arXiv subjects

Raymond H. Chan

Publications and source records attributed to Raymond H. Chan.

At least 19 recordsLinked to original sources

arXiv2026

Improving Diffusion Generative Models via Truncated Karhunen--Loève Expansion

Pretrained diffusion models exhibit a well-known training-sampling mismatch, often attributed to exposure bias and related distribution-shift effects. We provide a quantitative interpretation of this phenomenon through the notion of an effective noise level: empirically, a pretrained denoiser behaves as if trained at a noise level slightly below the nominal schedule. Motivated by this observation, we introduce a training-free sampling strategy based on truncating the Karhunen--Loève (KL) expansion of the Brownian motion driving the forward stochastic differential equation. Truncation yields a finite-dimensional forward process with a reduced noise level that can be adjusted independently of the time discretization. We prove uniform convergence of the truncated process to the original diffusion. To explain the resulting behaviour, we analyse a toy model in which the denoiser is exact but operates at a reduced effective noise level. The analysis predicts a non-monotone response to the sampling noise with a unique interior optimum, located by a one-dimensional sweep over the truncation order. We implement the approach through corresponding truncated reverse-time and probability-flow equations, without modifying the network architecture. Across CIFAR-10, CelebA, ImageNet, and latent-space Stable Diffusion, the truncation order consistently reveals a sweet spot, improving pretrained models in nearly all tested configurations. Training from scratch at a matched truncation order makes that order the network's own sweet spot, accelerates convergence by about $2.8\times$, and lowers the generation error on CIFAR-10 (Fréchet Inception Distance 7.14 to 5.47 at matched epochs; best checkpoint 6.74 to 5.23). A Lévy--Ciesielski comparison confirms that finite expansion is broadly beneficial.

cs.CV↗

arXiv2026

Pusa V1.0: Unlocking Temporal Control in Pretrained Video Diffusion Models via Vectorized Timestep Adaptation

The rapid advancement of video diffusion models has been hindered by fundamental limitations in temporal modeling, particularly the rigid synchronization of frame evolution imposed by conventional scalar timestep variables. While task-specific adaptations and autoregressive models have sought to address these challenges, they remain constrained by computational inefficiency, catastrophic forgetting, or narrow applicability. In this work, we present \textbf{Pusa} V1.0, a versatile model that leverages \textbf{vectorized timestep adaptation (VTA)} to enable fine-grained temporal control within a unified video diffusion framework. Note that VTA is a non-destructive adaptation, which means that it fully preserves the capabilities of the base model. Unlike conventional methods like Wan-I2V, which finetune a base text-to-video (T2V) model with abundant resources to do image-to-video (I2V), we achieve comparable results in a zero-shot manner after an ultra-efficient finetuning process based on VTA. Moreover, this method also unlocks many other zero-shot capabilities simultaneously, such as start-end frames and video extension -- all without task-specific training. Meanwhile, it keeps the T2V capability from the base model. Mechanistic analyses also reveal that our approach preserves the foundation model's generative priors while surgically injecting temporal dynamics, avoiding the combinatorial explosion inherent to the vectorized timestep. This work establishes a scalable, efficient, and versatile paradigm for next-generation video synthesis, democratizing high-fidelity video generation for research and industry alike.

cs.CV↗

arXiv2026

Beyond Text Prompts: Visual-to-Visual Generation as A Unified Paradigm

Humans often specify and create through visual artifacts: typography sheets, sketches, reference images, and annotated scenes. Yet modern visual generators still ask users to serialize this intent into text, a bottleneck that compresses signals like spatial structure, exact appearance, and glyph shape. We propose \textbf{\emph{visual-to-visual} (V2V)} generation, in which the user conditions a generative model with a visual specification page rather than a text prompt. The page is not an edit target, but a visual document that specifies the desired output. We introduce \textbf{V2V-Zero}, a training-free framework that exposes this interface in existing vision-language model (VLM) conditioned generators by replacing text-only conditioning with final-layer hidden states extracted from visual pages, exploiting the fact that the frozen VLM already maps both text and images into the generator's conditioning space. On GenEval, V2V-Zero reaches 0.85 with a frozen Qwen-Image backbone, closely matching its optimized text-to-image performance without fine-tuning. To evaluate the broader V2V space, we introduce \textbf{Simple-V2V Bench}, spanning seven visual-conditioning tasks and seven models, including GPT Image 2, Nano Banana 2, Seedream 5.0 Lite, open-weight baselines, and a video extension. V2V-Zero scores 32.7/100, outperforming evaluated open-weight image baselines and revealing a clear capability hierarchy: attribute binding is strong, content generation is unreliable, and structural control remains hard even for commercial systems. A HunyuanVideo-1.5 extension scores 20.2/100, showing the interface transfers beyond images. Mechanistic analysis shows the default reasoning path is primarily visually routed, with 95.0\% of conditioning-token attention mass on visual-page hidden states.

