Emission Image Reconstruction for Randoms-Precorrected PET Allowing Negative Sinogram Values

Most positron emission tomography (PET) emission scans are corrected for accidental coincidence (AC) events by real-time subtraction of delayed-window coincidences, leaving only the randoms-precorrected data available for image reconstruction. The real-time randoms precorrection compensates in mean for AC events but destroys the Poisson statistics. The exact log-likelihood for randoms-precorrected data is inconvenient, so practical approximations are needed for maximum likelihood or penalized-likelihood image reconstruction. Conventional approximations involve setting negative sinogram values to zero, which can induce positive systematic biases, particularly for scans with low counts per ray. We propose new likelihood approximations that allow negative sinogram values without requiring zero-thresholding. With negative sinogram values, the log-likelihood functions can be nonconcave, complicating maximization; nevertheless, we develop monotonic algorithms for the new models by modifying the separable paraboloidal surrogates and the maximum-likelihood expectation-maximization (ML-EM) methods. These algorithms ascend to local maximizers of the objective function. Analysis and simulation results show that the new shifted Poisson (SP) model is nearly free of systematic bias yet keeps low variance. Despite its simpler implementation, the new SP performs comparably to the saddle-point model which has shown the best performance (as to systematic bias and variance) in randoms-precorrected PET emission reconstruction.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85994/1/Fessler61.pd

고해상도 PET 시스템을 위한 PET 검출기의 3차원 위치 정보 정확도 향상 기술 개발

학위논문 (박사)-- 서울대학교 대학원 : 의과대학 협동과정 방사선응용생명과학전공, 2018. 2. 이재성.The positron emission tomography (PET) is a widely used imaging modality that provides biological information at the molecular level. The biological information in molecular and cellular level enables a new discovery in both pre-clinical studies and clinical cases. However, due to the fundamental limits of the spatial resolution in the PET system, the effectiveness of PET is limited when diagnosing small-sized lesions. Hence, improving the spatial resolution in PET is important for the maximization of the diagnosing power of the PET system. In this thesis, studies on enhancing 3-dimensional (3D) positioning accuracy in PET detector for the high resolution PET system were conducted and presented. The depth-of-interaction (DOI) encoding/decoding and inter-crystal scattering (ICS) event identification technologies were developed and evaluated in the PET detector and system level. Firstly, the DOI encoding PET detector was developed and detector performances were evaluated. Maximum-likelihood estimation based DOI decoding methodology was developed and optimization studies in several aspects were conducted to achieve the high z-axis positioning accuracy. Secondly, based on the developed DOI encoding/decoding technologies, a prototype DOI PET system was developed and system-level performances were evaluated. Phantom and animal imaging studies were conducted to evaluate imaging performances of the prototype DOI PET system. The proposed DOI encoding/decoding technology was successfully demonstrated at the system level showing its feasibility for the high resolution PET application. Thirdly, a new ICS event identification method was proposed: a new technology of classifying and identifying ICS events in PET detectors with light sharing design, which was not feasible with existing technologies. The proposed method was validated by conducting simulation and experimental studies. By recovering identified ICS events, which is improving x- and y-direction positioning accuracy in the PET detector, improvement in the PET intrinsic spatial resolution was observed. In conclusion, the technologies developed in this thesis enhanced the spatial resolution of the PET system.Chapter 1. Introduction 1 1.1. Background 1 1.2. Purpose of this study 5 Chapter 2. Depth-of-interaction PET detector 7 2.1. Background 7 2.2. Materials and methods 10 2.2.1. Continuous DOI-encoding detector 10 2.2.2. DOI decoding methodology 11 2.2.3. DOI detector optimization study 13 2.3. Results 19 2.3.1 DOI detector optimization results 19 2.3.2 DOI detector performances 23 2.4 Discussion 29 Chapter 3. Depth-of-interaction PET system 30 3.1. Background 30 3.2. Materials and methods 30 3.2.1. DOI-encoding PET detector 30 3.2.2. Prototype PET scanner 32 3.2.3. Detector performance evaluation 34 3.2.4. Spatial resolution measurement 35 3.2.5. Phantom and animal imaging studies 36 3.3. Results 37 3.3.1. Detector performance 37 3.3.2. Spatial resolution of prototype system 39 3.3.3. Phantom and animal imaging study 40 3.4 Discussion 43 Chapter 4. Inter-crystal event identification 45 4.1. Background 45 4.2. Materials and methods 47 4.2.1. ICS event identification 47 4.2.2. Monte Carlo simulation study 50 4.2.3. ICS event recovery scheme 51 4.2.4. Experimental study 52 4.3. Results 55 4.3.1. Simulation results 55 4.3.2. Experimental results 62 4.4. Discussion 68 Chapter 5. Conclusion 71 Bibliography 73 Abstract in Korean 77Docto

