arXiv subjects

Hsin-Hsiung Huang

Publications and source records attributed to Hsin-Hsiung Huang.

30 records · Page 2Linked to original sources

arXiv2025

A statistical reconstruction algorithm for positronium lifetime imaging using time-of-flight positron emission tomography

Positron emission tomography (PET) is an important modality for diagnosing diseases such as cancer and Alzheimer's disease, capable of revealing the uptake of radiolabeled molecules that target specific pathological markers of the diseases. Recently, positronium lifetime imaging (PLI) that adds to traditional PET the ability to explore properties of the tissue microenvironment beyond tracer uptake has been demonstrated with time-of-flight (TOF) PET and the use of non-pure positron emitters. However, achieving accurate reconstruction of lifetime images from data acquired by systems having a finite TOF resolution still presents a challenge. This paper focuses on the two-dimensional PLI, introducing a maximum likelihood estimation (MLE) method that employs an exponentially modified Gaussian (EMG) probability distribution that describes the positronium lifetime data produced by TOF PET. We evaluate the performance of our EMG-based MLE method against \st{traditional} approaches using exponential likelihood functions and penalized surrogate methods. Results from computer-simulated data reveal that the proposed EMG-MLE method can yield quantitatively accurate lifetime images. We also demonstrate that the proposed MLE formulation can be extended to handle PLI data containing multiple positron populations.

physics.med-ph↗

arXiv2024

Two-Step Mixed-Type Multivariate Bayesian Sparse Variable Selection with Shrinkage Priors

We introduce a Bayesian framework for mixed-type multivariate regression using continuous shrinkage priors. Our framework enables joint analysis of mixed continuous and discrete outcomes and facilitates variable selection from the $p$ covariates. Theoretical studies of Bayesian mixed-type multivariate response models have not been conducted previously and require more intricate arguments than the corresponding theory for univariate response models due to the correlations between the responses. In this paper, we investigate necessary and sufficient conditions for posterior contraction of our method when $p$ grows faster than sample size $n$. The existing literature on Bayesian high-dimensional asymptotics has focused only on cases where $p$ grows subexponentially with $n$. In contrast, we study the asymptotic regime where $p$ is allowed to grow exponentially in terms of $n$. We develop a novel two-step approach for variable selection which possesses the sure screening property and provably achieves posterior contraction even under exponential growth of $p$. We demonstrate the utility of our method through simulation studies and applications to real data, including a cancer genomics dataset where $n=174$ and $p=9183$. The R code to implement our method is available at https://github.com/raybai07/MtMBSP.

math.ST↗

arXiv2024

Fréchet Sufficient Dimension Reduction for Metric Space-Valued Data via Distance Covariance

We propose a novel Fréchet sufficient dimension reduction (SDR) method based on kernel distance covariance, tailored for metric space-valued responses such as count data, probability densities, and other complex structures. The method leverages a kernel-based transformation to map metric space-valued responses into a feature space, enabling efficient dimension reduction. By incorporating kernel distance covariance, the proposed approach offers enhanced flexibility and adaptability for datasets with diverse and non-Euclidean characteristics. The effectiveness of the method is demonstrated through synthetic simulations and several real-world applications. In all cases, the proposed method runs faster and consistently outperforms the existing Fréchet SDR approaches, demonstrating its broad applicability and robustness in addressing complex data challenges.

stat.ME↗

arXiv2024

Enhancing Positronium Lifetime Imaging through Two-Component Reconstruction in Time-of-Flight Positron Emission Tomography

Positron Emission Tomography (PET) is a crucial tool in medical imaging, particularly for diagnosing diseases like cancer and Alzheimer's. The advent of Positronium Lifetime Imaging (PLI) has opened new avenues for assessing the tissue micro-environment, which is vital for early-stage disease detection. In this study, we introduce a two-component reconstruction model for PLI in Time-of-Flight (TOF) PET, incorporating both ortho-positronium and para-positronium decays. Our model enhances the accuracy of positronium imaging by providing a more detailed representation of the tissue environment. We conducted simulation studies to evaluate the performance of our model and compared it with existing single-component models. The results demonstrate the superiority of the two-component model in capturing the intricacies of the tissue micro-environment, thus paving the way for more precise and informative PET diagnostics.

