해부학적 유도 PET 재구성: 매끄럽지 않은 사전 함수부터 딥러닝 접근까지

학위논문 (박사) -- 서울대학교 대학원 : 의과대학 의과학과, 2021. 2. 이재성.Advances in simultaneous positron emission tomography/magnetic resonance imaging (PET/MRI) technology have led to an active investigation of the anatomy-guided regularized PET image reconstruction algorithm based on MR images. Among the various priors proposed for anatomy-guided regularized PET image reconstruction, Bowsher’s method based on second-order smoothing priors sometimes suffers from over-smoothing of detailed structures. Therefore, in this study, we propose a Bowsher prior based on the l1 norm and an iteratively reweighting scheme to overcome the limitation of the original Bowsher method. In addition, we have derived a closed solution for iterative image reconstruction based on this non-smooth prior. A comparison study between the original l2 and proposed l1 Bowsher priors were conducted using computer simulation and real human data. In the simulation and real data application, small lesions with abnormal PET uptake were better detected by the proposed l1 Bowsher prior methods than the original Bowsher prior. The original l2 Bowsher leads to a decreased PET intensity in small lesions when there is no clear separation between the lesions and surrounding tissue in the anatomical prior. However, the proposed l1 Bowsher prior methods showed better contrast between the tumors and surrounding tissues owing to the intrinsic edge-preserving property of the prior which is attributed to the sparseness induced by l1 norm, especially in the iterative reweighting scheme. Besides, the proposed methods demonstrated lower bias and less hyper-parameter dependency on PET intensity estimation in the regions with matched anatomical boundaries in PET and MRI. Moreover, based on the formulation of l1 Bowsher prior, the unrolled network containing the conventional maximum-likelihood expectation-maximization (ML-EM) module was also proposed. The convolutional layers successfully learned the distribution of anatomically-guided PET images and the EM module corrected the intermediate outputs by comparing them with sinograms. The proposed unrolled network showed better performance than ordinary U-Net, where the regional uptake is less biased and deviated. Therefore, these methods will help improve the PET image quality based on the anatomical side information.양전자방출단층촬영 / 자기공명영상 (PET/MRI) 동시 획득 기술의 발전으로 MR 영상을 기반으로 한 해부학적 사전 함수로 정규화 된 PET 영상 재구성 알고리즘에 대한 심도있는 평가가 이루어졌다. 해부학 기반으로 정규화 된 PET 이미지 재구성을 위해 제안 된 다양한 사전 중 2차 평활화 사전함수에 기반한 Bowsher의 방법은 때때로 세부 구조의 과도한 평활화로 어려움을 겪는다. 따라서 본 연구에서는 원래 Bowsher 방법의 한계를 극복하기 위해 l1 norm에 기반한 Bowsher 사전 함수와 반복적인 재가중치 기법을 제안한다. 또한, 우리는 이 매끄럽지 않은 사전 함수를 이용한 반복적 이미지 재구성에 대해 닫힌 해를 도출했다. 원래 l2와 제안 된 l1 Bowsher 사전 함수 간의 비교 연구는 컴퓨터 시뮬레이션과 실제 데이터를 사용하여 수행되었다. 시뮬레이션 및 실제 데이터에서 비정상적인 PET 흡수를 가진 작은 병변은 원래 Bowsher 이전보다 제안 된 l1 Bowsher 사전 방법으로 더 잘 감지되었다. 원래의 l2 Bowsher는 해부학적 영상에서 병변과 주변 조직 사이에 명확한 분리가 없을 때 작은 병변에서의 PET 강도를 감소시킨다. 그러나 제안 된 l1 Bowsher 사전 방법은 특히 반복적 재가중치 기법에서 l1 노름에 의해 유도된 희소성에 기인한 특성으로 인해 종양과 주변 조직 사이에 더 나은 대비를 보여주었다. 또한 제안된 방법은 PET과 MRI의 해부학적 경계가 일치하는 영역에서 PET 강도 추정에 대한 편향이 더 낮고 하이퍼 파라미터 종속성이 적음을 보여주었다. 또한, l1Bowsher 사전 함수의 닫힌 해를 기반으로 기존의 ML-EM (maximum-likelihood expectation-maximization) 모듈을 포함하는 펼쳐진 네트워크도 제안되었다. 컨볼루션 레이어는 해부학적으로 유도 재구성된 PET 이미지의 분포를 성공적으로 학습했으며, EM 모듈은 중간 출력들을 사이노그램과 비교하여 결과 이미지가 잘 들어맞게 수정했다. 제안된 펼쳐진 네트워크는 지역의 흡수선량이 덜 편향되고 편차가 적어, 일반 U-Net보다 더 나은 성능을 보여주었다. 따라서 이러한 방법들은 해부학적 정보를 기반으로 PET 이미지 품질을 향상시키는 데 유용할 것이다.Chapter 1. Introduction 1 1.1. Backgrounds 1 1.1.1. Positron Emission Tomography 1 1.1.2. Maximum a Posterior Reconstruction 1 1.1.3. Anatomical Prior 2 1.1.4. Proposed l_1 Bowsher Prior 3 1.1.5. Deep Learning for MR-less Application 4 1.2. Purpose of the Research 4 Chapter 2. Anatomically-guided PET Reconstruction Using Bowsher Prior 6 2.1. Backgrounds 6 2.1.1. PET Data Model 6 2.1.2. Original Bowsher Prior 7 2.2. Methods and Materials 8 2.2.1. Proposed l_1 Bowsher Prior 8 2.2.2. Iterative Reweighting 13 2.2.3. Computer Simulations 15 2.2.4. Human Data 16 2.2.5. Image Analysis 17 2.3. Results 19 2.3.1. Simulation with Brain Phantom 19 2.3.2.Human Data 20 2.4. Discussions 25 Chapter 3. Deep Learning Approach for Anatomically-guided PET Reconstruction 31 3.1. Backgrounds 31 3.2. Methods and Materials 33 3.2.1. Douglas-Rachford Splitting 33 3.2.2. Network Architecture 34 3.2.3. Dataset and Training Details 35 3.2.4. Image Analysis 36 3.3. Results 37 3.4. Discussions 38 Chapter 4. Conclusions 40 Bibliography 41 Abstract in Korean (국문 초록) 52Docto

