Simplified Forward Model Research Articles

Estimation of Thickness and Radius of Hollow Metallic Spheres With a Simplified Forward Model

The measurement of metallic spherical objects in various industrial applications has a significant role in guaranteeing safety and product quality, which can be realized by the eddy-current testing technique without contact. In this study, for the measurement of thickness and radius of non-magnetic spherical shells, the original analytical model is simplified according to the asymptotic forms of the modified spherical Bessel functions. The simplified model contains only elementary functions, and can therefore accelerates the sphere property estimation by employing the optimization approach based on the Newton-Raphson method. In numerical simulation and experimental study, the proposed method can provide accurate spherical shell radii with less computational time compared with the original analytical model.

A generalized framework for the image formation model and disentanglement of CTF parameters in cryo-electron microscopy

In cryo-electron microscopy (cryo-EM), the microscope has a point spread function, whose Fourier transform, known as the Contrast Transfer Function (CTF), is determined by various parameters with a physical meaning (including height of the sample, magnetic lens aberrations, operating voltage, amplitude contrast, etc.). Some of the parameters are under experimental control, but they can also contain some experimental uncertainty and fluctuate over the course of data collection. While it is routine to use point estimates for the CTF parameters in a simplified forward model of image formation, we characterize here the uncertainty of the CTF by (1) framing the forward model of image formation as a probabilistic graphical model, (2) deriving conditional probabilities that leverage analytical linking functions, and (3) compare these results with existing approaches that model noise in frequency space, such as the “B-factor envelope” and the “white/coloured noise model”.

A clinically applicable strategy to estimate the in vivo distribution of mechanical material properties of the right ventricular wall.

A clinically applicable approach to estimate the in vivo mechanical material properties of the heart wall is presented. This optimization-based inverse estimation approach applies a shape-based objective functional combined with rigid body registration and incremental parameterization of heterogeneity to use standard clinical imaging data along with simplified representations of cardiac function to provide consistent and physically meaningful solution estimates. The capability of the inverse estimation algorithm is evaluated through application to two clinically obtained human datasets to estimate the passive elastic mechanical properties of the heart wall, with an emphasis on the right ventricle. One dataset corresponded to a subject with normal heart function, while the other corresponded to a subject with severe pulmonary hypertension, and therefore expected to have a substantially stiffer right ventricle. Patient-specific pressure-driven bi-ventricle finite element analysis was used as the forward model and the endocardial surface of the right ventricle was used as the target data for the inverse problem. By using the right ventricle alone as the target of the inverse problem the relative sensitivity of the objective function to the right ventricle properties is increased. The method was able to identify material properties to accurately match the corresponding shape of the simplified forward model to the clinically obtained target data, and the properties obtained for the example cases are consistent with the clinical expectation for the right ventricle. Additionally, the material property estimates indicate significant heterogeneity in the heart wall for both subjects, and more so for the subject with pulmonary hypertension.

UHR-DeepFMT: Ultra-High Spatial Resolution Reconstruction of Fluorescence Molecular Tomography Based on 3-D Fusion Dual-Sampling Deep Neural Network.

Fluorescence molecular tomography (FMT) is a promising and high sensitivity imaging modality that can reconstruct the three-dimensional (3D) distribution of interior fluorescent sources. However, the spatial resolution of FMT has encountered an insurmountable bottleneck and cannot be substantially improved, due to the simplified forward model and the severely ill-posed inverse problem. In this work, a 3D fusion dual-sampling convolutional neural network, namely UHR-DeepFMT, was proposed to achieve ultra-high spatial resolution reconstruction of FMT. Under this framework, the UHR-DeepFMT does not need to explicitly solve the FMT forward and inverse problems. Instead, it directly establishes an end-to-end mapping model to reconstruct the fluorescent sources, which can enormously eliminate the modeling errors. Besides, a novel fusion mechanism that integrates the dual-sampling strategy and the squeeze-and-excitation (SE) module is introduced into the skip connection of UHR-DeepFMT, which can significantly improve the spatial resolution by greatly alleviating the ill-posedness of the inverse problem. To evaluate the performance of UHR-DeepFMT network model, numerical simulations, physical phantom and in vivo experiments were conducted. The results demonstrated that the proposed UHR-DeepFMT can outperform the cutting-edge methods and achieve ultra-high spatial resolution reconstruction of FMT with the powerful ability to distinguish adjacent targets with a minimal edge-to-edge distance (EED) of 0.5 mm. It is assumed that this research is a significant improvement for FMT in terms of spatial resolution and overall imaging quality, which could promote the precise diagnosis and preclinical application of small animals in the future.

