Di Wu

Di Wu, Shicai Fan, Xue Zhou et al.

Reconstruction-based methods have been commonly used for unsupervised anomaly detection, in which a normal image is reconstructed and compared with the given test image to detect and locate anomalies. Recently, diffusion models have shown promising applications for anomaly detection due to their powerful generative ability. However, these models lack strict mathematical support for normal image reconstruction and unexpectedly suffer from low reconstruction quality. To address these issues, this paper proposes a novel and highly-interpretable method named Masked Diffusion Posterior Sampling (MDPS). In MDPS, the problem of normal image reconstruction is mathematically modeled as multiple diffusion posterior sampling for normal images based on the devised masked noisy observation model and the diffusion-based normal image prior under Bayesian framework. Using a metric designed from pixel-level and perceptual-level perspectives, MDPS can effectively compute the difference map between each normal posterior sample and the given test image. Anomaly scores are obtained by averaging all difference maps for multiple posterior samples. Exhaustive experiments on MVTec and BTAD datasets demonstrate that MDPS can achieve state-of-the-art performance in normal image reconstruction quality as well as anomaly detection and localization.

Tengjie Zheng, Jilan Mei, Di Wu et al.

Accurate learning of system dynamics is becoming increasingly crucial for advanced control and decision-making in engineering. However, real-world systems often exhibit multiple channels and highly nonlinear transition dynamics, challenging traditional modeling methods. To enable online learning for these systems, this paper formulates the system as Gaussian process state-space models (GPSSMs) and develops a recursive learning method. The main contributions are threefold. First, a heterogeneous multi-output kernel is designed, allowing each output dimension to adopt distinct kernel types, hyperparameters, and input variables, improving expressiveness in multi-dimensional dynamics learning. Second, an inducing-point management algorithm enhances computational efficiency through independent selection and pruning for each output dimension. Third, a unified recursive inference framework for GPSSMs is derived, supporting general moment matching approaches, including the extended Kalman filter (EKF), unscented Kalman filter (UKF), and assumed density filtering (ADF), enabling accurate learning under strong nonlinearity and significant noise. Experiments on synthetic and real-world datasets show that the proposed method matches the accuracy of SOTA offline GPSSMs with only 1/100 of the runtime, and surpasses SOTA online GPSSMs by around 70% in accuracy under heavy noise while using only 1/20 of the runtime.

Di Wu, Tongxin Zhang, Yuan Zhong et al.

Preliminary mission design requires an efficient and accurate approximation to the low-thrust rendezvous trajectories, which might be generally three-dimensional and involve multiple revolutions. In this paper, a new shaping method using cubic spline functions is developed for the analytical approximation, which shows advantages in the optimality and computational efficiency. The rendezvous constraints on the boundary states and transfer time are all satisfied analytically, under the assumption that the boundary conditions and segment numbers of cubic spline functions are designated in advance. Two specific shapes are then formulated according to whether they have free optimization parameters. The shape without free parameters provides an efficient and robust estimation, while the other one allows a subsequent optimization for the satisfaction of additional constraints such as the constraint on the thrust magnitude. Applications of the proposed method in combination with the particle swarm optimization algorithm are discussed through two typical interplanetary rendezvous missions, that is, an inclined multi-revolution trajectory from the Earth to asteroid Dionysus and a multi-rendezvous trajectory of sample return. Simulation examples show that the proposed method is superior to existing methods in terms of providing good estimation for the global search and generating suitable initial guess for the subsequent trajectory optimization.