Characterisation of computed tomography noise in projection space with applications to additive manufacturing

X-ray computed tomography can be used for defect detection in additive manufacturing. Typically, several x-ray projections of the product at hundreds of angles are used to reconstruct the object in 3D to look for any defects. The process can be time-consuming. This thesis aims to investigate if it is possible to conduct defect detection from a single projection to speed up the process. An additive manufacturing test sample was created with voids to see if they can be detected. The uncertainty of the projection was modelled using a compound Poisson distribution. This arises from x-ray photon arrivals being a Poisson process and each photon has random energy. This results in a linear relationship between the mean and variance of the grey values in the projection. Fitting of the compound Poisson distribution using the expectation maximisation algorithm was unsuccessful due to identifiability issues with the model. Instead, a gamma-distributed generalised linear model was fitted onto sample variance-mean data and used for variance prediction to quantify the uncertainty. Software, called aRTist, was used to simulate the projection and compared with the experimental projection in the face of uncertainty by treating each pixel as a hypothesis test. To overcome the imperfections of the simulation, the empirical null filter was used to cater for model misspecification so that sensible inference was achieved. This was done by locally normalising the test statistics using the mode. Voids with diameters in the order of millimetres were detectable. This thesis is a contribution to real-time quality control in additive manufacturing

Reduction of Limited Angle Artifacts in Medical Tomography via Image Reconstruction

Artifacts are unwanted effects in tomographic images that do not reflect the nature of the object. Their widespread occurrence makes their reduction and if possible removal an important subject in the development of tomographic image reconstruction algorithms. Limited angle artifacts are caused by the limited angular measurements, constraining the available tomographic information. This thesis focuses on reducing these artifacts via image reconstruction in two cases of incomplete measurements from: (1) the gaps left after the removal of high density objects such as dental fillings, screws and implants in computed tomography (CT) and (2) partial ring scanner configurations in positron emission tomography (PET). In order to include knowledge about the measurement and noise, prior terms were used within the reconstruction methods. Careful consideration was given to the trade-off between image blurring and noise reduction upon reconstruction of low-dose measurements.Development of reconstruction methods is an incremental process starting with testing on simple phantoms towards more clinically relevant ones by modeling the respective physical processes involved. In this work, phantoms were constructed to ensure that the proposed reconstruction methods addressed to the limited angle problem. The reconstructed images were assessed qualitatively and quantitatively in terms of noise reduction, edge sharpness and contrast recovery.Maximum a posteriori (MAP) estimation with median root prior (MRP) was selected for the reconstruction of limited angle measurements. MAP with MRP successfully reduced the artifacts caused by limited angle data in various datasets, tested with the reconstruction of both list-mode and projection data. In all cases, its performance was found to be superior to conventional reconstruction methods such as total-variation (TV) prior, maximum likelihood expectation maximization (MLEM) and filtered backprojection (FBP). MAP with MRP was also more robust with respect to parameter selection than MAP with TV prior.This thesis demonstrates the wide-range applicability of MAP with MRP in medical tomography, especially in low-dose imaging. Furthermore, we emphasize the importance of developing and testing reconstruction methods with application-specific phantoms, together with the properties and limitations of the measurements in mind

Accélération d'une approche régularisée de reconstruction en tomographie à rayons X avec réduction des artéfacts métalliques