Reproducibility of power spectrum, functional connectivity and network construction in resting-state EEG

BackgroundCharacteristics from resting-state electroencephalography (rsEEG) provides relevant information about individual differences in cognitive tasks and personality traits. Due to its increasing application, it is crucial to know the reproducibility of several analysis measures of rsEEG. New methodA new brain network construction method was proposed based on simplified forward model (SFM). In addition, we aimed to carry out an extensive examination of the reproducibility of the power spectrum and functional connectivity at both the sensor-level and the source-level. We systematically proposed multiple new pipelines by integration source imaging, time-course extraction and network reconstruction. Results/comparison with existing method(s)Our results revealed that the reproducibility of eyes-closed was slightly higher than that of eyes-open, and the relative power was more repeatable than the absolute power, especially in high-frequency bands. The reproducibility of the sensor-level was higher than that of the source-level, both for power and connectivity. Remarkably, connectivity measures could be separated into two classes according to their reproducibility. Notably, the reproducibility of power envelope correlation (PEC) was generally the highest among those connectivity measures which are insensitive to volume conduction effect. For the whole-brain network construction, single dipole modeling was better than the dimensionality reduction methods, such as mean or principal component analysis (PCA) of multiple dipoles of a region. ConclusionsIn conclusion, our results described the reproducibility of rsEEG power spectrum, connectivity measures, and network constructions, which could be considered in assessing inter-individual differences in brain-behavior relationships, as well as automatic biometric applications.

Deriving bathymetry and water properties from hyperspectral imagery by spectral matching using a full radiative transfer model

ABSTRACT Many existing techniques for estimating the optical properties of a body of water directly from a hyperspectral remote sensing spectrum are based on the idea of ‘spectral matching’ – that is, input parameters in a forward model are systematically varied until the measured and modelled spectra are sufficiently similar. This is usually done by using numerical optimization methods with a simplified forward model, or by precomputing a large library of spectra with a more realistic model, and then searching the library for the best match. In this letter, we show that is possible to combine the two approaches by using a full radiative transfer model in an optimization routine. We include results of running the algorithm on both simulated and measured data.

Time variation of Jupiter’s internal magnetic field consistent with zonal wind advection

Determination of the time dependency (secular variation) of a planet’s magnetic field provides a window into understanding the dynamo responsible for generating its field. However, of the six Solar System planets with active dynamos, secular variation has been firmly established only for Earth. Here, we compare magnetic field observations of Jupiter from the Pioneer 10 and 11, Voyager 1 and Ulysses spacecraft (acquired 1973–1992) with a new Juno reference model (JRM09). We find a consistent, systematic change in Jupiter’s field over this 45-year time span, which cannot be explained by changes in the magnetospheric field or by changing the assumed rotation rate of Jupiter. Through a simplified forward model, we find that the inferred change in the field is consistent with advection of the field by Jupiter’s zonal winds, projected down to 93–95% of Jupiter’s radius (where the electrical conductivity of the hydrogen envelope becomes sufficient to advect the field). This result demonstrates that zonal wind interactions with Jupiter’s magnetic field are important and lends independent support to atmospheric and gravitational-field determinations of the profile of Jupiter’s deep winds.

Regionally Resolved Diagnostic of Transport: A Simplified Forward Model for CO2

Abstract Simply diagnostic tools are useful for understanding transport processes in complex chemistry transport models (CTMs). For this purpose, a combined use of the airmass origin fractions (AOFs) and regionally resolved mean ages (RMAs) is presented. This approach merges the concept of the origin of air with the well-known theory of the mean age of air (AoA) for different regions covering the whole Earth. The authors show how the AoA calculated relative to Earth’s surface can be decomposed into regionally resolved components (i.e., into RMAs). Using both AOFs and RMAs, the authors discuss differences in the seasonality of transport from the Northern and Southern Hemispheres into the tropical tropopause layer (TTL), the asymmetries of the interhemispheric exchange, and differences in relation to the continental or oceanic origin of air. Furthermore, a simplified transport model for a chemically passive species (tracer) is formulated that has some potential to approximate the full transport within a CTM. This analytic approach uses the AOFs as well as the RMAs as parameters to propagate a tracer prescribed on Earth’s surface (lower boundary condition). This method is exactly valid for sources that change linearly with time in each of the considered regions. The authors analyze how well this approach approximates the propagation of CO2 from the planetary boundary layer (PBL) into the whole atmosphere. The CO2 values in the PBL are specified by the CarbonTracker dataset. The authors discuss how this approach can be used for inverse modeling of CO2.

