arXiv subjects

Jeonghwa Lee

Publications and source records attributed to Jeonghwa Lee.

7 recordsLinked to original sources

arXiv2026

High-Fidelity ROI CT Reconstruction with Limited Quantum Resources via Hybrid Classical-Quantum Refinement

Quantum optimization for computed tomography (CT) reconstruction is constrained by the number of binary variables required for image representation, making direct whole-image quantum reconstruction difficult for large or structurally complex objects. We propose a hybrid region-of-interest (ROI) refinement framework in which a coarse global image is first reconstructed by quantum tomographic reconstruction (QTR) and quantum compressed sensing tomographic reconstruction (QCSTR), filtered backprojection (FBP), or simultaneous algebraic reconstruction technique (SART), and quantum optimization is then applied only to the selected ROI through a residual projection-image formulation. This strategy reduces the effective QUBO size while preserving high-fidelity reconstruction in the target region. Experiments on three discrete phantom samples show that both QTR/QCSTR+QTR/QCSTR and SART+QTR/QCSTR achieve accurate ROI reconstruction for moderate-size cases under a reduced-angle setting. For the largest and most complex sample, the quality of the coarse global estimate becomes critical, and the best result is obtained when a stable classical coarse reconstruction is combined with second-stage ROI-only QTR/QCSTR. Among the tested pipelines, SART+QTR/QCSTR achieves the lowest average ROI RMSE and MAE. The results indicate that the practical advantage of quantum-assisted CT reconstruction lies in reserving quantum optimization for local refinement while using classical reconstruction to stabilize the global background.

quant-ph↗

arXiv2025

Scaling Limit of Dependent Random Walk

Recently, a generalized Bernoulli process (GBP) was developed as a stationary binary sequence that can have long-range dependence. In this paper, we find the scaling limit of a random walk that follows GBP. The result is a new class of non-Markovian diffusion processes. The limiting processes include continuous-time stochastic processes with stationary increments whose correlation decays with an exponential rate, a power law, or an exponentially tempered power law. The limit densities solve a time tempered fractional diffusion equation or time fractional diffusion equation. The second-family of Mittag-Leffler distribution and exponential distribution arise as special cases of the limiting distributions. Subordinated processes are considered as time-changed L\'evy processes, and the governing equations and dependence structure of the subordinated processes are discussed.

math.PR↗

arXiv2024

Fractional binomial regression model for count data with excess zeros

This paper proposes a new generalized linear model with the fractional binomial distribution. Zero-inflated Poisson/negative binomial distributions are used for count data with many zeros. To analyze the association of such a count variable with covariates, zero-inflated Poisson/negative binomial regression models are widely used. In this work, we develop a regression model with the fractional binomial distribution that can serve as an additional tool for modeling the count response variable with covariates. The consistency of maximum likelihood estimators of the proposed model is investigated theoretically and empirically with simulations. The practicality of the proposed model is examined through data analysis. The results show that our model is as versatile as or more versatile than the existing zero-inflated models, and especially, it has a better fit with left-skewed discrete data than other models. However, the proposed model faces computational obstacles and will require more work in the future to implement this model on various count data with excess zeros.

stat.ME↗

arXiv2024

On the construction of stationary processes and random fields

We propose a new method to construct a stationary process and random field with a given decreasing covariance function and any one-dimensional marginal distribution. The result is a new class of stationary processes and random fields. The construction method utilizes a correlated binary sequence, and it allows a simple and practical way to model dependence structures in a stationary process and random field as its dependence structure is induced by the correlation structure of a few disjoint sets in the support set of the marginal distribution. Simulation results of the proposed models are provided, which show the empirical behavior of a sample path.

stat.ME↗

arXiv2023

Noncentral moderate deviations for fractional Skellam processes

The term \emph{moderate deviations} is often used in the literature to mean a class of large deviation principles that, in some sense, fills the gap between a convergence in probability to zero (governed by a large deviation principle) and a weak convergence to a centered Normal distribution. We talk about \emph{noncentral moderate deviations} when the weak convergence is towards a non-Gaussian distribution. In this paper we present noncentral moderate deviation results for two fractional Skellam processes in the literature (see Kerss, Leonenko and Sikorskii, 2014). We also establish that, for the fractional Skellam process of type 2 (for which we can refer the recent results for compound fractional Poisson processes in Beghin and Macci (2022)), the convergences to zero are usually faster because we can prove suitable inequalities between rate functions.

math.PR↗

arXiv2023

Generalized Bernoulli Process and Fractional Binomial Distribution

Recently, a generalized Bernoulli process (GBP) was developed as a stationary binary sequence whose covariance function obeys a power law. In this paper, we further develop generalized Bernoulli processes, reveal their asymptotic behaviors, and find applications. We show that a GBP can have the same scaling limit as the fractional Poisson process. Considering that the Poisson process approximates the Bernoulli process under certain conditions, the connection we found between GBP and the fractional Poisson process is thought of as its counterpart under long-range dependence. When applied to indicator data, a GBP outperforms a Markov chain in the presence of long-range dependence. Fractional binomial models are defined as the sum in GBPs, and it is shown that when applied to count data with excess zeros, a fractional binomial model outperforms zero-inflated models that are used extensively for such data in current literature.

math.PR↗

arXiv2022

A finite-state stationary process with long-range dependence and fractional multinomial distribution

We propose a discrete-time, finite-state stationary process that can possess long-range dependence. Among the interesting features of this process is that each state can have different long-term dependency, i.e., the indicator sequence can have different Hurst index for different states. Also, inter-arrival time for each state follows heavy tail distribution, with different states showing different tail behavior. A possible application of this process is to model over-dispersed multinomial distribution. In particular, we define fractional multinomial distribution from our model.

math.PR↗