arXiv subjects

Tongyu Li

Publications and source records attributed to Tongyu Li.

16 recordsLinked to original sources

arXiv2026

Statistical Inference on Gradient Flows

Gradient-based algorithms are central to modern statistical estimation, yet their statistical analysis is often restricted to fixed-time behavior, such as convergence to a population target or fluctuations at a prescribed iteration. In many applications, however, uncertainty quantification is needed along the entire optimization path, especially when the stopping time is data-dependent or divergent. In this paper, we develop a theory for time-uniform statistical inference on gradient flows arising from empirical risk minimization. We prove a uniform central limit theorem that characterizes the deviation between empirical and population gradient flows as a continuous-time Gaussian process over the entire nonnegative real line. Building on this result, we introduce an algorithm-aware covariance estimator that evolves jointly with the gradient flow and avoids matrix inversion, resampling, or sample splitting. We show that the covariance estimator is uniformly consistent over time and use it to construct confidence intervals for the target parameter with asymptotically valid coverage. Our results connect optimization dynamics with statistical inference and provide practical tools for uncertainty quantification in gradient-based methods.

math.ST↗

arXiv2026

DeepFilters: Scattering-Aware Pupil Engineering with Learned Digital Filter Reconstruction for Extended Depth of Field Microscopy

Extended depth of field microscopy encodes axial information into a single acquisition through engineered point spread functions, but conventional and deep optics approaches are subject to degradation in scattering tissue. We introduce DeepFilters, a scattering-aware deep optics framework that jointly optimizes a parameterized pupil filter and a digital-filter-based reconstruction network through a calibrated differentiable forward model to achieve broad generalization without retraining. Incorporating empirical scattering kernels, physics-guided regularization, and a hybrid genetic-gradient initialization strategy, DeepFilters extends the PSF from 16 micron to >400 micron in clear media and enables signal recovery beyond 120 micron deep in biological tissues, validated across fixed brain slices and sea urchin embryos.

physics.optics↗

arXiv2026

Multi-transport Distributional Regression

We study distribution-on-distribution regression problems in which a response distribution depends on multiple distributional predictors. Such settings arise naturally in applications where the outcome distribution is driven by several heterogeneous distributional sources, yet remain challenging due to the nonlinear geometry of the Wasserstein space. We propose an intrinsic regression framework that aggregates predictor-specific transported distributions through a weighted Fr\'echet mean in the Wasserstein space. The resulting model admits multiple distributional predictors, assigns interpretable weights quantifying their relative contributions, and defines a flexible regression operator that is invariant to auxiliary construction choices, such as the selection of a reference distribution. From a theoretical perspective, we establish identifiability of the induced regression operator and derive asymptotic guarantees for its estimation under a predictive Wasserstein semi-norm, which directly characterizes convergence of the composite prediction map. Extensive simulation studies and a real data application demonstrate the improved predictive performance and interpretability of the proposed approach compared with existing Wasserstein regression methods.

stat.ME↗

arXiv2025

Mid-Infrared Photothermal Relaxation Intensity Diffraction Tomography for Video-rate Volumetric Chemical Imaging

Three-dimensional molecular imaging of living cells is essential for unraveling cellular metabolism and response to therapies. However, existing volumetric methods, including fluorescence microscopy and quantitative phase imaging, either require fluorescent labels or lack chemical specificity. Mid-infrared (mid-IR) photothermal microscopy provides label-free spectroscopic contrast with sub-micrometer resolution but is limited by slow acquisition rates, precluding 3D live-cell studies. Here, we present a photothermal relaxation intensity diffraction tomography (PRIDT) system that encodes mid-IR absorption induced refractive index change via a photothermal relaxation scheme and recovers it through intensity diffraction tomography. PRIDT achieves video-rate volumetric chemical imaging with up to 15 Hz per wavelength and offers lateral and axial resolutions of 264 nm and 1.12 um over a volumetric field of view of 50x50x10 um3. We showcase high-speed PRIDT imaging of protein and lipid metabolism in ovarian cancer cells and lipid-droplet dynamics in live cells. PRIDT opens new avenues for rapid, quantitative, three-dimensional molecular imaging in living systems.