physics.med-ph↗

arXiv2024

Nonlinear Regression Analysis

Nonlinear regression analysis is a popular and important tool for scientists and engineers. In this article, we introduce theories and methods of nonlinear regression and its statistical inferences using the frequentist and Bayesian statistical modeling and computation. Least squares with the Gauss-Newton method is the most widely used approach to parameters estimation. Under the assumption of normally distributed errors, maximum likelihood estimation is equivalent to least squares estimation. The Wald confidence regions for parameters in a nonlinear regression model are affected by the curvatures in the mean function. Furthermore, we introduce the Newton-Raphson method and the generalized least squares method to deal with variance heterogeneity. Examples of simulation data analysis are provided to illustrate important properties of confidence regions and the statistical inferences using the nonlinear least squares estimation and Bayesian inference.

stat.ME↗

arXiv2024

A Framework of Zero-Inflated Bayesian Negative Binomial Regression Models For Spatiotemporal Data

Spatiotemporal data analysis with massive zeros is widely used in many areas such as epidemiology and public health. We use a Bayesian framework to fit zero-inflated negative binomial models and employ a set of latent variables from Pólya-Gamma distributions to derive an efficient Gibbs sampler. The proposed model accommodates varying spatial and temporal random effects through Gaussian process priors, which have both the simplicity and flexibility in modeling nonlinear relationships through a covariance function. To conquer the computation bottleneck that GPs may suffer when the sample size is large, we adopt the nearest-neighbor GP approach that approximates the covariance matrix using local experts. For the simulation study, we adopt multiple settings with varying sizes of spatial locations to evaluate the performance of the proposed model such as spatial and temporal random effects estimation and compare the result to other methods. We also apply the proposed model to the COVID-19 death counts in the state of Florida, USA from 3/25/2020 through 7/29/2020 to examine relationships between social vulnerability and COVID-19 deaths.

stat.ME↗

arXiv2024

Robust Sufficient Dimension Reduction via $α$-Distance Covariance

We introduce a novel sufficient dimension-reduction (SDR) method which is robust against outliers using $α$-distance covariance (dCov) in dimension-reduction problems. Under very mild conditions on the predictors, the central subspace is effectively estimated and model-free advantage without estimating link function based on the projection on the Stiefel manifold. We establish the convergence property of the proposed estimation under some regularity conditions. We compare the performance of our method with existing SDR methods by simulation and real data analysis and show that our algorithm improves the computational efficiency and effectiveness.

stat.ME↗

arXiv2023

Multiple Imputation Method for High-Dimensional Neuroimaging Data

Missingness is a common issue for neuroimaging data, and neglecting it in downstream statistical analysis can introduce bias and lead to misguided inferential conclusions. It is therefore crucial to conduct appropriate statistical methods to address this issue. While multiple imputation is a popular technique for handling missing data, its application to neuroimaging data is hindered by high dimensionality and complex dependence structures of multivariate neuroimaging variables. To tackle this challenge, we propose a novel approach, named High Dimensional Multiple Imputation (HIMA), based on Bayesian models. HIMA develops a new computational strategy for sampling large covariance matrices based on a robustly estimated posterior mode, which drastically enhances computational efficiency and numerical stability. To assess the effectiveness of HIMA, we conducted extensive simulation studies and real-data analysis using neuroimaging data from a Schizophrenia study. HIMA showcases a computational efficiency improvement of over 2000 times when compared to traditional approaches, while also producing imputed datasets with improved precision and stability.

