Total variation-based neutron computed tomography

Abstract

We perform the neutron computed tomography reconstruction problem via an inverse problem formulation with a total variation penalty. In the case of highly under-resolved angular measurements, the total variation penalty suppresses high-frequency artifacts which appear in filtered back projections. In order to efficiently compute solutions for this problem, we implement a variation of the split Bregman algorithm; due to the error-forgetting nature of the algorithm, the computational cost of updating can be significantly reduced via very inexact approximate linear solvers. We present the effectiveness of the algorithm in the significantly low-angular sampling case using synthetic test problems as well as data obtained from a high flux neutron source. The algorithm removes artifacts and can even roughly capture small features when an extremely low number of angles are used.

Improved Acquisition and Reconstruction for Wavelength-Resolved Neutron Tomography

“…Model-based image reconstruction [ 21 ] approaches have been developed for the last few decades and are well established to be the method of choice when dealing with sparse, limited-view and noisy tomographic datasets. In the scientific user facility community, such methods have been developed for electron tomography [ 22 , 23 , 24 ], synchrotron based X-ray CT [ 11 , 25 , 26 ] and neutron laminography and tomography [ 16 , 17 , 18 , 19 ]. In this section, we briefly explain the core ideas behind MBIR and how we have adapted it for the WRNT systems in order to perform hyper-spectral tomography.…”

“…The MBIR algorithm works by minimizing a cost function that balances a data-fitting term that incorporates a physics based model for the imaging system and noise characteristics of the detector, and a regularization term that incorporates a model for the underlying 3D object itself (such as local smoothness). MBIR methods have enabled significant improvements in performance for several tomography applications including for neutron tomography [ 16 , 17 , 18 , 19 ] especially when dealing with sparse and low signal-to-noise ratio (SNR) data; a scenario that is also common in WRNT as we seek to provide high-quality real-time feedback to users in the course of an experiment. We demonstrate the utility of our proposed method by implementing this system at the SNAP beam line of the Spallation Neutron Source (SNS) at the Oak Ridge National Laboratory (ORNL) and demonstrate real-time feedback capability during the course of a WRNT of a magnetite sample.…”

Algorithm-driven Advances for Scientific CT Instruments: From Model-based to Deep Learning-based Approaches

“…where ρ is a function that penalizes differences between neighboring voxels, β is a parameter that adjusts the weight assigned to the regularization terms, χ is a set containing all pairs of neighboring voxels in 3D and w ij are weights associated with each pair of voxels. MBIR algorithms based on combining models in (2) and (3) have been developed for parallel beam electron tomography [1], [24]- [27], synchrotron based X-ray CT [8], [10], and neutron tomography [28], [29] enabling significantly higher quality reconstructions compared to the analytic reconstruction algorithms from sparse, limitedview and low-SNR data routinely encountered in these applications. The development of MBIR methods April 19, 2021 DRAFT has shown that it is possible to achieve similar image quality as the analytic reconstruction methods using about one-half or even one-fourth the typical number of measurements made [8], [28] at X-ray and neutron-CT instruments -thereby potentially enabling 2X-4X more samples to be measured at these instruments than would have been possible when analytic reconstruction methods were used.…”

ACQUIRE: an inexact iteratively reweighted norm approach for TV-based Poisson image restoration

“…Assumptions (1) and b > 0 ensure that, for any given y ≥ 0, D KL is a nonnegative, convex, coercive, twice continuosly differentiable function in R n + (see, e.g., [5,25]). Its gradient and Hessian are given by…”

“…When the matrix A comes from the discretization of a convolution operator and it is normalized as in (1), the constraint n i=1 x i = m j=1 y i can be added, since the convolution performs a modification of the intensity distribution, while the total intensity remains constants. 1 In other words, common choices of S are S = S 1 := {x ∈ R n : x ≥ 0} or S = S 2 := {x ∈ R n :…”