 50 keV, the difference was less than 1% for multiple detector widths and for both homogeneous and heterogeneous phantoms.Conclusion:As part of the optimization of a medical CBI system, an efficient and accurate forward model was constructed in C++ to estimate the output of CBI system. The model characterized individual components contributing to CBI output and increased computational efficiency over Monte Carlo simulations. It is now used in the development of novel post‐processing algorithms that reduce image blur by reversing undesired contribution from outside the region of interest.

CH4 retrieval from hyperspectral satellite measurements in short-wave infrared: sensitivity study and preliminary test with GOSAT data

One of the important science requirements of monitoring atmospheric methane abundances from hyperspectral measurements is to establish a highly accurate retrieval algorithm. This paper aimed to describe a retrieval algorithm based on a series of sensitivity study with an effective and accurate forward model, which was applied to realize online calculation of absorption coefficient and backscattered solar radiance. The sensitivity study consisted of band selection, interference factors analysis, and retrieval model construction. The band selection analysis indicated that the 1.65 μm band (5,900–6,150 cm−1) associated with the 2.06 μm band (4,800–4,900 cm−1) retained more than 90 % of the information content of CH4, CO2, and temperature, and more than 85 % of that of H2O in the retrieval. Investigation of the interference factors showed that H2O, temperature, and CO2 will cause unacceptable errors if they are not revised. This also showed that revising temperature and H2O with a profile model is more efficient than with a temperature offset and a H2O scale factor model. A preliminarily test using the Greenhouse gases Observing SATellite Level 1B spectral data indicated that most of the retrieval errors were less than 1 %, which is acceptable for methane flux estimation.

Application of stochastic Galerkin FEM to the complete electrode model of electrical impedance tomography

The aim of electrical impedance tomography is to determine the internal conductivity distribution of some physical body from boundary measurements of current and voltage. The most accurate forward model for impedance tomography is the complete electrode model, which consists of the conductivity equation coupled with boundary conditions that take into account the electrode shapes and the contact resistances at the corresponding interfaces. If the reconstruction task of impedance tomography is recast as a Bayesian inference problem, it is essential to be able to solve the complete electrode model forward problem with the conductivity and the contact resistances treated as a random field and random variables, respectively. In this work, we apply a stochastic Galerkin finite element method to the ensuing elliptic stochastic boundary value problem and compare the results with Monte Carlo simulations.

Time reversal and microwave techniques for solving inverse problem in Non-Destructive Evaluation

Non-Destructive Evaluation (NDE) methods are used to inspect materials without damaging their usefulness. The key problem in NDE is the inverse problem which involves reconstructing materials’ physical profiles, like inner discontinuity etc., using information in the measured NDE signal. Inverse problem solutions in NDE can be classified as model-based and system-based approach. In model-based approach, an accurate forward model is used in an iterative framework. This approach provides a resultant materials' physical profile that minimizes the error between the measured signal and a simulated signal. However, this approach requires repeated calculations of a numerical model in each iteration, making it computationally demanding. This paper presents a model-based method that also provides a direct approach to inversion using principles of time reversal. Time reversal focusing is based on the fact that when a wave solution is reversed in time and back-propagated the wave comes to focus at the source. Using a computational model, this paper applies principles of time reversal to microwave NDE data to solve the inverse problem of defect detection in dielectric materials. A two-dimensional finite difference time domain (FDTD) model, for simulating the propagation of forward and time reversed wave fields, is developed. A dielectric sample with artificial defects, illuminated by a Gaussian modulated pulse, is used in the simulations. The microwave measurements are recorded, time reversed and propagated using the FDTD model to highlight the scatterer/defect. Maxima in the energy image indicate locations of defects. Simulation results demonstrate the feasibility of the technique to detect defects in dielectric materials. The FDTD model is validated using experimental data.

Utility of a novel error-stepping method to improve gradient-based parameter identification by increasing the smoothness of the local objective surface: A case-study of pulmonary mechanics

Accurate model parameter identification relies on accurate forward model simulations to guide convergence. However, some forward simulation methodologies lack the precision required to properly define the local objective surface and can cause failed parameter identification.The role of objective surface smoothness in identification of a pulmonary mechanics model was assessed using forward simulation from a novel error-stepping method and a proprietary Runge–Kutta method. The objective surfaces were compared via the identified parameter discrepancy generated in a Monte Carlo simulation and the local smoothness of the objective surfaces they generate.The error-stepping method generated significantly smoother error surfaces in each of the cases tested (p<0.0001) and more accurate model parameter estimates than the Runge–Kutta method in three of the four cases tested (p<0.0001) despite a 75% reduction in computational cost. Of note, parameter discrepancy in most cases was limited to a particular oblique plane, indicating a non-intuitive multi-parameter trade-off was occurring.The error-stepping method consistently improved or equalled the outcomes of the Runge–Kutta time-integration method for forward simulations of the pulmonary mechanics model. This study indicates that accurate parameter identification relies on accurate definition of the local objective function, and that parameter trade-off can occur on oblique planes resulting prematurely halted parameter convergence.

