Optimizing dual-energy CT technique for iodine-based contrast-to-noise ratio, a theoretical study.

BACKGROUND: Dual-energy CT (DECT) systems provide valuable material-specific information by simultaneously acquiring two spectral measurements, resulting in superior image quality and contrast-to-noise ratio (CNR) while reducing radiation exposure and contrast agent usage. The selection of DECT scan parameters, including x-ray tube settings and fluence, is critical for the stability of the reconstruction process and hence the overall image quality. PURPOSE: The goal of this study is to propose a systematic theoretical method for determining the optimal DECT parameters for minimal noise and maximum CNR in virtual monochromatic images (VMIs) for fixed subject size and total radiation dose. METHODS: The noise propagation in the process of projection based material estimation from DECT measurements is analyzed. The main components of the study are the mean pixel variances for the sinogram and monochromatic image and the CNR, which were shown to depend on the Jacobian matrix of the sinograms-to-DECT measurements map. Analytic estimates for the mean sinogram and monochromatic image pixel variances and the CNR as functions of tube potentials, fluence, and VMI energy are derived, and then used in a virtual phantom experiment as an objective function for optimizing the tube settings and VMI energy to minimize the image noise and maximize the CNR. RESULTS: It was shown that DECT measurements corresponding to kV settings that maximize the square of Jacobian determinant values over a domain of interest lead to improved stability of basis material reconstructions. Instances of non-uniqueness in DECT were addressed, focusing on scenarios where the Jacobian determinant becomes zero within the domain of interest despite significant spectral separation. The presence of non-uniqueness can lead to singular solutions during the inversion of sinograms-to-DECT measurements, underscoring the importance of considering uniqueness properties in parameter selection. Additionally, the optimal VMI energy and tube potentials for maximal CNR was determined. When the x-ray beam filter material was fixed at 2 mm of aluminum and the photon fluence for low and high kV scans were considered equal, the tube potential pair of 60/120 kV led to the maximal iodine CNR in the VMI at 53 keV. CONCLUSIONS: Optimizing DECT scan parameters to maximize the CNR can be done in a systematic way. Also, choosing the parameters that maximize the Jacobian determinant over the set of expected line integrals leads to more stable reconstructions due to the reduced amplification of the measurement noise. Since the values of the Jacobian determinant depend strongly on the imaging task, careful consideration of all of the relevant factors is needed when implementing the proposed framework.

Fermi pencil beams and off-axis laser detection.

This paper concerns the analytic reconstruction of properties for narrow laser beams propagating in turbulent atmospheres. We consider the setting of off-axis measurements based on wide-angle single scattering of light detected away from the main path of the beam. Light propagation in the beam itself is modeled by macroscopic approximations of radiative transfer equations that take the form of Fermi pencil beam or fractional Fermi pencil beam equations. This allows for a simplified reconstruction procedure of the beam's constitutive parameters, in particular, its direction of propagation and the location of the emitting source.

Simple Bayesian reconstruction and forecasting of stream water temperature for ecologists-A tool using air temperature, optionally flow, in a time series decomposition approach.

Mitigating the impacts of global warming on wildlife entails four practical steps. First, we need to study how processes of interest vary with temperature. Second, we need to build good temperature scenarios. Third, processes can be forecast accordingly. Only then can we perform the fourth step, testing mitigating measures. While having good temperature data is essential, this is not straightforward for stream ecologists and managers. Water temperature (WT) data are often short and incomplete and future projections are currently not routinely available. There is a need for generic models which address this data gap with good resolution and current models are partly lacking. Here, we expand a previously published hierarchical Bayesian model that was driven by air temperature (AT) and flow (Q) as a second covariate. The new model can hindcast and forecast WT time series at a daily time step. It also allows a better appraisal of real uncertainties in the warming of water temperatures in rivers compared to the previous version, stemming from its hybrid structure between time series decomposition and regression. This model decomposes all-time series using seasonal sinusoidal periodic signals and time varying means and amplitudes. It then links the contrasted frequency signals of WT (daily and six month) through regressions to that of AT and optionally Q for better resolution. We apply this model to two contrasting case study rivers. For one case study, AT only is available as a covariate. This expanded model further improves the already good fitting and predictive capabilities of its earlier version while additionally highlighting warming uncertainties. The code is available online and can easily be run for other temperate rivers.

