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Qing Zou

Publications and source records attributed to Qing Zou.

18 recordsLinked to original sources
arXiv2026

General Value Functions for Remaining Useful Life and Failure-Mode Prediction

Remaining useful life (RUL) prediction and failure-mode classification are central tasks in predictive maintenance. Many data-driven pipelines use fixed-window supervised learning with complete terminal labels; such routes do not naturally encode the temporal recursion linking successive degradation-state predictions when observations are partial or unit identities are unavailable. We formulate prognostics as vector General Value Function (GVF) prediction on an absorbing degradation process, treating RUL and failure-mode probabilities as temporally consistent targets rather than independent window-level labels, and estimate them with a multi-step temporal-difference estimator, TD($n,\lambda$). Supporting theory identifies the Bellman fixed point of the vector GVFs, characterizes the linear projected-TD limit and its relation to complete-return Monte Carlo regression under realizability, and explains when bootstrapped TD targets are less variable than Monte Carlo returns. On an event-triggered multimode simulation and NASA C-MAPSS label-scarce stitch data, TD improves RUL and failure-mode prediction relative to a supervised same-backbone Monte Carlo control, especially under scarce complete labels. Practically, fragmented, identity-free degradation records can contribute local Bellman transitions instead of being discarded until complete run-to-failure labels are available.

stat.ML↗
arXiv2026

Path-Coupled Bellman Flows for Distributional Reinforcement Learning

Distributional reinforcement learning (DRL) models the full return distribution, but existing finite-support or quantile-based methods rely on projections, while recent flow-based approaches can suffer from \emph{boundary mismatch} at the flow source or from \emph{high-variance} bootstrapping when current and successor noises are independent. We propose Path-Coupled Bellman Flows (PCBF), a continuous-time DRL method that learns return distributions with flow matching using \textbf{source-consistent Bellman-coupled paths}: the current path starts from the required base prior at $t{=}0$, reaches the Bellman target at $t{=}1$, and maintains a pathwise affine relation to the successor flow at intermediate times (without requiring time-$t$ marginals to satisfy a distributional Bellman fixed point for all $t$). PCBF couples current and successor return flows through shared base noise and uses a $\lambda$-parameterized control-variate target: $\lambda{=}0$ recovers an unbiased sample Bellman target, while $\lambda{>}0$ trades controlled bias for variance reduction. Experiments on analytically tractable MRPs, OGBench, and D4RL show improved distributional fidelity and training stability, and competitive offline RL performance.

cs.LG↗
arXiv2025

MoRe-3DGSMR: Motion-resolved reconstruction framework for free-breathing pulmonary MRI based on 3D Gaussian representation

This study presents an unsupervised, motion-resolved reconstruction framework for high-resolution, free-breathing pulmonary magnetic resonance imaging (MRI), utilizing a three-dimensional Gaussian representation (3DGS). The proposed method leverages 3DGS to address the challenges of motion-resolved 3D isotropic pulmonary MRI reconstruction by enabling data smoothing between voxels for continuous spatial representation. Pulmonary MRI data acquisition is performed using a golden-angle radial sampling trajectory, with respiratory motion signals extracted from the center of k-space in each radial spoke. Based on the estimated motion signal, the k-space data is sorted into multiple respiratory phases. A 3DGS framework is then applied to reconstruct a reference image volume from the first motion state. Subsequently, a patient-specific convolutional neural network is trained to estimate the deformation vector fields (DVFs), which are used to generate the remaining motion states through spatial transformation of the reference volume. The proposed reconstruction pipeline is evaluated on six datasets from six subjects and bench-marked against three state-of-the-art reconstruction methods. The experimental findings demonstrate that the proposed reconstruction framework effectively reconstructs high-resolution, motion-resolved pulmonary MR images. Compared with existing approaches, it achieves superior image quality, reflected by higher signal-to-noise ratio and contrast-to-noise ratio. The proposed unsupervised 3DGS-based reconstruction method enables accurate motion-resolved pulmonary MRI with isotropic spatial resolution. Its superior performance in image quality metrics over state-of-the-art methods highlights its potential as a robust solution for clinical pulmonary MR imaging.

eess.IV↗
arXiv2025

Three-Dimensional MRI Reconstruction with Gaussian Representations: Tackling the Undersampling Problem

