Blind polychromatic X-ray CT reconstruction from Poisson measurements

We develop a sparse image reconstruction method for Poisson distributed polychromatic X-ray computed tomography (CT) measurements under the blind scenario where the material of the inspected object and the incident energy spectrum are unknown. We employ our mass-attenuation spectrum parameterization of the noiseless measurements for single-material objects and express the mass-attenuation spectrum as a linear combination of B-spline basis functions of order one. A block coordinate descent algorithm is developed for constrained minimization of a penalized Poisson negative log-likelihood (NLL) cost function, where constraints and penalty terms ensure nonnegativity of the spline coefficients and nonnegativity and sparsity of the density-map image; the image sparsity is imposed using a convex total-variation (TV) norm penalty term. This algorithm alternates between a Nesterov’s proximal-gradient (NPG) step for estimating the density-map image and a limited-memory Broyden-Fletcher-Goldfarb-Shanno with box constraints (LBFGS- B) step for estimating the incident-spectrum parameters. We establish conditions for biconvexity of the penalized NLL objective function, which, if satisfied, ensures monotonicity of the NPG-BFGS iteration. We also show that the penalized NLL objective satisfies the Kurdyka-Łojasiewicz property, which is important for establishing local convergence of block-coordinate descent schemes in biconvex optimization problems. Simulation examples demonstrate the performance of the proposed scheme

A Conway–Maxwell–Poisson (CMP) model to address data dispersion on positron emission tomography

Positron emission tomography (PET) in medicine exploits the properties of positron-emitting unstable nuclei. The pairs of γ- rays emitted after annihilation are revealed by coincidence detectors and stored as projections in a sinogram. It is well known that radioactive decay follows a Poisson distribution; however, deviation from Poisson statistics occurs on PET projection data prior to reconstruction due to physical effects, measurement errors, correction of deadtime, scatter, and random coincidences. A model that describes the statistical behavior of measured and corrected PET data can aid in understanding the statistical nature of the data: it is a prerequisite to develop efficient reconstruction and processing methods and to reduce noise. The deviation from Poisson statistics in PET data could be described by the Conway-Maxwell-Poisson (CMP) distribution model, which is characterized by the centring parameter λ and the dispersion parameter ν, the latter quantifying the deviation from a Poisson distribution model. In particular, the parameter ν allows quantifying over-dispersion (ν<1) or under-dispersion (ν>1) of data. A simple and efficient method for λ and ν parameters estimation is introduced and assessed using Monte Carlo simulation for a wide range of activity values. The application of the method to simulated and experimental PET phantom data demonstrated that the CMP distribution parameters could detect deviation from the Poisson distribution both in raw and corrected PET data. It may be usefully implemented in image reconstruction algorithms and quantitative PET data analysis, especially in low counting emission data, as in dynamic PET data, where the method demonstrated the best accuracy

Physical component analysis of galaxy cluster weak gravitational lensing data

We present a novel approach for reconstructing the projected mass distribution of clusters of galaxies from sparse and noisy weak gravitational lensing shear data. The reconstructions are regularised using knowledge gained from numerical simulations of clusters: trial mass distributions are constructed from N physically-motivated components, each of which has the universal density profile and characteristic geometry observed in simulated clusters. The parameters of these components are assumed to be distributed \emph{a priori} in the same way as they are in the simulated clusters. Sampling mass distributions from the components' parameters' posterior probability density function allows estimates of the mass distribution to be generated, with error bars. The appropriate number of components is inferred from the data itself via the Bayesian evidence, and is typically found to be small, reflecting the quality of the simulated data used in this work. Ensemble average mass maps are found to be robust to the details of the noise realisation, and succeed in recovering the input mass distribution (from a realistic simulated cluster) over a wide range of scales. We comment on the residuals of the reconstruction and their implications, and discuss the extension of the method to include strong lensing information.Comment: 12 pages, 7 figure

Reconstruction and measurement of (100) MeV energy electromagnetic activity from π0 arrow γγ decays in the MicroBooNE LArTPC

We present results on the reconstruction of electromagnetic (EM) activity from photons produced in charged current νμ interactions with final state π0s. We employ a fully-automated reconstruction chain capable of identifying EM showers of (100) MeV energy, relying on a combination of traditional reconstruction techniques together with novel machine-learning approaches. These studies demonstrate good energy resolution, and good agreement between data and simulation, relying on the reconstructed invariant π0 mass and other photon distributions for validation. The reconstruction techniques developed are applied to a selection of νμ + Ar → μ + π0 + X candidate events to demonstrate the potential for calorimetric separation of photons from electrons and reconstruction of π0 kinematics