Grouped-Coordinate Ascent Algorithms for Penalized-Likelihood Transmission Image Reconstruction

Presents a new class of algorithms for penalized-likelihood reconstruction of attenuation maps from low-count transmission scans. We derive the algorithms by applying to the transmission log-likelihood a version of the convexity technique developed by De Pierro for emission tomography. The new class includes the single-coordinate ascent (SCA) algorithm and Lange's convex algorithm for transmission tomography as special cases. The new grouped-coordinate ascent (GCA) algorithms in the class overcome several limitations associated with previous algorithms. (1) Fewer exponentiations are required than in the transmission maximum likelihood-expectation maximization (ML-EM) algorithm or in the SCA algorithm. (2) The algorithms intrinsically accommodate nonnegativity constraints, unlike many gradient-based methods. (3) The algorithms are easily parallelizable, unlike the SCA algorithm and perhaps line-search algorithms. We show that the GCA algorithms converge faster than the SCA algorithm, even on conventional workstations. An example from a low-count positron emission tomography (PET) transmission scan illustrates the method.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/86021/1/Fessler93.pd

Compressive Sensing of Signals Generated in Plastic Scintillators in a Novel J-PET Instrument

The J-PET scanner, which allows for single bed imaging of the whole human body, is currently under development at the Jagiellonian University. The dis- cussed detector offers improvement of the Time of Flight (TOF) resolution due to the use of fast plastic scintillators and dedicated electronics allowing for sam- pling in the voltage domain of signals with durations of few nanoseconds. In this paper we show that recovery of the whole signal, based on only a few samples, is possible. In order to do that, we incorporate the training signals into the Tikhonov regularization framework and we perform the Principal Component Analysis decomposition, which is well known for its compaction properties. The method yields a simple closed form analytical solution that does not require iter- ative processing. Moreover, from the Bayes theory the properties of regularized solution, especially its covariance matrix, may be easily derived. This is the key to introduce and prove the formula for calculations of the signal recovery error. In this paper we show that an average recovery error is approximately inversely proportional to the number of acquired samples

Penalized-Likelihood Estimators and Noise Analysis for Randoms-Precorrected PET Transmission Scans

This paper analyzes and compares image reconstruction methods based on practical approximations to the exact log likelihood of randoms precorrected positron emission tomography (PET) measurements. The methods apply to both emission and transmission tomography, however, in this paper the authors focus on transmission tomography. The results of experimental PET transmission scans and variance approximations demonstrate that the shifted Poisson (SP) method avoids the systematic bias of the conventional data-weighted least squares (WLS) method and leads to significantly lower variance than conventional statistical methods based on the log likelihood of the ordinary Poisson (OF) model. The authors develop covariance approximations to analyze the propagation of noise from attenuation maps into emission images via the attenuation correction factors (ACF's). Empirical pixel and region variances from real transmission data agree closely with the analytical predictions. Both the approximations and the empirical results show that the performance differences between the OP model and SP model are even larger, when considering noise propagation from the transmission images into the final emission images, than the differences in the attenuation maps themselves.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85852/1/Fessler84.pd

Development and Implementation of Fully 3D Statistical Image Reconstruction Algorithms for Helical CT and Half-Ring PET Insert System

X-ray computed tomography: CT) and positron emission tomography: PET) have become widely used imaging modalities for screening, diagnosis, and image-guided treatment planning. Along with the increased clinical use are increased demands for high image quality with reduced ionizing radiation dose to the patient. Despite their significantly high computational cost, statistical iterative reconstruction algorithms are known to reconstruct high-quality images from noisy tomographic datasets. The overall goal of this work is to design statistical reconstruction software for clinical x-ray CT scanners, and for a novel PET system that utilizes high-resolution detectors within the field of view of a whole-body PET scanner. The complex choices involved in the development and implementation of image reconstruction algorithms are fundamentally linked to the ways in which the data is acquired, and they require detailed knowledge of the various sources of signal degradation. Both of the imaging modalities investigated in this work have their own set of challenges. However, by utilizing an underlying statistical model for the measured data, we are able to use a common framework for this class of tomographic problems. We first present the details of a new fully 3D regularized statistical reconstruction algorithm for multislice helical CT. To reduce the computation time, the algorithm was carefully parallelized by identifying and taking advantage of the specific symmetry found in helical CT. Some basic image quality measures were evaluated using measured phantom and clinical datasets, and they indicate that our algorithm achieves comparable or superior performance over the fast analytical methods considered in this work. Next, we present our fully 3D reconstruction efforts for a high-resolution half-ring PET insert. We found that this unusual geometry requires extensive redevelopment of existing reconstruction methods in PET. We redesigned the major components of the data modeling process and incorporated them into our reconstruction algorithms. The algorithms were tested using simulated Monte Carlo data and phantom data acquired by a PET insert prototype system. Overall, we have developed new, computationally efficient methods to perform fully 3D statistical reconstructions on clinically-sized datasets