cs.CV↗

arXiv2026

Extending Pretrained 10-Second ECG Foundation Models to Longer Horizons

Electrocardiogram (ECG) foundation models pretrained on typical diagnostic 10-second ECG segments, have demonstrated strong transferability across a range of clinical applications. However, many real-world applications produce recordings that are typically longer, and are varied in duration during inference time. These 10-second models have no built-in way to combine information across time. Extending them to longer horizons introduces two challenges: structural incompatibilities arising from input-length disparities, and semantic challenges that limit meaningful temporal aggregation. We propose a parameter-efficient framework that extends pretrained ECG foundation models to longer and variable-length ECGs without retraining the backbone. Guided by a frozen pretrained 10-second model, we introduce a lightweight plug-in module that extends the model in two complementary ways: (i) structurally compatible long-sequence processing and (ii) semantically informed temporal modeling. Experiments on multiple long-horizon ECG tasks, datasets, and foundation model backbones demonstrate that our method enables robust long-horizon extension from pretrained snapshot models, consistently outperforming sliding-window and pooling-based baselines with strong parameter efficiency.

cs.LG↗

arXiv2026

Wavefront super-resolution for Adaptive Optics systems on ground-based telescopes

In ground-based astronomy, Adaptive Optics (AO) is a pivotal technique, engineered to correct wavefront phase distortions and thereby enhance the quality of the observed images. Integral to an AO system is the wavefront sensor (WFS), which is crucial for detecting wavefront aberrations from guide stars, essential for phase calculations. Many models based on a single-WFS model have been proposed to obtain the high-resolution phase of the incoming wavefront. In this paper, we delve into the realm of multiple WFSs within the framework of state-of-the-art telescope setups for high-resolution phase reconstruction. We propose a model for reconstructing a high-resolution wavefront from a sequence of wavefront gradient data from multiple WFSs in a multi-frame post-processing setting. Our model is based on the turbulence statistics and the Taylor frozen flow hypothesis, incorporating knowledge of the wind velocities in atmospheric turbulence layers. We also introduce an $H_2$ regularization term, especially for atmospheric characteristics under von Karman statistics, and provide a theoretical analysis for $H^2$ space within $H^{11/6}$. Numerical simulations are conducted to demonstrate the robustness and effectiveness of our regularization term and multi-WFS reconstruction strategy under identical experimental conditions.

astro-ph.IM↗

arXiv2026

A Mathematical Explanation of Transformers

The Transformer architecture has revolutionized the field of sequence modeling and underpins the recent breakthroughs in large language models (LLMs). However, a comprehensive mathematical theory that explains its structure and operations remains elusive. In this work, we propose a novel continuous framework that rigorously interprets the Transformer as a discretization of a structured integro-differential equation. Within this formulation, the self-attention mechanism emerges naturally as a non-local integral operator, and layer normalization is characterized as a projection to a time-dependent constraint. This operator-theoretic and variational perspective offers a unified and interpretable foundation for understanding the architecture's core components, including attention, feedforward layers, and normalization. Our approach extends beyond previous theoretical analyses by embedding the entire Transformer operation in continuous domains for both token indices and feature dimensions. This leads to a principled and flexible framework that not only deepens on theoretical insight but also offers new directions for architecture design, analysis, and control-based interpretations. This new interpretation provides a step toward bridging the gap between deep learning architectures and continuous mathematical modeling, and contributes a foundational perspective to the ongoing development of interpretable and theoretically grounded neural network models.

cs.LG↗

arXiv2026

Coupled Reconstruction of 2D Blood Flow and Vessel Geometry from Noisy Images via Physics-Informed Neural Networks and Quasi-Conformal Mapping

