Iterative CT reconstruction from few projections for the nondestructive post irradiation examination of nuclear fuel assemblies

The core components (e.g. fuel assemblies, spacer grids, control rods) of the nuclear reactors encounter harsh environment due to high temperature, physical stress, and a tremendous level of radiation. The integrity of these elements is crucial for safe operation of the nuclear power plants. The Post Irradiation Examination (PIE) can reveal information about the integrity of the elements during normal operations and off‐normal events. Computed tomography (CT) is a tool for evaluating the structural integrity of elements non-destructively. CT requires many projections to be acquired from different view angles after which a mathematical algorithm is adopted for reconstruction. Obtaining many projections is laborious and expensive in nuclear industries. Reconstructions from a small number of projections are explored to achieve faster and cost-efficient PIE. Classical reconstruction algorithms (e.g. filtered back projection) cannot offer stable reconstructions from few projections and create severe streaking artifacts. In this thesis, conventional algorithms are reviewed, and new algorithms are developed for reconstructions of the nuclear fuel assemblies using few projections. CT reconstruction from few projections falls into two categories: the sparse-view CT and the limited-angle CT or tomosynthesis. Iterative reconstruction algorithms are developed for both cases in the field of compressed sensing (CS). The performance of the algorithms is assessed using simulated projections and validated through real projections. The thesis also describes the systematic strategy towards establishing the conditions of reconstructions and finds the optimal imaging parameters for reconstructions of the fuel assemblies from few projections. --Abstract, page iii

An algorithm for constrained one-step inversion of spectral CT data

We develop a primal-dual algorithm that allows for one-step inversion of spectral CT transmission photon counts data to a basis map decomposition. The algorithm allows for image constraints to be enforced on the basis maps during the inversion. The derivation of the algorithm makes use of a local upper bounding quadratic approximation to generate descent steps for non-convex spectral CT data discrepancy terms, combined with a new convex-concave optimization algorithm. Convergence of the algorithm is demonstrated on simulated spectral CT data. Simulations with noise and anthropomorphic phantoms show examples of how to employ the constrained one-step algorithm for spectral CT data.Comment: Submitted to Physics in Medicine and Biolog

GÜÇLENDİRİLMİŞ GRADYAN MİNİMİZASYONU KULLANARAK MEDİKAL GÖRÜNTÜLERDE GÜRÜLTÜ ARINDIRMA

Medikal görüntüler doğası gereği farklı gürültü tipleri ve seviyelerine maruz kalmaktadır. Medikal görüntülerin oluşturulmasında kullanılan rekonstrüksiyon algoritmalarının temel amacı, oluşan bu gürültünün giderilmesi ve çözünürlüğün arttırılması için en verimli yöntemlerin kullanılmasıdır. Bu yöntemler kullanılırken filtreleme, düzenleyiciler ve gürültü giderici operatörler kullanıp gürültünün arındırılması amaçlanmaktadır. Sıkıştırılmış algılamanın medikal görüntülemede aktif olarak kullanılmaya başlanmasından sonra, görüntüyü daha seyrek forma dönüştüren toplam değişinti (TD) en küçüklemesi ile görüntü üzerindeki gürültü azaltılarak ufak detayların ve kenarların daha net biçimde korunması sağlanmıştır. Lokal bir gradyan operatörü olan toplam değişinti algoritması bu çalışmada kısmi gradyan yönlerinde kullanılan komşuluk seviyesi arttırılarak daha güçlü bir gürültü giderici olarak yeniden tasarlanmıştır. Çalışma kapsamında, tasarlanan bu yeni güçlendirilmiş gradyan minimizasyonunun medikal görüntülerde mevcut farklı Gauss, Poisson ve Gauss+Poisson gürültü seviyeleri üzerinde gürültü arındırma başarısı klasik TD ile karşılaştırılmıştır. Sonuçlar pik sinyal-gürültü oranı, yapısal benzerlik ve kontrast-gürültü oranı metrikleri ve görsel analiz kullanılarak karşılaştırılmış ve önerilen yeni güçlendirilmiş gradyan minimizasyonu yönteminin mevcut klasik TD algoritmasından daha iyi gürültü arındırma potansiyeline sahip olduğu gösterilmiştir