physics.optics↗

arXiv2025

Dual-wavelength Fourier Ptychographic Topography

We introduce a dual-wavelength Fourier ptychographic topography (FPT) method that extends the lambda/2 height-range limit of single-wavelength FPT. By reconstructing complex fields at two illumination wavelengths and exploiting their phase difference, the method achieves an effective synthetic wavelength lambda_s and an unambiguous range of lambda_s/2 without reducing lateral resolution. A noise-robust wrapped-number search is used to select per-pixel integer pairs (k1, k2), and a global refinement with circular TV regularization and soft bounds improves stability and preserves height discontinuities. The approach is validated through rigorous scattering-model-based simulations and experiments on structured silicon samples, demonstrating accurate height recovery in regimes where single-wavelength FPT exhibits phase wrapping. We analyze the limits of the FPT forward model and identify aspect ratio (AR) and phase modulation transfer function (ph-MTF) as key predictors of reconstruction fidelity. Simulations and experiments show that increasing AR beyond a practical threshold causes loss of high-frequency phase transfer and destabilizes dual-wavelength unwrapping. Within this AR range, dual-wavelength FPT provides robust, high-resolution topography suitable for semiconductor and industrial metrology.

physics.optics↗

arXiv2025

Transfer-Function Approach to Substrate-Enhanced Diffraction Tomography

Forward and backward scattering provide complementary volumetric and interfacial information, yet conventional three-dimensional (3D) imaging typically accesses only one. In this Letter, we present a substrate-enhanced diffraction tomography approach that simultaneously recovers both channels under multi-angle epi-illumination.This geometry captures one forward- and two backward-scattering bands in axially symmetric Fourier regions, where their complementary coverage enables phase-absorption separation in a non-Hermitian spectrum. Explicit 3D transfer functions are derived for both channels, and an axial Kramers-Kronig relation is established to incorporate substrate-induced boundary conditions in a unified framework. Our results establish a label-free, high-resolution 3D imaging modality that surpasses the limits of existing methods.

physics.optics↗

arXiv2025

A General Test for Independent and Identically Distributed Hypothesis

We propose a simple and intuitive test for arguably the most prevailing hypothesis in statistics that data are independent and identically distributed (IID), based on a newly introduced off-diagonal sequential U-process. This IID test is fully nonparametric and applicable to random objects in general spaces, while requiring no specific alternatives such as structural breaks or serial dependence, which allows for detecting general types of violations of the IID assumption. An easy-to-implement jackknife multiplier bootstrap is tailored to produce critical values of the test. Under mild conditions, we establish Gaussian approximation for the proposed U-processes, and derive non-asymptotic coupling and Kolmogorov distance bounds for its maximum and the bootstrapped version, providing rigorous theoretical guarantees. Simulations and real data applications are conducted to demonstrate the usefulness and versatility compared with existing methods.

stat.ME↗

arXiv2025

Functional Tensor Regression

Tensor regression has attracted significant attention in statistical research. This study tackles the challenge of handling covariates with smooth varying structures. We introduce a novel framework, termed functional tensor regression, which incorporates both the tensor and functional aspects of the covariate. To address the high dimensionality and functional continuity of the regression coefficient, we employ a low Tucker rank decomposition along with smooth regularization for the functional mode. We develop a functional Riemannian Gauss--Newton algorithm that demonstrates a provable quadratic convergence rate, while the estimation error bound is based on the tensor covariate dimension. Simulations and a neuroimaging analysis illustrate the finite sample performance of the proposed method.

stat.ME↗

arXiv2025

Function-on-function Differential Regression

Function-on-function regression has been a topic of substantial interest due to its broad applicability, where the relation between functional predictor and response is concerned. In this article, we propose a new framework for modeling the regression mapping that extends beyond integral type, motivated by the prevalence of physical phenomena governed by differential relations, which is referred to as function-on-function differential regression. However, a key challenge lies in representing the differential regression operator, unlike functions that can be expressed by expansions. As a main contribution, we introduce a new notion of model identification involving differential operators, defined through their action on functions. Based on this action-aware identification, we are able to develop a regularization method for estimation using operator reproducing kernel Hilbert spaces. Then a goodness-of-fit test is constructed, which facilitates model checking for differential regression relations. We establish a Bahadur representation for the regression estimator with various theoretical implications, such as the minimax optimality of the proposed estimator, and the validity and consistency of the proposed test. To illustrate the effectiveness of our method, we conduct simulation studies and an application to a real data example on the thermodynamic energy equation.