Blood flow imaging provides important information for hemodynamic behavior within the vascular system and plays an essential role in medical diagnosis and treatment planning. However, obtaining high-quality flow images remains a significant challenge. In this work, we address the problem of denoising flow images that may suffer from artifacts due to short acquisition times or device-induced errors. We formulate this task as an optimization problem, where the objective is to minimize the discrepancy between the modeled velocity field, constrained to satisfy the Navier-Stokes equations, and the observed noisy velocity data. To solve this problem, we decompose it into two subproblems: a fluid subproblem and a geometry subproblem. The fluid subproblem leverages a Physics-Informed Neural Network to reconstruct the velocity field from noisy observations, assuming a fixed domain. The geometry subproblem aims to infer the underlying flow region by optimizing a quasi-conformal mapping that deforms a reference domain. These two subproblems are solved in an alternating Gauss-Seidel fashion, iteratively refining both the velocity field and the domain. Upon convergence, the framework yields a high-quality reconstruction of the flow image. We validate the proposed method through experiments on synthetic flow data in a converging channel geometry under varying levels of Gaussian noise, and on real-like flow data in an aortic geometry with signal-dependent noise. The results demonstrate the effectiveness and robustness of the approach. Additionally, ablation studies are conducted to assess the influence of key hyperparameters.

math.NA↗

arXiv2025

Blind Adaptive Local Denoising for CEST Imaging

Chemical Exchange Saturation Transfer (CEST) MRI enables molecular-level visualization of low-concentration metabolites by leveraging proton exchange dynamics. However, its clinical translation is hindered by inherent challenges: spatially varying noise arising from hardware limitations, and complex imaging protocols introduce heteroscedasticity in CEST data, perturbing the accuracy of quantitative contrast mapping such as amide proton transfer (APT) imaging. Traditional denoising methods are not designed for this complex noise and often alter the underlying information that is critical for biomedical analysis. To overcome these limitations, we propose a new Blind Adaptive Local Denoising (BALD) method. BALD exploits the self-similar nature of CEST data to derive an adaptive variance-stabilizing transform that equalizes the noise distributions across CEST pixels without prior knowledge of noise characteristics. Then, BALD performs two-stage denoising on a linear transformation of data to disentangle molecular signals from noise. A local SVD decomposition is used as a linear transform to prevent spatial and spectral denoising artifacts. We conducted extensive validation experiments on multiple phantoms and \textit{in vivo} CEST scans. In these experiments, BALD consistently outperformed state-of-the-art CEST denoisers in both denoising metrics and downstream tasks such as molecular concentration maps estimation and cancer detection.

cs.CV↗

arXiv2025

LamiGauss: Pitching Radiative Gaussian for Sparse-View X-ray Laminography Reconstruction

X-ray Computed Laminography (CL) is essential for non-destructive inspection of plate-like structures in applications such as microchips and composite battery materials, where traditional computed tomography (CT) struggles due to geometric constraints. However, reconstructing high-quality volumes from laminographic projections remains challenging, particularly under highly sparse-view acquisition conditions. In this paper, we propose a reconstruction algorithm, namely LamiGauss, that combines Gaussian Splatting radiative rasterization with a dedicated detector-to-world transformation model incorporating the laminographic tilt angle. LamiGauss leverages an initialization strategy that explicitly filters out common laminographic artifacts from the preliminary reconstruction, preventing redundant Gaussians from being allocated to false structures and thereby concentrating model capacity on representing the genuine object. Our approach effectively optimizes directly from sparse projections, enabling accurate and efficient reconstruction with limited data. Extensive experiments on both synthetic and real datasets demonstrate the effectiveness and superiority of the proposed method over existing techniques. LamiGauss uses only 3$\%$ of full views to achieve superior performance over the iterative method optimized on a full dataset.

cs.CV↗

arXiv2025

Blind Restoration of High-Resolution Ultrasound Video

Ultrasound imaging is widely applied in clinical practice, yet ultrasound videos often suffer from low signal-to-noise ratios (SNR) and limited resolutions, posing challenges for diagnosis and analysis. Variations in equipment and acquisition settings can further exacerbate differences in data distribution and noise levels, reducing the generalizability of pre-trained models. This work presents a self-supervised ultrasound video super-resolution algorithm called Deep Ultrasound Prior (DUP). DUP employs a video-adaptive optimization process of a neural network that enhances the resolution of given ultrasound videos without requiring paired training data while simultaneously removing noise. Quantitative and visual evaluations demonstrate that DUP outperforms existing super-resolution algorithms, leading to substantial improvements for downstream applications.