Compressed Sensing for Few-View Multi-Pinhole Spect with Applications to Preclinical Imaging

Single Photon Emission Computed Tomography (SPECT) can be used to identify and quantify changes in molecular and cellular targets involved in disease. A radiopharmaceutical that targets a specific metabolic function is administered to a subject and planar projections are formed by imaging emissions at different view angles around the subject. The reconstruction task is to determine the distribution of radioactivity within the subject from the projections. We present a reconstruction approach that utilizes only a few view angles, resulting in a highly underdetermined system, which could be used for dynamic imaging applications designed to quantify physiologic processes altered with disease. We developed an approach to solving the underdetermined problem that incorporates a fast matrix- based multi-pinhole projection model into a primal-dual algorithm (Chambolle-Pock), tailored to perform penalized data fidelity minimization using the reconstruction’s total variation as a sparse regularizer. The resulting algorithm was implemented on a Graphics Processing Unit (GPU), and validated by solving an idealized quadratic problem. Simulated noisy data from a digital rat thorax phantom was reconstructed using a range of regularizing parameters and primal-dual scale factors to control the smoothness of the reconstruction and the step-size in the iterative algorithm, respectively. The approach was characterized by evaluating data fidelity, convergence, and noise properties. The proposed approach was then applied to few-view experimental data obtained in a preclinical SPECT study. 99mTc-labeled macroaggregated albumin (MAA) that accumulates in the lung was administered to a rat and multi-pinhole image data was acquired and reconstructed. The results demonstrate MAA uptake in the lungs is accurately quantified over a wide range of activity levels using as few as three view angles. In a pilot experiment, we also showed using 15 and 60 view angles that uptake of 99mTc-hexamethylpropyleneamineoxime in hyperoxia-exposed rats is higher than that in control rats, consistent with previous studies in our laboratory. Overall these experiments demonstrate the potential utility of the proposed method for few-view three-dimensional reconstruction of SPECT data for dynamic preclinical studies

Non-Convex and Geometric Methods for Tomography and Label Learning

Data labeling is a fundamental problem of mathematical data analysis in which each data point is assigned exactly one single label (prototype) from a finite predefined set. In this thesis we study two challenging extensions, where either the input data cannot be observed directly or prototypes are not available beforehand. The main application of the first setting is discrete tomography. We propose several non-convex variational as well as smooth geometric approaches to joint image label assignment and reconstruction from indirect measurements with known prototypes. In particular, we consider spatial regularization of assignments, based on the KL-divergence, which takes into account the smooth geometry of discrete probability distributions endowed with the Fisher-Rao (information) metric, i.e. the assignment manifold. Finally, the geometric point of view leads to a smooth flow evolving on a Riemannian submanifold including the tomographic projection constraints directly into the geometry of assignments. Furthermore we investigate corresponding implicit numerical schemes which amount to solving a sequence of convex problems. Likewise, for the second setting, when the prototypes are absent, we introduce and study a smooth dynamical system for unsupervised data labeling which evolves by geometric integration on the assignment manifold. Rigorously abstracting from ``data-label'' to ``data-data'' decisions leads to interpretable low-rank data representations, which themselves are parameterized by label assignments. The resulting self-assignment flow simultaneously performs learning of latent prototypes in the very same framework while they are used for inference. Moreover, a single parameter, the scale of regularization in terms of spatial context, drives the entire process. By smooth geodesic interpolation between different normalizations of self-assignment matrices on the positive definite matrix manifold, a one-parameter family of self-assignment flows is defined. Accordingly, the proposed approach can be characterized from different viewpoints such as discrete optimal transport, normalized spectral cuts and combinatorial optimization by completely positive factorizations, each with additional built-in spatial regularization