stat.ME↗

arXiv2022

Robust Regularized Low-Rank Matrix Models for Regression and Classification

While matrix variate regression models have been studied in many existing works, classical statistical and computational methods for the analysis of the regression coefficient estimation are highly affected by high dimensional and noisy matrix-valued predictors. To address these issues, this paper proposes a framework of matrix variate regression models based on a rank constraint, vector regularization (e.g., sparsity), and a general loss function with three special cases considered: ordinary matrix regression, robust matrix regression, and matrix logistic regression. We also propose an alternating projected gradient descent algorithm. Based on analyzing our objective functions on manifolds with bounded curvature, we show that the algorithm is guaranteed to converge, all accumulation points of the iterates have estimation errors in the order of $O(1/\sqrt{n})$ asymptotically and substantially attaining the minimax rate. Our theoretical analysis can be applied to general optimization problems on manifolds with bounded curvature and can be considered an important technical contribution to this work. We validate the proposed method through simulation studies and real image data examples.

stat.ML↗

arXiv2020

The Unsupervised Method of Vessel Movement Trajectory Prediction

In real-world application scenarios, it is crucial for marine navigators and security analysts to predict vessel movement trajectories at sea based on the Automated Identification System (AIS) data in a given time span. This article presents an unsupervised method of ship movement trajectory prediction which represents the data in a three-dimensional space which consists of time difference between points, the scaled error distance between the tested and its predicted forward and backward locations, and the space-time angle. The representation feature space reduces the search scope for the next point to a collection of candidates which fit the local path prediction well, and therefore improve the accuracy. Unlike most statistical learning or deep learning methods, the proposed clustering-based trajectory reconstruction method does not require computationally expensive model training. This makes real-time reliable and accurate prediction feasible without using a training set. Our results show that the most prediction trajectories accurately consist of the true vessel paths.

cs.CV↗

arXiv2019

Photon allocation strategy in region-of-interest tomographic imaging

Photon counting detection is a promising approach toward effectively reducing the radiation dose in x-ray computed tomography (CT). Full CT reconstruction from a fraction of the detected photons required by scintillation-based detectors has been demonstrated. Current efforts in photon-counting CT have focused mainly on reconstruction techniques. In medical and industrial x-ray computed tomography (CT) applications, truncated projection from the region-of-interest (ROI) is another effective way of dose reduction, as information from the ROI is usually sufficient for diagnostic purpose. Projection truncation poses an ill-conditioned inverse problem, which can be improved by including projections from the exterior region. However, this trade-off between the interior reconstruction quality and the additional exterior measurement (extra dose) has not been studied. In this manuscript, we explore the number of detected x-ray photons as a new dimension for measurement engineering. Specifically, we design a flexible, photon-efficient measurement strategy for ROI reconstruction by incorporating the photon statistics at extremely low flux level (~10 photons per pixel). The optimized photon-allocation strategy shows 10 ~ 15-fold lower ROI reconstruction error than truncated projections, and 2-fold lower than whole-volume CT scan. Our analysis in few-photon interior tomography could serve as a new framework for dose-efficient, task-specific x-ray image acquisition design.

physics.med-ph↗

arXiv2016

An Affine-Invariant Bayesian Cluster Process

In order to identify clusters of objects with features transformed by unknown affine transformations, we develop a Bayesian cluster process which is invariant with respect to certain linear transformations of the feature space and able to cluster data without knowing the number of clusters in advance. Specifically, our proposed method can identify clusters invariant to orthogonal transformations under model I, invariant to scaling-coordinate orthogonal transformations under model II, or invariant to arbitrary non-singular linear transformations under model III. The proposed split-merge algorithm leads to an irreducible and aperiodic Markov chain, which is also efficient at identifying clusters reasonably well for various applications. We illustrate the applications of our approach to both synthetic and real data such as leukemia gene expression data for model I; wine data and two half-moons benchmark data for model II; three-dimensional Denmark road geographic coordinate system data and an arbitrary non-singular transformed two half-moons data for model III. These examples show that the proposed method could be widely applied in many fields, especially for finding the number of clusters and identifying clusters of samples of interest in aerial photography and genomic data.

stat.ME↗