Three-Dimensional Gaussian Splatting (3DGS) has shown substantial promise in the field of computer vision, but remains unexplored in the field of magnetic resonance imaging (MRI). This study explores its potential for the reconstruction of isotropic resolution 3D MRI from undersampled k-space data. We introduce a novel framework termed 3D Gaussian MRI (3DGSMR), which employs 3D Gaussian distributions as an explicit representation for MR volumes. Experimental evaluations indicate that this method can effectively reconstruct voxelized MR images, achieving a quality on par with that of well-established 3D MRI reconstruction techniques found in the literature. Notably, the 3DGSMR scheme operates under a self-supervised framework, obviating the need for extensive training datasets or prior model training. This approach introduces significant innovations to the domain, notably the adaptation of 3DGS to MRI reconstruction and the novel application of the existing 3DGS methodology to decompose MR signals, which are presented in a complex-valued format.

eess.IV↗
arXiv2024

Graph Image Prior for Unsupervised Dynamic Cardiac Cine MRI Reconstruction

The inductive bias of the convolutional neural network (CNN) can be a strong prior for image restoration, which is known as the Deep Image Prior (DIP). Recently, DIP is utilized in unsupervised dynamic MRI reconstruction, which adopts a generative model from the latent space to the image space. However, existing methods usually use a pyramid-shaped CNN generator shared by all frames, embedding the temporal modeling within the latent space, which may hamper the model expression capability. In this work, we propose a novel scheme for dynamic MRI representation, named ``Graph Image Prior'' (GIP). GIP adopts a two-stage generative network in a new modeling methodology, which first employs independent CNNs to recover the image structure for each frame, and then exploits the spatio-temporal correlations within the feature space parameterized by a graph model. A graph convolutional network is utilized for feature fusion and dynamic image generation. In addition, we devise an ADMM algorithm to alternately optimize the images and the network parameters to improve the reconstruction performance. Experiments were conducted on cardiac cine MRI reconstruction, which demonstrate that GIP outperforms compressed sensing methods and other DIP-based unsupervised methods, significantly reducing the performance gap with state-of-the-art supervised algorithms. Moreover, GIP displays superior generalization ability when transferred to a different reconstruction setting, without the need for any additional data.

eess.IV↗
arXiv2023

Efficient online cross-covariance monitoring with incremental SVD: An approach for the detection of emerging dependency patterns in IoT systems

The development of the manufacturing systems has made it increasingly necessary to monitor the data generated by multiple interconnected subsystems with rapid incoming of samples. Based on incremental Singular Value Decomposition (ISVD), we develop a general online monitoring approach for the relationship of data generated from two interconnected subsystems, where each subsystem produces big data streams with several variation patterns in normal working condition. When special situation happens and new associations occur, a very small amount of computation is sufficient to update the system status and compute the control statistics by using this approach. The proposed method reduces computational overhead and retains only a small number of pairs of possible dependent patterns at each step. The validation of the method through simulation studies and a case study on semiconductor manufacturing processes further supports its effectiveness.

eess.SY↗
arXiv2022

Joint cardiac $T_1$ mapping and cardiac function estimation using a deep manifold framework

In this work, we proposed a continuous-acquisition strategy using a gradient echo (GRE) inversion recovery sequence based on spiral trajectories to simultaneously obtain the $T_1$ mapping and CINE imaging. The acquisition is using a free-breathing and ungated fashion. An approach based on variational auto-encoder(VAE) is used for the motion estimation from the centered k-space data. The motion signal is then used to train a deep manifold reconstruction algorithm for image reconstruction. Once the network is trained, we can excite the latent vectors (the estimated motion signals and the contrast signal) in any way as we wanted to generate the image frames in the time series. We can estimate the $T_1$ mapping using the generated image frames where only contrast is varying. We can also generate the breath-hold CINE in different contrast.

eess.IV↗
arXiv2021

Variational manifold learning from incomplete data: application to multislice dynamic MRI