A hierarchical bayesian model to quantify uncertainty of stream water temperature forecasts.

Providing generic and cost effective modelling approaches to reconstruct and forecast freshwater temperature using predictors as air temperature and water discharge is a prerequisite to understanding ecological processes underlying the impact of water temperature and of global warming on continental aquatic ecosystems. Using air temperature as a simple linear predictor of water temperature can lead to significant bias in forecasts as it does not disentangle seasonality and long term trends in the signal. Here, we develop an alternative approach based on hierarchical Bayesian statistical time series modelling of water temperature, air temperature and water discharge using seasonal sinusoidal periodic signals and time varying means and amplitudes. Fitting and forecasting performances of this approach are compared with that of simple linear regression between water and air temperatures using i) an emotive simulated example, ii) application to three French coastal streams with contrasting bio-geographical conditions and sizes. The time series modelling approach better fit data and does not exhibit forecasting bias in long term trends contrary to the linear regression. This new model also allows for more accurate forecasts of water temperature than linear regression together with a fair assessment of the uncertainty around forecasting. Warming of water temperature forecast by our hierarchical Bayesian model was slower and more uncertain than that expected with the classical regression approach. These new forecasts are in a form that is readily usable in further ecological analyses and will allow weighting of outcomes from different scenarios to manage climate change impacts on freshwater wildlife.

Ultrasound-modulated bioluminescence tomography.

We propose a method to reconstruct the density of a luminescent source in a highly scattering medium from ultrasound-modulated optical measurements. Our approach is based on the solution to a hybrid inverse source problem for the diffusion equation.

Inverse scattering and acousto-optic imaging.

We propose a tomographic method to reconstruct the optical properties of a highly scattering medium from incoherent acousto-optic measurements. The method is based on the solution to an inverse problem for the diffusion equation and makes use of the principle of interior control of boundary measurements by an external wave field.

Transport- and diffusion-based optical tomography in small domains: a comparative study.

We compare reconstructions based on the radiative transport and diffusion equations in optical tomography for media of small sizes. While it is well known that the diffusion approximation is less accurate to describe light propagation in such media, it has not yet been shown how this inaccuracy affects the images obtained with model-based iterative image reconstructions schemes. Using synthetic nondifferential data we calculate the error in the reconstructed images of optical properties as functions of source modulation frequency, noise level in measurement, and diffusion extrapolation length. We observe that the differences between diffusion and transport reconstructions are large when high modulation frequencies and noise-free data are used in the reconstructions. When the noise in data reaches a certain level, approximately 12% in our simulations, the differences between diffusion- and transport-based reconstructions become almost indistinguishable. Given that state-of-the-art optical imaging systems operate at much lower noise levels, the benefits of transport-based reconstructions of small imaging domains can be realized with most of the currently available systems. However, transport-based reconstructions are considerably slower than diffusion-based reconstructions.

Radiative transfer equations with varying refractive index: a mathematical perspective.

Established mathematical techniques to model the energy density of high-frequency waves in random media by radiative transfer equations and to model the small mean-free-path limit of radiative transfer solutions by diffusion equations are reviewed. These techniques are then applied to the derivation of radiative transfer and diffusion equations for the radiance, also known as specific intensity, of electromagnetic waves in situations where the refractive index of the underlying structure varies smoothly in space.

Algorithm for solving the equation of radiative transfer in the frequency domain.

We present an algorithm that provides a frequency-domain solution of the equation of radiative transfer (ERT) for heterogeneous media of arbitrary shape. Although an ERT is more accurate than a diffusion equation, no ERT code for the widely employed frequency-domain case has been developed to date. In this work the ERT is discretized by a combination of discrete-ordinate and finite-volume methods. Two numerical simulations are presented.

Generalized diffusion model in optical tomography with clear layers.

We introduce a generalized diffusion equation that models the propagation of photons in highly scattering domains with thin nonscattering clear layers. Classical diffusion models break down in the presence of clear layers. The model that we propose accurately accounts for the clear-layer effects and has a computational cost comparable to that of classical diffusion. It is based on modeling the propagation in the clear layer as a local tangential diffusion process. It can be justified mathematically in the limit of small mean free paths and is shown numerically to be very accurate in two- and three-dimensional idealized cases. We believe that this model can be used as an accurate forward model in optical tomography.