Machine Learning-based Techniques to Address Spectral Distortions in Photon Counting X-ray Computed Tomography

Spectral CT using a photon counting x-ray detector (PCXD) shows great potential for measuring material composition based on energy dependent x-ray attenuation. Spectral CT is especially suited for imaging with K-edge contrast agents to address the otherwise limited contrast in soft tissues. We have developed a micro-CT system based on a PCXD. This system enables full spectrum CT in which the energy thresholds of the PCXD are swept to sample the full energy spectrum for each detector element and projection angle. Measurements provided by the PCXD, however, are distorted due to undesirable physical eects in the detector and are very noisy due to photon starvation. In this work, we proposed two methods based on machine learning to address the spectral distortion issue and to improve the material decomposition. This rst approach is to model distortions using an articial neural network (ANN) and compensate for the distortion in a statistical reconstruction. The second approach is to directly correct for the distortion in the projections. Both technique can be done as a calibration process where the neural network can be trained using 3D printed phantoms data to learn the distortion model or the correction model of the spectral distortion. This replaces the need for synchrotron measurements required in conventional technique to derive the distortion model parametrically which could be costly and time consuming. The results demonstrate experimental feasibility and potential advantages of ANN-based distortion modeling and correction for more accurate K-edge imaging with a PCXD. Given the computational eciency with which the ANN can be applied to projection data, the proposed scheme can be readily integrated into existing CT reconstruction pipelines.

Knowledge Modeling for The Outcome of Brain Stereotactic Radiosurgery

Purpose: To build a model that will predict the survival time for patients that were treated with stereotactic radiosurgery for brain metastases using support vector machine (SVM) regression.

Methods and Materials: This study utilized data from 481 patients, which were equally divided into training and validation datasets randomly. The SVM model used a Gaussian RBF function, along with various parameters, such as the size of the epsilon insensitive region and the cost parameter (C) that are used to control the amount of error tolerated by the model. The predictor variables for the SVM model consisted of the actual survival time of the patient, the number of brain metastases, the graded prognostic assessment (GPA) and Karnofsky Performance Scale (KPS) scores, prescription dose, and the largest planning target volume (PTV). The response of the model is the survival time of the patient. The resulting survival time predictions were analyzed against the actual survival times by single parameter classification and two-parameter classification. The predicted mean survival times within each classification were compared with the actual values to obtain the confidence interval associated with the model’s predictions. In addition to visualizing the data on plots using the means and error bars, the correlation coefficients between the actual and predicted means of the survival times were calculated during each step of the classification.

Results: The number of metastases and KPS scores, were consistently shown to be the strongest predictors in the single parameter classification, and were subsequently used as first classifiers in the two-parameter classification. When the survival times were analyzed with the number of metastases as the first classifier, the best correlation was obtained for patients with 3 metastases, while patients with 4 or 5 metastases had significantly worse results. When the KPS score was used as the first classifier, patients with a KPS score of 60 and 90/100 had similar strong correlation results. These mixed results are likely due to the limited data available for patients with more than 3 metastases or KPS scores of 60 or less.

Conclusions: The number of metastases and the KPS score both showed to be strong predictors of patient survival time. The model was less accurate for patients with more metastases and certain KPS scores due to the lack of training data.

Sensor Planning for Bayesian Nonparametric Target Modeling

Bayesian nonparametric models, such as the Gaussian process and the Dirichlet process, have been extensively applied for target kinematics modeling in various applications including environmental monitoring, traffic planning, endangered species tracking, dynamic scene analysis, autonomous robot navigation, and human motion modeling. As shown by these successful applications, Bayesian nonparametric models are able to adjust their complexities adaptively from data as necessary, and are resistant to overfitting or underfitting. However, most existing works assume that the sensor measurements used to learn the Bayesian nonparametric target kinematics models are obtained a priori or that the target kinematics can be measured by the sensor at any given time throughout the task. Little work has been done for controlling the sensor with bounded field of view to obtain measurements of mobile targets that are most informative for reducing the uncertainty of the Bayesian nonparametric models. To present the systematic sensor planning approach to leaning Bayesian nonparametric models, the Gaussian process target kinematics model is introduced at first, which is capable of describing time-invariant spatial phenomena, such as ocean currents, temperature distributions and wind velocity fields. The Dirichlet process-Gaussian process target kinematics model is subsequently discussed for modeling mixture of mobile targets, such as pedestrian motion patterns.