Current deep learning-based manifold learning algorithms such as the variational autoencoder (VAE) require fully sampled data to learn the probability density of real-world datasets. Once learned, the density can be used for a variety of tasks, including data imputation. However, fully sampled data is often unavailable in a variety of problems, including the recovery of dynamic and high-resolution MRI data considered in this work. To overcome this problem, we introduce a novel variational approach to learn a manifold from undersampled data. The VAE uses a decoder fed by latent vectors, drawn from a conditional density estimated from the fully sampled images using an encoder. Since fully sampled images are not available in our setting, we approximate the conditional density of the latent vectors by a parametric model whose parameters are estimated from the undersampled measurements using back-propagation. We use the framework for the joint alignment and recovery of multislice free breathing and ungated cardiac MRI data from highly undersampled measurements. Most of the current self-gating and manifold cardiac MRI approaches consider the independent recovery of images from each slice; these methods are not capable of exploiting the inter-slice redundancies in the datasets and require sophisticated post-processing or manual approaches to align the images from different slices. By contrast, the proposed scheme is able to align the multislice data and exploit the redundancies. Experimental results demonstrate the utility of the proposed scheme in dynamic imaging alignment and reconstructions.

eess.IV↗
arXiv2021

Dynamic imaging using Motion-Compensated SmooThness Regularization on Manifolds (MoCo-SToRM)

We introduce an unsupervised motion-compensated reconstruction scheme for high-resolution free-breathing pulmonary MRI. We model the image frames in the time series as the deformed version of the 3D template image volume. We assume the deformation maps to be points on a smooth manifold in high-dimensional space. Specifically, we model the deformation map at each time instant as the output of a CNN-based generator that has the same weight for all time-frames, driven by a low-dimensional latent vector. The time series of latent vectors account for the dynamics in the dataset, including respiratory motion and bulk motion. The template image volume, the parameters of the generator, and the latent vectors are learned directly from the k-t space data in an unsupervised fashion. Our experimental results show improved reconstructions compared to state-of-the-art methods, especially in the context of bulk motion during the scans.

eess.IV↗
arXiv2021

Dynamic imaging using motion-compensated smoothness regularization on manifolds (MoCo-SToRM)

We introduce an unsupervised deep manifold learning algorithm for motion-compensated dynamic MRI. We assume that the motion fields in a free-breathing lung MRI dataset live on a manifold. The motion field at each time instant is modeled as the output of a deep generative model, driven by low-dimensional time-varying latent vectors that capture the temporal variability. The images at each time instant are modeled as the deformed version of an image template using the above motion fields. The template, the parameters of the deep generator, and the latent vectors are learned from the k-t space data in an unsupervised fashion. The manifold motion model serves as a regularizer, making the joint estimation of the motion fields and images from few radial spokes/frame well-posed. The utility of the algorithm is demonstrated in the context of motion-compensated high-resolution lung MRI.

eess.IV↗
arXiv2021

Joint alignment and reconstruction of multislice dynamic MRI using variational manifold learning

Free-breathing cardiac MRI schemes are emerging as competitive alternatives to breath-held cine MRI protocols, enabling applicability to pediatric and other population groups that cannot hold their breath. Because the data from the slices are acquired sequentially, the cardiac/respiratory motion patterns may be different for each slice; current free-breathing approaches perform independent recovery of each slice. In addition to not being able to exploit the inter-slice redundancies, manual intervention or sophisticated post-processing methods are needed to align the images post-recovery for quantification. To overcome these challenges, we propose an unsupervised variational deep manifold learning scheme for the joint alignment and reconstruction of multislice dynamic MRI. The proposed scheme jointly learns the parameters of the deep network as well as the latent vectors for each slice, which capture the motion-induced dynamic variations, from the k-t space data of the specific subject. The variational framework minimizes the non-uniqueness in the representation, thus offering improved alignment and reconstructions.

eess.IV↗
arXiv2021

Deep Image Prior using Stein's Unbiased Risk Estimator: SURE-DIP

Deep learning algorithms that rely on extensive training data are revolutionizing image recovery from ill-posed measurements. Training data is scarce in many imaging applications, including ultra-high-resolution imaging. The deep image prior (DIP) algorithm was introduced for single-shot image recovery, completely eliminating the need for training data. A challenge with this scheme is the need for early stopping to minimize the overfitting of the CNN parameters to the noise in the measurements. We introduce a generalized Stein's unbiased risk estimate (GSURE) loss metric to minimize the overfitting. Our experiments show that the SURE-DIP approach minimizes the overfitting issues, thus offering significantly improved performance over classical DIP schemes. We also use the SURE-DIP approach with model-based unrolling architectures, which offers improved performance over direct inversion schemes.