stat.ME↗

arXiv2025

Whitened Score Diffusion: A Structured Prior for Imaging Inverse Problems

Conventional score-based diffusion models (DMs) may struggle with anisotropic Gaussian diffusion processes due to the required inversion of covariance matrices in the denoising score matching training objective \cite{vincent_connection_2011}. We propose Whitened Score (WS) diffusion models, a novel framework based on stochastic differential equations that learns the Whitened Score function instead of the standard score. This approach circumvents covariance inversion, extending score-based DMs by enabling stable training of DMs on arbitrary Gaussian forward noising processes. WS DMs establish equivalence with flow matching for arbitrary Gaussian noise, allow for tailored spectral inductive biases, and provide strong Bayesian priors for imaging inverse problems with structured noise. We experiment with a variety of computational imaging tasks using the CIFAR, CelebA ($64\times64$), and CelebA-HQ ($256\times256$) datasets and demonstrate that WS diffusion priors trained on anisotropic Gaussian noising processes consistently outperform conventional diffusion priors based on isotropic Gaussian noise. Our code is open-sourced at \href{https://github.com/jeffreyalido/wsdiffusion}{\texttt{github.com/jeffreyalido/wsdiffusion}}.

eess.IV↗

arXiv2025

Reflection-mode Multi-slice Fourier Ptychographic Tomography

Diffraction tomography (DT) has been widely explored in transmission-mode configurations, enabling high-resolution, label-free 3D imaging. However, industrial metrology applications, such as semiconductor inspection, typically involve opaque or highly reflective substrates (e.g., silicon or metal), necessitating a reflection-mode imaging configuration. In this work, we introduce reflection-mode Multi-Slice Fourier Ptychographic Tomography (rMS-FPT) that achieves high-resolution, volumetric imaging of multi-layered, strongly scattering samples on reflective substrates. We develop a reflection-mode multi-slice beam propagation method (rMSBP) to model multiple scattering and substrate interactions, enabling precise 3D reconstruction. By incorporating darkfield measurements, rMS-FPT enhances resolution beyond the traditional brightfield limit and provides sub-micrometer lateral resolution while achieving optical sectioning. We validate rMS-FPT through numerical simulations on a four-layer resolution target and experimental demonstrations using a reflection-mode LED array microscope. Experiments on a two-layer resolution target and a multi-layer scattering sample confirm the method's effectiveness. Our optimized implementation enables rapid imaging, covering a 1.2 mm $\times$ 1.2 mm area in 1.6 seconds, reconstructing over $10^9$ voxels within a 0.4 mm$^3$ volume. This work represents a significant step in extending DT to reflection-mode configurations, providing a robust and scalable solution for 3D metrology and industrial inspection.

physics.optics↗

arXiv2024

Reflection-mode diffraction tomography of multiple-scattering samples on a reflective substrate from intensity images

We introduce a novel reflection-mode diffraction tomography technique that enables simultaneous recovery of forward and backward scattering information for high-resolution 3D refractive index reconstruction. Our technique works by imaging a sample on a highly reflective substrate and employing a novel multiple-scattering model and reconstruction algorithm. It combines the modified Born series as the forward model, Bloch and perfect electric conductor boundary conditions to handle oblique incidence and substrate reflections, and the adjoint method for efficient gradient computation in solving the inverse-scattering problem. We validate the technique through simulations and experiments, achieving accurate reconstructions in samples with high refractive index contrasts and complex geometries. Forward scattering captures smooth axial features, while backward scattering reveals complementary interfacial details. Experimental results on dual-layer resolution targets, 3D randomly distributed beads, phase structures obscured by highly scattering fibers, fixed breast cancer cells, and fixed \emph{C. elegans} demonstrate its robustness and versatility. This technique holds promise for applications in semiconductor metrology and biomedical imaging.