Novel information theoretic functions are developed for these introduced Bayesian nonparametric target kinematics models to represent the expected utility of measurements as a function of sensor control inputs and random environmental variables. A Gaussian process expected Kullback Leibler divergence is developed as the expectation of the KL divergence between the current (prior) and posterior Gaussian process target kinematics models with respect to the future measurements. Then, this approach is extended to develop a new information value function that can be used to estimate target kinematics described by a Dirichlet process-Gaussian process mixture model. A theorem is proposed that shows the novel information theoretic functions are bounded. Based on this theorem, efficient estimators of the new information theoretic functions are designed, which are proved to be unbiased with the variance of the resultant approximation error decreasing linearly as the number of samples increases. Computational complexities for optimizing the novel information theoretic functions under sensor dynamics constraints are studied, and are proved to be NP-hard. A cumulative lower bound is then proposed to reduce the computational complexity to polynomial time.

Three sensor planning algorithms are developed according to the assumptions on the target kinematics and the sensor dynamics. For problems where the control space of the sensor is discrete, a greedy algorithm is proposed. The efficiency of the greedy algorithm is demonstrated by a numerical experiment with data of ocean currents obtained by moored buoys. A sweep line algorithm is developed for applications where the sensor control space is continuous and unconstrained. Synthetic simulations as well as physical experiments with ground robots and a surveillance camera are conducted to evaluate the performance of the sweep line algorithm. Moreover, a lexicographic algorithm is designed based on the cumulative lower bound of the novel information theoretic functions, for the scenario where the sensor dynamics are constrained. Numerical experiments with real data collected from indoor pedestrians by a commercial pan-tilt camera are performed to examine the lexicographic algorithm. Results from both the numerical simulations and the physical experiments show that the three sensor planning algorithms proposed in this dissertation based on the novel information theoretic functions are superior at learning the target kinematics with

little or no prior knowledge

A Molecular-scale Programmable Stochastic Process Based On Resonance Energy Transfer Networks: Modeling And Applications

While molecular and cellular processes are often modeled as stochastic processes, such as Brownian motion, chemical reaction networks and gene regulatory networks, there are few attempts to program a molecular-scale process to physically implement stochastic processes. DNA has been used as a substrate for programming molecular interactions, but its applications are restricted to deterministic functions and unfavorable properties such as slow processing, thermal annealing, aqueous solvents and difficult readout limit them to proof-of-concept purposes. To date, whether there exists a molecular process that can be programmed to implement stochastic processes for practical applications remains unknown.

In this dissertation, a fully specified Resonance Energy Transfer (RET) network between chromophores is accurately fabricated via DNA self-assembly, and the exciton dynamics in the RET network physically implement a stochastic process, specifically a continuous-time Markov chain (CTMC), which has a direct mapping to the physical geometry of the chromophore network. Excited by a light source, a RET network generates random samples in the temporal domain in the form of fluorescence photons which can be detected by a photon detector. The intrinsic sampling distribution of a RET network is derived as a phase-type distribution configured by its CTMC model. The conclusion is that the exciton dynamics in a RET network implement a general and important class of stochastic processes that can be directly and accurately programmed and used for practical applications of photonics and optoelectronics. Different approaches to using RET networks exist with vast potential applications. As an entropy source that can directly generate samples from virtually arbitrary distributions, RET networks can benefit applications that rely on generating random samples such as 1) fluorescent taggants and 2) stochastic computing.

By using RET networks between chromophores to implement fluorescent taggants with temporally coded signatures, the taggant design is not constrained by resolvable dyes and has a significantly larger coding capacity than spectrally or lifetime coded fluorescent taggants. Meanwhile, the taggant detection process becomes highly efficient, and the Maximum Likelihood Estimation (MLE) based taggant identification guarantees high accuracy even with only a few hundred detected photons.

Meanwhile, RET-based sampling units (RSU) can be constructed to accelerate probabilistic algorithms for wide applications in machine learning and data analytics. Because probabilistic algorithms often rely on iteratively sampling from parameterized distributions, they can be inefficient in practice on the deterministic hardware traditional computers use, especially for high-dimensional and complex problems. As an efficient universal sampling unit, the proposed RSU can be integrated into a processor / GPU as specialized functional units or organized as a discrete accelerator to bring substantial speedups and power savings.