eess.IV↗
arXiv2021

Dynamic imaging using a deep generative SToRM (Gen-SToRM) model

We introduce a generative smoothness regularization on manifolds (SToRM) model for the recovery of dynamic image data from highly undersampled measurements. The model assumes that the images in the dataset are non-linear mappings of low-dimensional latent vectors. We use the deep convolutional neural network (CNN) to represent the non-linear transformation. The parameters of the generator as well as the low-dimensional latent vectors are jointly estimated only from the undersampled measurements. This approach is different from traditional CNN approaches that require extensive fully sampled training data. We penalize the norm of the gradients of the non-linear mapping to constrain the manifold to be smooth, while temporal gradients of the latent vectors are penalized to obtain a smoothly varying time-series. The proposed scheme brings in the spatial regularization provided by the convolutional network. The main benefit of the proposed scheme is the improvement in image quality and the orders-of-magnitude reduction in memory demand compared to traditional manifold models. To minimize the computational complexity of the algorithm, we introduce an efficient progressive training-in-time approach and an approximate cost function. These approaches speed up the image reconstructions and offers better reconstruction performance.

eess.IV↗
arXiv2021

Recovery of surfaces and functions in high dimensions: sampling theory and links to neural networks

Several imaging algorithms including patch-based image denoising, image time series recovery, and convolutional neural networks can be thought of as methods that exploit the manifold structure of signals. While the empirical performance of these algorithms is impressive, the understanding of recovery of the signals and functions that live on manifold is less understood. In this paper, we focus on the recovery of signals that live on a union of surfaces. In particular, we consider signals living on a union of smooth band-limited surfaces in high dimensions. We show that an exponential mapping transforms the data to a union of low-dimensional subspaces. Using this relation, we introduce a sampling theoretical framework for the recovery of smooth surfaces from few samples and the learning of functions living on smooth surfaces. The low-rank property of the features is used to determine the number of measurements needed to recover the surface. Moreover, the low-rank property of the features also provides an efficient approach, which resembles a neural network, for the local representation of multidimensional functions on the surface.

eess.SP↗
arXiv2021

Deep Generative SToRM model for dynamic imaging

We introduce a novel generative smoothness regularization on manifolds (SToRM) model for the recovery of dynamic image data from highly undersampled measurements. The proposed generative framework represents the image time series as a smooth non-linear function of low-dimensional latent vectors that capture the cardiac and respiratory phases. The non-linear function is represented using a deep convolutional neural network (CNN). Unlike the popular CNN approaches that require extensive fully-sampled training data that is not available in this setting, the parameters of the CNN generator as well as the latent vectors are jointly estimated from the undersampled measurements using stochastic gradient descent. We penalize the norm of the gradient of the generator to encourage the learning of a smooth surface/manifold, while temporal gradients of the latent vectors are penalized to encourage the time series to be smooth. The main benefits of the proposed scheme are (a) the quite significant reduction in memory demand compared to the analysis based SToRM model, and (b) the spatial regularization brought in by the CNN model. We also introduce efficient progressive approaches to minimize the computational complexity of the algorithm.

eess.IV↗
arXiv2019

Sampling of Planar Curves: Theory and Fast Algorithms

We introduce a continuous domain framework for the recovery of a planar curve from a few samples. We model the curve as the zero level set of a trigonometric polynomial. We show that the exponential feature maps of the points on the curve lie on a low-dimensional subspace. We show that the null-space vector of the feature matrix can be used to uniquely identify the curve, given a sufficient number of samples. The worst-case theoretical guarantees show that the number of samples required for unique recovery depends on the bandwidth of the underlying trigonometric polynomial, which is a measure of the complexity of the curve. We introduce an iterative algorithm that relies on the low-rank property of the feature maps to recover the curves when the samples are noisy or when the true bandwidth of the curve is unknown. We also demonstrate the preliminary utility of the proposed curve representation in the context of image segmentation.

eess.SP↗
arXiv2019

Sampling of surfaces and functions in high dimensional spaces

We introduce a sampling theoretic framework for the recovery of smooth surfaces and functions living on smooth surfaces from few samples. The proposed approach can be thought of as a nonlinear generalization of union of subspace models widely used in signal processing. This scheme relies on an exponential lifting of the original data points to feature space, where the features live on union of subspaces. The low-rank property of the features are used to recover the surfaces as well as to determine the number of measurements needed to recover the surface. The low-rank property of the features also provides an efficient approach which resembles a neural network for the local representation of multidimensional functions on the surface; the significantly reduced number of parameters make the computational structure attractive for learning inference from limited labeled training data.

eess.SP↗