cs.CV↗

arXiv2025

PiLocNet: Physics-informed neural network on 3D localization with rotating point spread function

For the 3D localization problem using point spread function (PSF) engineering, we propose a novel enhancement of our previously introduced localization neural network, LocNet. The improved network is a physics-informed neural network (PINN) that we call PiLocNet. Previous works on the localization problem may be categorized separately into model-based optimization and neural network approaches. Our PiLocNet combines the unique strengths of both approaches by incorporating forward-model-based information into the network via a data-fitting loss term that constrains the neural network to yield results that are physically sensible. We additionally incorporate certain regularization terms from the variational method, which further improves the robustness of the network in the presence of image noise, as we show for the Poisson and Gaussian noise models. This framework accords interpretability to the neural network, and the results we obtain show its superiority. Although the paper focuses on the use of single-lobe rotating PSF to encode the full 3D source location, we expect the method to be widely applicable to other PSFs and imaging problems that are constrained by known forward processes.

cs.LG↗

arXiv2024

Bilateral Signal Warping for Left Ventricular Hypertrophy Diagnosis

Left Ventricular Hypertrophy (LVH) is a major cardiovascular risk factor, linked to heart failure, arrhythmia, and sudden cardiac death, often resulting from chronic stress like hypertension. Electrocardiography (ECG), while varying in sensitivity, is widely accessible and cost-effective for detecting LVH-related morphological changes. This work introduces a bilateral signal warping (BSW) approach to improve ECG-based LVH diagnosis. Our method creates a library of heartbeat prototypes from patients with consistent ECG patterns. After preprocessing to eliminate baseline wander and detect R peaks, we apply BSW to cluster heartbeats, generating prototypes for both normal and LVH classes. We compare each new record to these references to support diagnosis. Experimental results show promising potential for practical application in clinical settings.

eess.SP↗

arXiv2024

Single-Shot Plug-and-Play Methods for Inverse Problems

The utilisation of Plug-and-Play (PnP) priors in inverse problems has become increasingly prominent in recent years. This preference is based on the mathematical equivalence between the general proximal operator and the regularised denoiser, facilitating the adaptation of various off-the-shelf denoiser priors to a wide range of inverse problems. However, existing PnP models predominantly rely on pre-trained denoisers using large datasets. In this work, we introduce Single-Shot PnP methods (SS-PnP), shifting the focus to solving inverse problems with minimal data. First, we integrate Single-Shot proximal denoisers into iterative methods, enabling training with single instances. Second, we propose implicit neural priors based on a novel function that preserves relevant frequencies to capture fine details while avoiding the issue of vanishing gradients. We demonstrate, through extensive numerical and visual experiments, that our method leads to better approximations.

cs.CV↗

arXiv2024

Super-resolving Real-world Image Illumination Enhancement: A New Dataset and A Conditional Diffusion Model

Most existing super-resolution methods and datasets have been developed to improve the image quality in well-lighted conditions. However, these methods do not work well in real-world low-light conditions as the images captured in such conditions lose most important information and contain significant unknown noises. To solve this problem, we propose a SRRIIE dataset with an efficient conditional diffusion probabilistic models-based method. The proposed dataset contains 4800 paired low-high quality images. To ensure that the dataset are able to model the real-world image degradation in low-illumination environments, we capture images using an ILDC camera and an optical zoom lens with exposure levels ranging from -6 EV to 0 EV and ISO levels ranging from 50 to 12800. We comprehensively evaluate with various reconstruction and perceptual metrics and demonstrate the practicabilities of the SRRIIE dataset for deep learning-based methods. We show that most existing methods are less effective in preserving the structures and sharpness of restored images from complicated noises. To overcome this problem, we revise the condition for Raw sensor data and propose a novel time-melding condition for diffusion probabilistic model. Comprehensive quantitative and qualitative experimental results on the real-world benchmark datasets demonstrate the feasibility and effectivenesses of the proposed conditional diffusion probabilistic model on Raw sensor data. Code and dataset will be available at https://github.com/Yaofang-Liu/Super-Resolving

cs.CV↗

arXiv2024

Real-Time Localization and Bimodal Point Pattern Analysis of Palms Using UAV Imagery