TH‐A‐103‐02: Initial Accuracy Assessment of a Post‐Processing DECT Method for Linear Attenuation Coefficient Estimation On a Commercial Fan Beam CT Scanner

Purpose: A post‐processing dual‐energy CT (pDECT) method for non‐invasive estimation of photon cross‐section information has been experimentally implemented on a commercial CT scanner and an initial accuracy assessment performed in an idealized phantom geometry. Methods: Eight test materials of known composition were used to compare pDECT‐estimated linear attenuation coefficients to NIST reference values over the energy range of 10‐1,000keV. CT sinogram data was acquired on a commercial fan beam CT scanner at 90 and 140kVp. Improvement from increased spectral separation was also investigated by additional filtration of the high‐energy beam with 0.5mm of tin. pDECT accuracy was compared using images reconstructed with a conventional filtered backprojection (FBP) algorithm and an in‐house statistical iterative reconstruction algorithm, Alternating Minimization (AM), since AM has been shown to reconstruct images with less random and systematic error than FBP. Results: Mean accuracy of pDECT‐estimated linear attenuation coefficients, assessed by averaging pixels (N&gt;149) within the test material, were found to be within 1% of reference for energies between 30‐1,000 keV, with errors rising to 3––6% at 10 keV. However, the sensitivity of the pDECT process to reconstructed image uncertainties leads to large pixel‐to‐pixel variations of estimated attenuation coefficients; in some cases a coefficient of variation on the order of 20% is seen. The AM algorithm noise advantage leads to attenuation coefficient standard deviations roughly 40% to 60% less than FBP. Measurements using increased spectral separation returned similar mean accuracy and slightly less pixel‐to‐pixel variation even when scanning with 25% of the unfiltered dose. Conclusion: The advantage of the AM algorithm over FBP in this idealized pDECT scenario is less random uncertainty. Increased spectral separation better conditions the pDECT problem. Future work intends to investigate pDECT accuracy in more complex phantom geometries where AM reconstruction may confer more advantage due to its more physically accurate forward model. This work was supported in part from grants (R01 CA 75371 and R01 CA149305, J. Williamson, Principal Investigator) awarded by the National Institutes of Health and a grant funded by Varian Medical Systems.

Approximation error method for full-wave tomography

In ultrasound tomography (UT), the speed of sound (SOS) is reconstructed based on ultrasound measurements made on the surface of the object. As a part of the reconstruction process, which includes the solution of the inverse problem, propagation of acoustic signals in the medium is simulated using a forward model. Consequently, modeling errors can generate artifacts into reconstructed SOS. Accurate full-wave models can be computationally heavy and thus impractical in many real applications. On the other hand, approximate models typically lead to less accurate reconstructions. In this study, measurement noise and modeling errors of UT are modeled in Bayesian framework, and a numerical method that takes both errors into account is developed. The performance of the method is investigated by numerical simulations in which artifacts generated by a fast but less accurate forward model and approximate boundary conditions are compensated.

SMOS Semi-Empirical Ocean Forward Model Adjustment

A prerequisite for the successful retrieval of geophysical parameters from remote sensing measurements is the development of an accurate forward model. The European Space Agency Soil Moisture and Ocean Salinity (SMOS), carrying onboard an L-band interferometric radiometer (Microwave Interferometric Radiometer using Aperture Synthesis), was launched on November 2009. Due to the lack of L-band passive ocean measurements from space, several prelaunch forward models were developed and initially used in the SMOS ocean salinity operational processor. In this paper, an update of the prelaunch semi-empirical forward model is presented, using for the first time, real SMOS data. In particular, the ocean surface emissivity modulation at L-band due to rough sea surface is reviewed and reanalyzed. A new model definition is provided with the help of a simple neural network. The improvement is quantified in terms of retrieved salinity accuracy compared with the climatology and concerns essentially the range of wind speeds higher than 12 m·s <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> .

On the [formula omitted]-adaptive solution of complete electrode model forward problems of electrical impedance tomography

Electrical impedance tomography is a noninvasive imaging technique based on measurements of currents and voltages on the boundary of the object of interest. The most accurate forward model for impedance tomography is the complete electrode model that takes into account the electrode shapes and the contact impedances at the corresponding interfaces; many practical reconstruction algorithms of electrical impedance tomography require repetitive computation of accurate forward solutions for the complete model. In this work, we introduce an hp-adaptive finite element method for solving the complete electrode forward problem and demonstrate its functionality via two-dimensional numerical studies.