Résumé Ce travail porte sur l'imagerie par tomographie à rayons X des vaisseaux périphériques traités par angioplastie avec implantation d'un tuteur endovasculaire métallique. On cherche à détecter le développement de la resténose en mesurant la lumière du vaisseau sanguin imagé. Cette application nécessite la reconstruction d'images de haute résolution. De plus, la présence du tuteur métallique cause l'apparition d'artéfacts qui nuisent à la précision de la mesure dans les images reconstruites dans les appareils tomographiques utilisés en milieu clinique. On propose donc de réaliser la reconstruction à l'aide d'un algorithme axé sur la maximisation pénalisée de la log-vraisemblance conditionnelle de l'image. Cet algorithme est déduit d'un modèle de formation des données qui tient compte de la variation non linéaire de l'atténuation des photons X dans l'objet selon leur énergie, ainsi que du caractère polychromatique du faisceau X. L'algorithme réduit donc effectivement les artéfacts causés spécifiquement par le tuteur métallique. De plus, il peut être configuré de manière à obtenir un compromis satisfaisant entre la résolution de l'image et la variance de l'image reconstruite, selon le niveau de bruit des données. Cette méthode de reconstruction est reconnue pour donner des images d'excellente qualité. Toutefois, le temps de calcul nécessaire à la convergence de cet algorithme est excessivement long. Le but de ce travail est donc de réduire le temps de calcul de cet algorithme de reconstruction itératif. Cette réduction passe par la critique de la formulation du problème et de la méthode de reconstruction, ainsi que par la mise en oeuvre d'approches alternatives.---------- Abstract This thesis is concerned with X-ray tomography of peripheral vessels that have undergone angioplasty with implantation of an endovascular metal stent. We seek to detect the onset of restenosis by measuring the lumen of the imaged blood vessel. This application requires the reconstruction of high-resolution images. In addition, the presence of a metal stent causes streak artifacts that complicate the lumen measurements in images obtained with the usual algorithms, like those implemented in clinical scanners. A regularized statistical reconstruction algorithm, hinged on the maximization of the conditional log-likelihood of the image, is preferable in this case. We choose a variant deduced from a data formation model that takes into account the nonlinear variation of X~photon attenuation to photon energy, as well as the polychromatic character of the X-ray beam. This algorithm effectively reduces the artifacts specifically caused by the metal structures. Moreover, the algorithm may be set to determine a good compromise between image resolution and variance, according to data noise. This reconstruction method is thus known to yield images of excellent quality. However, the runtime to convergence is excessively long. The goal of this work is to reduce the reconstruction runtime

Improved Modeling and Image Generation for Fluorescence Molecular Tomography (FMT) and Positron Emission Tomography (PET)

In this thesis, we aim to improve quantitative medical imaging with advanced image generation algorithms. We focus on two specific imaging modalities: fluorescence molecular tomography (FMT) and positron emission tomography (PET). For FMT, we present a novel photon propagation model for its forward model, and in addition, we propose and investigate a reconstruction algorithm for its inverse problem. In the first part, we develop a novel Neumann-series-based radiative transfer equation (RTE) that incorporates reflection boundary conditions in the model. In addition, we propose a novel reconstruction technique for diffuse optical imaging that incorporates this Neumann-series-based RTE as forward model. The proposed model is assessed using a simulated 3D diffuse optical imaging setup, and the results demonstrate the importance of considering photon reflection at boundaries when performing photon propagation modeling. In the second part, we propose a statistical reconstruction algorithm for FMT. The algorithm is based on sparsity-initialized maximum-likelihood expectation maximization (MLEM), taking into account the Poisson nature of data in FMT and the sparse nature of images. The proposed method is compared with a pure sparse reconstruction method as well as a uniform-initialized MLEM reconstruction method. Results indicate the proposed method is more robust to noise and shows improved qualitative and quantitative performance. For PET, we present an MRI-guided partial volume correction algorithm for brain imaging, aiming to recover qualitative and quantitative loss due to the limited resolution of PET system, while keeping image noise at a low level. The proposed method is based on an iterative deconvolution model with regularization using parallel level sets. A non-smooth optimization algorithm is developed so that the proposed method can be feasibly applied for 3D images and avoid additional blurring caused by conventional smooth optimization process. We evaluate the proposed method using both simulation data and in vivo human data collected from the Baltimore Longitudinal Study of Aging (BLSA). Our proposed method is shown to generate images with reduced noise and improved structure details, as well as increased number of statistically significant voxels in study of aging. Results demonstrate our method has promise to provide superior performance in clinical imaging scenarios

Aeronautical engineering: A continuing bibliography with indexes (supplement 292)

This bibliography lists 675 reports, articles, and other documents recently introduced into the NASA scientific and technical information system database. Subject coverage includes the following: design, construction and testing of aircraft and aircraft engines; aircraft components, equipment, and systems; ground support systems; and theoretical and applied aspects of aerodynamics and general fluid dynamics