Understanding the spatial distribution of palms within tropical forests is essential for effective ecological monitoring, conservation strategies, and the sustainable integration of natural forest products into local and global supply chains. However, the analysis of remotely sensed data in these environments faces significant challenges, such as overlapping palm and tree crowns, uneven shading across the canopy surface, and the heterogeneous nature of the forest landscapes, which often affect the performance of palm detection and segmentation algorithms. To overcome these issues, we introduce PalmDSNet, a deep learning framework for real-time detection, segmentation, and counting of canopy palms. Additionally, we employ a bimodal reproduction algorithm that simulates palm spatial propagation to further enhance the understanding of these point patterns using PalmDSNet's results. We used UAV-captured imagery to create orthomosaics from 21 sites across western Ecuadorian tropical forests, covering a gradient from the everwet Chocó forests near Colombia to the drier forests of southwestern Ecuador. Expert annotations were used to create a comprehensive dataset, including 7,356 bounding boxes on image patches and 7,603 palm centers across five orthomosaics, encompassing a total area of 449 hectares. By combining PalmDSNet with the bimodal reproduction algorithm, which optimizes parameters for both local and global spatial variability, we effectively simulate the spatial distribution of palms in diverse and dense tropical environments, validating its utility for advanced applications in tropical forest monitoring and remote sensing analysis.

cs.CV↗

arXiv2024

A Mathematical Explanation of UNet

The UNet architecture has transformed image segmentation. UNet's versatility and accuracy have driven its widespread adoption, significantly advancing fields reliant on machine learning problems with images. In this work, we give a clear and concise mathematical explanation of UNet. We explain what is the meaning and function of each of the components of UNet. We will show that UNet is solving a control problem. We decompose the control variables using multigrid methods. Then, operator-splitting techniques is used to solve the problem, whose architecture exactly recovers the UNet architecture. Our result shows that UNet is a one-step operator-splitting algorithm for the control problem.

cs.CV↗

arXiv2024

Redefining Temporal Modeling in Video Diffusion: The Vectorized Timestep Approach

Diffusion models have revolutionized image generation, and their extension to video generation has shown promise. However, current video diffusion models~(VDMs) rely on a scalar timestep variable applied at the clip level, which limits their ability to model complex temporal dependencies needed for various tasks like image-to-video generation. To address this limitation, we propose a frame-aware video diffusion model~(FVDM), which introduces a novel vectorized timestep variable~(VTV). Unlike conventional VDMs, our approach allows each frame to follow an independent noise schedule, enhancing the model's capacity to capture fine-grained temporal dependencies. FVDM's flexibility is demonstrated across multiple tasks, including standard video generation, image-to-video generation, video interpolation, and long video synthesis. Through a diverse set of VTV configurations, we achieve superior quality in generated videos, overcoming challenges such as catastrophic forgetting during fine-tuning and limited generalizability in zero-shot methods.Our empirical evaluations show that FVDM outperforms state-of-the-art methods in video generation quality, while also excelling in extended tasks. By addressing fundamental shortcomings in existing VDMs, FVDM sets a new paradigm in video synthesis, offering a robust framework with significant implications for generative modeling and multimedia applications.

cs.CV↗

arXiv2024

Double-well Net for Image Segmentation

In this study, our goal is to integrate classical mathematical models with deep neural networks by introducing two novel deep neural network models for image segmentation known as Double-well Nets. Drawing inspirations from the Potts model, our models leverage neural networks to represent a region force functional. We extend the well-know MBO (Merriman-Bence-Osher) scheme to solve the Potts model. The widely recognized Potts model is approximated using a double-well potential and then solved by an operator-splitting method, which turns out to be an extension of the well-known MBO scheme. Subsequently, we replace the region force functional in the Potts model with a UNet-type network, which is data-driven and is designed to capture multiscale features of images, and also introduce control variables to enhance effectiveness. The resulting algorithm is a neural network activated by a function that minimizes the double-well potential. What sets our proposed Double-well Nets apart from many existing deep learning methods for image segmentation is their strong mathematical foundation. They are derived from the network approximation theory and employ the MBO scheme to approximately solve the Potts model. By incorporating mathematical principles, Double-well Nets bridge the MBO scheme and neural networks, and offer an alternative perspective for designing networks with mathematical backgrounds. Through comprehensive experiments, we demonstrate the performance of Double-well Nets, showcasing their superior accuracy and robustness compared to state-of-the-art neural networks. Overall, our work represents a valuable contribution to the field of image segmentation by combining the strengths of classical variational models and deep neural networks. The Double-well Nets introduce an innovative approach that leverages mathematical foundations to enhance segmentation performance.

cs.CV↗