The influence of visual motion on interceptive actions and perception

Visual information is an essential guide when interacting with moving objects, yet it can also be deceiving. For instance, motion can induce illusory position shifts, such that a moving ball can seem to have bounced past its true point of contact with the ground. Some evidence suggests illusory motion-induced position shifts bias pointing tasks to a greater extent than they do perceptual judgments. This, however, appears at odds with other findings and with our success when intercepting moving objects. Here we examined the accuracy of interceptive movements and of perceptual judgments in relation to simulated bounces. Participants were asked to intercept a moving disc at its bounce location by positioning a virtual paddle, and then to report where the disc had landed. Results showed that interceptive actions were accurate whereas perceptual judgments were inaccurate, biased in the direction of motion. Successful interceptions necessitated accurate information concerning both the location and timing of the bounce, so motor planning evidently had privileged access to an accurate forward model of bounce timing and location. This would explain why people can be accurate when intercepting a moving object, but lack insight into the accurate information that had guided their actions when asked to make a perceptual judgment.

On the feasibility of a fast forward model for Doppler interferometry in the infrared

AbstractA fast forward radiative transfer model to compute the emitted limb radiances for use in recovering line‐of‐sight Doppler winds from thermal line emission has been developed and evaluated. This study was formulated around the Stratospheric Wind Interferometer for Transport Studies (SWIFT) instrument—a limb imaging, field widened, phase‐stepping Michelson interferometer. The fast forward model is required to simulate a four‐point interferogram from which line‐of‐sight winds may be computed. The model, RT‐SWIFT (Radiative Transfer for SWIFT), is part of an effort to develop the capability of providing simultaneous measurements of horizontal wind velocity vectors and ozone concentration in the stratosphere for improving our understanding of global stratospheric dynamics and for studies in ozone transport.Based in part on RT‐MIPAS (Radiative Transfer for the Michelson Interferometer for Passive Atmospheric Sounding), RT‐SWIFT uses a linear regression algorithm to parametrize the effective layer optical depths and can simulate the effect of variable ozone, nitrous oxide, water vapour and atmospheric winds. Trace gases are included as fixed climatological profiles.The model development involved the selection of two suitable databases consisting of appropriate atmospheric absorber and wind profiles, and the accurate line‐by‐line modelling of their transmittances; one for generating regression coefficients and one consisting of simulated measurements for independent evaluation. The development also required selecting suitable predictors for the absorbers, winds and viewing geometry.One‐dimensional inversion results using RT‐SWIFT with simulated measurements indicate that the model leads to wind and ozone error levels of about 3 to 5 m s−1 and 3 to 15% respectively for altitudes above ∼24 km. While further investment in model development and optimization is warranted, this demonstration study indicates that a sufficiently accurate fast forward model for near real‐time assimilation, and inversion, of horizontal Doppler wind measurements from thermal line emission is feasible. © 2011 Crown in the right of Canada. Published by John Wiley &amp; Sons Ltd.

An H∞ approach for robust estimation of material parameters in electrical capacitance tomography

The stable solution of ill-posed inverse problems like that of electrical capacitance tomography (ECT) relies on the availability of an accurate forward model. However, due to discretization or neglected effects model errors are omnipresent. The error amplitudes of these model errors are often in the same range as typical measurement errors and can even increase their amplitude. In this paper, we present an H∞ filter approach for robust parameter estimation in ECT. We work out the performance of H∞ theory compared to other methods (in particular Kalman filters) and demonstrate the improved error handling due to robust filter theory.

Modeling and reconstruction of optical tomography for endoscopic applications: Simulation demonstration

Applications of optical tomography in noninvasive cancer imaging have been restricted to specific organs that can be measured or transilluminated externally. However, these external measurements are limited to superficial area or small animals, and inaccurate or immeasurable for imaging the internal organ deep inside the large body. Endoscopic optical tomography (EOT) overcomes this limitation and improves this inaccuracy or immeasurability by taking the detector closer to the region of interest with a minimally invasive approach. In this letter, we present an endoscopic algorithm for EOT, including establishing a realistic endoscopic geometry, constructing an accurate forward model and advancing an effective inverse reconstruction algorithm. Bioluminescent mode based simulations show the accuracy and effectiveness of the endoscopic algorithm in both localization and quantification.

Crack identification in a freely vibrating plate using Bayesian parameter estimation

In this paper a new approach is proposed for identifying the presence and location of a crack in a simply supported plate undergoing free vibration. Specifically, the approach uses a Markov-chain Monte-Carlo implementation of Bayes’ Rule to estimate the crack parameters (i.e., its location, orientation, and size) and their probability distributions. Special attention is paid to developing a fast and accurate forward model for the response of the cracked plate. To generate the required time series, a semi-analytical free response is calculated using an FEM based eigen-solution. To speed up the simulations, modified elements are used at the crack tips; this permits a more course mesh without sacrificing accuracy. The approach is demonstrated to be effective at identifying all of the crack parameters. Furthermore, a natural by-product of this method is that it also provides a confidence (credible) interval for each of these parameters. The results show the utility and accuracy of this method in identifying cracks of various sizes, orientations, and locations.