arXiv subjects

Xiaolin Zhu

Publications and source records attributed to Xiaolin Zhu.

5 recordsLinked to original sources

arXiv2026

Fractional Volterra-type operators from Bergman spaces with two-sided doubling weights to Hardy spaces

For $ω\in\calD$, we give necessary and sufficient symbol conditions for the boundedness and compactness of the Riemann--Liouville family$V^φ_{α,β}:A^p_ω\to H^q$ for every $0 0$: without any additional weight assumption when $α\geβ$, and, when $α<β$, under the condition $p(β-α)<d_-(ω)$, where $d_-(ω)$ is the critical reverse-doubling exponent. We prove that this inequality is exactly equivalent to the naturally shifted source weight retaining the two-sided doubling and tail geometry required by the reduction; an integrable logarithmic example shows that the endpoint fails. The extension from power weights is not formal, because the reduction replaces $ω$ by $ω(z)(1-|z|^2)^{p(α-β)}$, and a negative shift may destroy even integrability. Combining moment-induced Littlewood--Paley theory for doubling Bergman spaces with an exact coefficient-multiplier comparison, we establish the required Riemann--Liouville transfer, including the finite-dimensional exceptional modes at positive integral shift orders. A finite-codimensional range decomposition and a fractional $g$-function reduction then reduce both questions to a single weighted area-map problem. Within the admissible parameter set, the effects of $α$ are absorbed by the shifted source weight and bounded model corrections, so the final symbol conditions depend on $β$. The thresholds $p=2$ and $p=q$ yield pointwise, Carleson, tent-integral, and non-tangential maximal criteria. In the tent-integral range, boundedness already implies compactness.

math.FA↗

arXiv2026

Two Regularity Problems on Analytic Tent Spaces

We study two regularity problems on Hardy-type analytic tent spaces $\mathcal{AT}^p_{q,α}$ on the unit disk: fractional integration and randomization of Taylor coefficients. For fractional integration, we characterize completely the boundedness and compactness of the Hadamard, Flett, and Riemann--Liouville operators between analytic tent spaces, and obtain parallel results for analytic Triebel--Lizorkin spaces. In particular, the case $t=0$ yields a complete solution to the corresponding embedding problem for analytic tent spaces. For randomization, we characterize completely when the random Taylor series $\mathcal{R}f$ belongs almost surely to an analytic tent space whenever $f\in \mathcal{AT}^p_{q,α}$, and we also obtain the Triebel--Lizorkin counterpart. As part of the proof, we identify the random symbol space associated with $\mathcal{AT}^p_{q,α}$ and solve the embedding problem from analytic tent spaces into mixed norm spaces. These results extend classical theorems of Hardy--Littlewood and Littlewood, as well as their later analogues for Bergman and mixed norm spaces.

math.FA↗

arXiv2026

Democratizing planetary-scale analysis: An ultra-lightweight Earth embedding database for accurate and flexible global land monitoring

The rapid evolution of satellite-borne Earth Observation (EO) systems has revolutionized terrestrial monitoring, yielding petabyte-scale archives. However, the immense computational and storage requirements for global-scale analysis often preclude widespread use, hindering planetary-scale studies. To address these barriers, we present Embedded Seamless Data (ESD), an ultra-lightweight, 30-m global Earth embedding database spanning the 25-year period from 2000 to 2024. By transforming high-dimensional, multi-sensor observations from the Landsat series (5, 7, 8, and 9) and MODIS Terra into information-dense, quantized latent vectors, ESD distills essential geophysical and semantic features into a unified latent space. Utilizing the ESDNet architecture and Finite Scalar Quantization (FSQ), the dataset achieves a transformative ~340-fold reduction in data volume compared to raw archives. This compression allows the entire global land surface for a single year to be encapsulated within approximately 2.4 TB, enabling decadal-scale global analysis on standard local workstations. Rigorous validation demonstrates high reconstructive fidelity (MAE: 0.0130; RMSE: 0.0179; CC: 0.8543). By condensing the annual phenological cycle into 12 temporal steps, the embeddings provide inherent denoising and a semantically organized space that outperforms raw reflectance in land-cover classification, achieving 79.74% accuracy (vs. 76.92% for raw fusion). With robust few-shot learning capabilities and longitudinal consistency, ESD provides a versatile foundation for democratizing planetary-scale research and advancing next-generation geospatial artificial intelligence.

cs.CV↗

arXiv2024

DP-MDM: Detail-Preserving MR Reconstruction via Multiple Diffusion Models

Detail features of magnetic resonance images play a cru-cial role in accurate medical diagnosis and treatment, as they capture subtle changes that pose challenges for doc-tors when performing precise judgments. However, the widely utilized naive diffusion model has limitations, as it fails to accurately capture more intricate details. To en-hance the quality of MRI reconstruction, we propose a comprehensive detail-preserving reconstruction method using multiple diffusion models to extract structure and detail features in k-space domain instead of image do-main. Moreover, virtual binary modal masks are utilized to refine the range of values in k-space data through highly adaptive center windows, which allows the model to focus its attention more efficiently. Last but not least, an inverted pyramid structure is employed, where the top-down image information gradually decreases, ena-bling a cascade representation. The framework effective-ly represents multi-scale sampled data, taking into ac-count the sparsity of the inverted pyramid architecture, and utilizes cascade training data distribution to repre-sent multi-scale data. Through a step-by-step refinement approach, the method refines the approximation of de-tails. Finally, the proposed method was evaluated by con-ducting experiments on clinical and public datasets. The results demonstrate that the proposed method outper-forms other methods.

cs.CV↗

arXiv2024

Human-annotated label noise and their impact on ConvNets for remote sensing image scene classification

Convolutional neural networks (ConvNets) have been successfully applied to satellite image scene classification. Human-labeled training datasets are essential for ConvNets to perform accurate classification. Errors in human-annotated training datasets are unavoidable due to the complexity of satellite images. However, the distribution of real-world human-annotated label noises on remote sensing images and their impact on ConvNets have not been investigated. To fill this research gap, this study, for the first time, collected real-world labels from 32 participants and explored how their annotated label noise affect three representative ConvNets (VGG16, GoogleNet, and ResNet-50) for remote sensing image scene classification. We found that: (1) human-annotated label noise exhibits significant class and instance dependence; (2) an additional 1% of human-annotated label noise in training data leads to 0.5% reduction in the overall accuracy of ConvNets classification; (3) the error pattern of ConvNet predictions was strongly correlated with that of participant's labels. To uncover the mechanism underlying the impact of human labeling errors on ConvNets, we further compared it with three types of simulated label noise: uniform noise, class-dependent noise and instance-dependent noise. Our results show that the impact of human-annotated label noise on ConvNets significantly differs from all three types of simulated label noise, while both class dependence and instance dependence contribute to the impact of human-annotated label noise on ConvNets. These observations necessitate a reevaluation of the handling of noisy labels, and we anticipate that our real-world label noise dataset would facilitate the future development and assessment of label-noise learning algorithms.

cs.CV↗