Information content and sensitivity of the 3<i>β</i> + 2<i>α</i> lidar measurement system for aerosol microphysical retrievals

Abstract. There is considerable interest in retrieving profiles of aerosol effective radius, total number concentration, and complex refractive index from lidar measurements of extinction and backscatter at several wavelengths. The combination of three backscatter channels plus two extinction channels (3β + 2α) is particularly important since it is believed to be the minimum configuration necessary for the retrieval of aerosol microphysical properties and because the technological readiness of lidar systems permits this configuration on both an airborne and future spaceborne instrument. The second-generation NASA Langley airborne High Spectral Resolution Lidar (HSRL-2) has been making 3β + 2α measurements since 2012. The planned NASA Aerosol/Clouds/Ecosystems (ACE) satellite mission also recommends the 3β + 2α combination.Here we develop a deeper understanding of the information content and sensitivities of the 3β + 2α system in terms of aerosol microphysical parameters of interest. We use a retrieval-free methodology to determine the basic sensitivities of the measurements independent of retrieval assumptions and constraints. We calculate information content and uncertainty metrics using tools borrowed from the optimal estimation methodology based on Bayes' theorem, using a simplified forward model look-up table, with no explicit inversion. The forward model is simplified to represent spherical particles, monomodal log-normal size distributions, and wavelength-independent refractive indices. Since we only use the forward model with no retrieval, the given simplified aerosol scenario is applicable as a best case for all existing retrievals in the absence of additional constraints. Retrieval-dependent errors due to mismatch between retrieval assumptions and true atmospheric aerosols are not included in this sensitivity study, and neither are retrieval errors that may be introduced in the inversion process. The choice of a simplified model adds clarity to the understanding of the uncertainties in such retrievals, since it allows for separately assessing the sensitivities and uncertainties of the measurements alone that cannot be corrected by any potential or theoretical improvements to retrieval methodology but must instead be addressed by adding information content.The sensitivity metrics allow for identifying (1) information content of the measurements vs. a priori information; (2) error bars on the retrieved parameters; and (3) potential sources of cross-talk or "compensating" errors wherein different retrieval parameters are not independently captured by the measurements. The results suggest that the 3β + 2α measurement system is underdetermined with respect to the full suite of microphysical parameters considered in this study and that additional information is required, in the form of additional coincident measurements (e.g., sun-photometer or polarimeter) or a priori retrieval constraints. A specific recommendation is given for addressing cross-talk between effective radius and total number concentration.

Simplified EEG inverse solution for BCI real-time implementation.

EEG brain imaging has become a promising approach in Brain-computer interface applications. However, accurate reconstruction of active regions and computational burden are still open issues. In this paper, we propose to use a simplified forward model that includes the reduction of the cortical dipoles based on Brodmann areas together with state-of-the-art EEG brain imaging techniques. With this approach the well known Beamformers and Greedy Search inverse solutions become feasible for real-time implementation, while guaranteeing lower localization error than previous approaches used in BCI. This methodology was tested with synthetic and real EEG data from a visual attention study. Results show zero localization error in terms of active cortical regions estimation in single 1 s trial datasets, with a computation time of 1.1 s in a non-specialized personal computer. These results open the possibility to obtain in real-time information of active cortical regions in Brain-computer interfaces.

Bayesian image restoration for mosaic active imaging

In this paper, we focus on the restoration of images acquired with a new active imaging concept. This new instrument generates a mosaic of active imaging acquisitions. We first describe a simplified forward model of this so-called ''mosaic active imaging''. We also assume a prior on the distribution of images, using the \ac{TV}, and deduce a restoration algorithm. This algorithm iterates one step for the estimation of the restored image and one step for the estimation of the acquisition parameters. We then provide the details useful to the implementation of these two steps. In particular, we show that the image estimation can be performed with graph-cuts. This allows a fast resolution of this image estimation step. Finally, we detail numerical experiments showing that acquisitions made with a mosaic active imaging device can be restored even under severe noise levels, with few acquisitions.

Parametric Inversion Technique for Location of Cylindrical Structures by Cross-Hole Measurements

A new parametric inversion technique to locate cylindrical structures has been developed for borehole radar cross-hole measurements. The technique calculates prediction errors, focusing on curve shapes of first-arrival times, and explicitly uses known parameters on a target. Two schemes to compare the measured first-arrival time curves with the calculated ones are proposed. One is by taking the errors between curve gradients of measured and calculated first-arrival times, and the other is by taking the cross correlation between calculated first-arrival times and measured data. The schemes do not need to select the true first-arrival times, which makes this inversion technique robust and easy to use. This technique is validated with synthetic data sets modeling a metallic pipe in homogeneous and heterogeneous medium models. By both models, the inversion technique is able to retrieve the exact location of the pipe, though it employs a rather simple forward model, which can be solved by only geometrical calculations. The technique is applied to measured data sets, and it successfully estimates a pipe location in good agreement with known information. The inversion is also used for an air-filled subsurface cavity with a very simplified forward model, which considers only Snell's law at the cavity-subsurface media interface. It is also able to locate the cavity at a similar location estimated by other conventional techniques