physics.optics↗

arXiv2024

Physics-encoded Spatio-temporal Regression

Physics-informed methods have gained a great success in analyzing data with partial differential equation (PDE) constraints, which are ubiquitous when modeling dynamical systems. Different from the common penalty-based approach, this work promotes adherence to the underlying physical mechanism that facilitates statistical procedures. The motivating application concerns modeling fluorescence recovery after photobleaching, which is used for characterization of diffusion processes. We propose a physics-encoded regression model for handling spatio-temporally distributed data, which enables principled interpretability, parsimonious computation and efficient estimation by exploiting the structure of solutions of a governing evolution equation. The rate of convergence attaining the minimax optimality is theoretically demonstrated, generalizing the result obtained for the spatial regression. We conduct simulation studies to assess the performance of our proposed estimator and illustrate its usage in the aforementioned real data example.

stat.ME↗

arXiv2022

Imaging with an ultra-thin reciprocal lens

Imaging is of great importance in everyday life and various fields of science and technology. Conventional imaging is achieved by bending light rays originating from an object with a lens. Such ray bending requires space-variant structures, inevitably introducing a geometric center to the lens. To overcome the limitations arising from the conventional imaging mechanism, we consider imaging elements that employ a different mechanism, which we call reciprocal lenses. This type of imaging element relies on ray shifting, enabled by momentum-space-variant phase modulations in periodic structures. As such, it has the distinct advantage of not requiring alignment with a geometric center. Moreover, upright real images can be produced directly with a single reciprocal lens as the directions of rays are not changed. We realized an ultra-thin reciprocal lens based on a photonic crystal slab. We characterized the ray shifting behavior of the reciprocal lens and demonstrated imaging. Our work gives an alternative mechanism for imaging, and provides a new way to modulate electromagnetic waves.

physics.optics↗

arXiv2021

Full description of dipole orientation in organic light-emitting diodes

Considerable progress has been made in organic light-emitting diodes (OLEDs) to achieve high external quantum efficiency (EQE), among which the dipole orientation of OLED emitters has a remarkable effect. In most cases, EQE of the OLED emitter is theoretically predicted with only one orientation factor to match with corresponding experiments. Here, we develop a distribution theory with three independent parameters to fully describe the relationship between dipole orientations and power densities. Furthermore, we propose an optimal experiment configuration for measuring such distribution parameters. Measuring the unpolarized spectrum can dig more information of dipole orientation distributions with a rather simple way. Our theory provides a universal plot of the OLED dipole orientation, paving the way for designing more complicated OLED structures.

physics.optics↗

arXiv2021

Prioritize Crowdsourced Test Reports via Deep Screenshot Understanding

Crowdsourced testing is increasingly dominant in mobile application (app) testing, but it is a great burden for app developers to inspect the incredible number of test reports. Many researches have been proposed to deal with test reports based only on texts or additionally simple image features. However, in mobile app testing, texts contained in test reports are condensed and the information is inadequate. Many screenshots are included as complements that contain much richer information beyond texts. This trend motivates us to prioritize crowdsourced test reports based on a deep screenshot understanding. In this paper, we present a novel crowdsourced test report prioritization approach, namely DeepPrior. We first represent the crowdsourced test reports with a novelly introduced feature, namely DeepFeature, that includes all the widgets along with their texts, coordinates, types, and even intents based on the deep analysis of the app screenshots, and the textual descriptions in the crowdsourced test reports. DeepFeature includes the Bug Feature, which directly describes the bugs, and the Context Feature, which depicts the thorough context of the bug. The similarity of the DeepFeature is used to represent the test reports' similarity and prioritize the crowdsourced test reports. We formally define the similarity as DeepSimilarity. We also conduct an empirical experiment to evaluate the effectiveness of the proposed technique with a large dataset group. The results show that DeepPrior is promising, and it outperforms the state-of-the-art approach with less than half the overhead.

cs.SE↗