Xiuheng Wang

Xinjue Wang, Xiuheng Wang, Esa Ollila et al.

Hyperspectral image (HSI) deconvolution is a challenging ill-posed inverse problem, made difficult by the data's high dimensionality.We propose a parameter-parsimonious framework based on a low-rank Canonical Polyadic Decomposition (CPD) of the entire latent HSI $\mathbf{\mathcal{X}} \in \mathbb{R}^{P\times Q \times N}$.This approach recasts the problem from recovering a large-scale image with $PQN$ variables to estimating the CPD factors with $(P+Q+N)R$ variables.This model also enables a structure-aware, anisotropic Total Variation (TV) regularization applied only to the spatial factors, preserving the smooth spectral signatures.An efficient algorithm based on the Proximal Alternating Linearized Minimization (PALM) framework is developed to solve the resulting non-convex optimization problem.Experiments confirm the model's efficiency, showing a numerous parameter reduction of over two orders of magnitude and a compelling trade-off between model compactness and reconstruction accuracy.

Xiuheng Wang, Ricardo Borsoi, Arnaud Breloy et al.

Non-parametric change-point detection in streaming time series data is a long-standing challenge in signal processing. Recent advancements in statistics and machine learning have increasingly addressed this problem for data residing on Riemannian manifolds. One prominent strategy involves monitoring abrupt changes in the center of mass of the time series. Implemented in a streaming fashion, this strategy, however, requires careful step size tuning when computing the updates of the center of mass. In this paper, we propose to leverage robust centroid on manifolds from M-estimation theory to address this issue. Our proposal consists of comparing two centroid estimates: the classical Karcher mean (sensitive to change) versus one defined from Huber's function (robust to change). This comparison leads to the definition of a test statistic whose performance is less sensitive to the underlying estimation method. We propose a stochastic Riemannian optimization algorithm to estimate both robust centroids efficiently. Experiments conducted on both simulated and real-world data across two representative manifolds demonstrate the superior performance of our proposed method.