Novel PET Systems and Image Reconstruction with Actively Controlled Geometry

Positron Emission Tomography (PET) provides in vivo measurement of imaging ligands that are labeled with positron emitting radionuclide. Since its invention, most PET scanners have been designed to have a group of gamma ray detectors arranged in a ring geometry, accommodating the whole patient body. Virtual Pinhole PET incorporates higher resolution detectors being placed close to the Region-of-Interest (ROI) within the imaging Field-of-View (FOV) of the whole-body scanner, providing better image resolution and contrast recover. To further adapt this technology to a wider range of diseases, we proposed a second generation of virtual pinhole PET using actively controlled high resolution detectors integrated on a robotic arm. When the whole system is integrated to a commercial PET scanner, we achieved positioning repeatability within 0.5 mm. Monte Carlo simulation shows that by focusing the high-resolution detectors to a specific organ of interest, we can achieve better resolution, sensitivity and contrast recovery. In another direction, we proposed a portable, versatile and low cost PET imaging system for Point-of-Care (POC) applications. It consists of one or more movable detectors in coincidence with a detector array behind a patient. The movable detectors make it possible for the operator to control the scanning trajectory freely to achieve optimal coverage and sensitivity for patient specific imaging tasks. Since this system does not require a conventional full ring geometry, it can be built portable and low cost for bed-side or intraoperative use. We developed a proof-of-principle prototype that consists of a compact high resolution silicon photomultiplier detector mounted on a hand-held probe and a half ring of conventional detectors. The probe is attached to a MicroScribe device, which tracks the location and orientation of the probe as it moves. We also performed Monte Carlo simulations for two POC PET geometries with Time-of-Flight (TOF) capability. To support the development of such PET systems with unconventional geometries, a fully 3D image reconstruction framework has been developed for PET systems with arbitrary geometry. For POC PET and the second generation robotic Virtual Pinhole PET, new challenges emerge and our targeted applications require more efficiently image reconstruction that provides imaging results in near real time. Inspired by the previous work, we developed a list mode GPU-based image reconstruction framework with the capability to model dynamically changing geometry. Ordered-Subset MAP-EM algorithm is implemented on multi-GPU platform to achieve fast reconstruction in the order of seconds per iteration, under practical data rate. We tested this using both experimental and simulation data, for whole body PET scanner and unconventional PET scanners. Future application of adaptive imaging requires near real time performance for large statistics, which requires additional acceleration of this framework

Improving the Timing Resolution of Positron Emission Tomography Detectors Using Boosted Learning -- A Residual Physics Approach

Artificial intelligence (AI) is entering medical imaging, mainly enhancing image reconstruction. Nevertheless, improvements throughout the entire processing, from signal detection to computation, potentially offer significant benefits. This work presents a novel and versatile approach to detector optimization using machine learning (ML) and residual physics. We apply the concept to positron emission tomography (PET), intending to improve the coincidence time resolution (CTR). PET visualizes metabolic processes in the body by detecting photons with scintillation detectors. Improved CTR performance offers the advantage of reducing radioactive dose exposure for patients. Modern PET detectors with sophisticated concepts and read-out topologies represent complex physical and electronic systems requiring dedicated calibration techniques. Traditional methods primarily depend on analytical formulations successfully describing the main detector characteristics. However, when accounting for higher-order effects, additional complexities arise matching theoretical models to experimental reality. Our work addresses this challenge by combining traditional calibration with AI and residual physics, presenting a highly promising approach. We present a residual physics-based strategy using gradient tree boosting and physics-guided data generation. The explainable AI framework SHapley Additive exPlanations (SHAP) was used to identify known physical effects with learned patterns. In addition, the models were tested against basic physical laws. We were able to improve the CTR significantly (more than 20%) for clinically relevant detectors of 19 mm height, reaching CTRs of 185 ps (450-550 keV)