Searcharxiv⌕ Search

arXiv subjects

Guorong Hu

Publications and source records attributed to Guorong Hu.

18 recordsLinked to original sources
arXiv2026

Point Spread Function Engineering Using Implicit Neural Representations

Point spread function (PSF) engineering through pupil plane modulation is a technique used in microscopy to achieve specific imaging properties, such as depth encoding or extended depth of field. Existing PSF design methods often rely on extensive domain knowledge and task-specific basis functions, making it difficult to generalize across different applications. We treat the PSF engineering task as a phase retrieval problem and propose a neural field pupil design method that optimizes a phase profile for any arbitrary, user-defined 3D PSF distribution. This provides a flexible framework for 3D PSF engineering for various applications with implicit regularization that proves robust to initialization compared to pixel-wise optimization methods

physics.optics↗
arXiv2026

Lipschitz spaces adapted to Schr\"{o}dinger operators on the Heisenberg group

Let $L =-\Delta_{\mathbb{H}^n} +V$ be the Sch\"{o}dinger operator on the Heisenberg group $\mathbb{H}^n$, where $\Delta_{\mathbb{H}^n}$ is the sub-Laplacian, and $V$ is a nonnegative potential belonging to the reverse H\"{o}lder class $RH_q(\mathbb{H}^n)$ for some $q > Q/2$, where $Q:=2n+2$ is the homogeneous dimension of $\mathbb{H}^n$. In this paper, motivated by the work of De Le\'{o}n-Contreras and Torrea \cite{DT}, we introduce the Lipschitz spaces $\Lambda_L^\alpha (\mathbb{H}^n)$, $0< \alpha <2$, adapted to $L$ via a pointwise second-order difference condition involving the critical radius function $\rho$ related to $V$, and also introduce another type of Lipschitz spaces $\Gamma^{\alpha/2}_L(\mathbb{H}^n)$, $0< \alpha <\infty$, adapted to $L$ in terms of the heat semigroup $e^{-tL}$. We show that for $0< \alpha <2-(Q/q)$, $\Lambda_{L}^\alpha (\mathbb{H}^n) =\Gamma_L^{\alpha/2} (\mathbb{H}^n)$ with equivalent norms. Applications of $\Gamma^{\alpha/2}_L(\mathbb{H}^n)$ to the regularity of the fractional powers of the operator $L$ are also given.

math.AP↗
arXiv2026

Littlewood-Paley and Carleson measure characterizations of Lipschitz spaces adapted to Schr\"{o}dinger operators

Let $L =-\Delta +V$ be a Schr\"{o}dinger operator on $\mathbb{R}^n$, $n \geq 3$, with the potential $V$ being nonnegative and belonging to the reverse H\"{o}lder class $RH_q$ for some $q >n/2$. For $0< \alpha <2$, the Lipschitz space $\Lambda_L^\alpha(\mathbb{R}^n)$ adapted to $L$ is defined as the space of all measurable functions $f$ on $\mathbb{R}^n$ such that \[ \|f\|_{\Lambda_L^\alpha}:= \|\rho(\cdot)^{-\alpha}f(\cdot)\|_{L^\infty}+ \sup_{z \in \mathbb{R}^n \backslash \{0\}} \frac{\|f(\cdot + z) + f(\cdot -z) -2 f(\cdot)\|_{L^\infty}}{|z|^\alpha} <\infty, \] where $\rho$ is the critical radius function related to $L$. In this paper, we provide characterizations of $\Lambda^\alpha_L(\mathbb{R}^n)$ in terms of Littlewood-Paley-type decompositions and Carleson measures, for $0< \alpha < 2 -(n /q)$.

math.CA↗
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

Coordinate-conditioned Deconvolution for Scalable Spatially Varying High-Throughput Imaging

Wide-field fluorescence microscopy with compact optics often suffers from spatially varying blur due to field-dependent aberrations, vignetting, and sensor truncation, while finite sensor sampling imposes an inherent trade-off between field of view (FOV) and resolution. Computational Miniaturized Mesoscope (CM2) alleviate the sampling limit by multiplexing multiple sub-views onto a single sensor, but introduce view crosstalk and a highly ill-conditioned inverse problem compounded by spatially variant point spread functions (PSFs). Prior learning-based spatially varying (SV) reconstruction methods typically rely on global SV operators with fixed input sizes, resulting in memory and training costs that scale poorly with image dimensions. We propose SV-CoDe (Spatially Varying Coordinate-conditioned Deconvolution), a scalable deep learning framework that achieves uniform, high-resolution reconstruction across a 6.5 mm FOV. Unlike conventional methods, SV-CoDe employs coordinate-conditioned convolutions to locally adapt reconstruction kernels; this enables patch-based training that decouples parameter count from FOV size. SV-CoDe achieves the best image quality in both simulated and experimental measurements while requiring 10x less model size and 10x less training data than prior baselines. Trained purely on physics-based simulations, the network robustly generalizes to bead phantoms, weakly scattering brain slices, and freely moving C. elegans. SV-CoDe offers a scalable, physics-aware solution for correcting SV blur in compact optical systems and is readily extendable to a broad range of biomedical imaging applications.

eess.IV↗
arXiv2025

On the rate of convergence in the CLT for LSS of large-dimensional sample covariance matrices

This paper investigates the rate of convergence for the central limit theorem of linear spectral statistic (LSS) associated with large-dimensional sample covariance matrices. We consider matrices of the form ${\mathbf B}_n=\frac{1}{n}{\mathbf T}_p^{1/2}{\mathbf X}_n{\mathbf X}_n^*{\mathbf T}_p^{1/2},$ where ${\mathbf X}_n= (x_{i j} ) $ is a $p \times n$ matrix whose entries are independent and identically distributed (i.i.d.) real or complex variables, and ${\mathbf T} _p$ is a $p\times p$ nonrandom Hermitian nonnegative definite matrix with its spectral norm uniformly bounded in $p$. Employing Stein's method, we establish that if the entries $x_{ij}$ satisfy $\mathbb{E}|x_{ij}|^{10}<\infty$ and the ratio of the dimension to sample size $p/n\to y>0$ as $n\to\infty$, then the convergence rate of the normalized LSS of ${\mathbf B}_n$ to the standard normal distribution, measured in the Kolmogorov-Smirnov distance, is $O(n^{-1/2+\kappa})$ for any fixed $\kappa>0$.

math.PR↗
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↗
arXiv2025

Besov and Triebel-Lizorkin spaces on homogeneous groups

This paper develops a theory of Besov spaces $\dot{\mathbf{B}}^{\sigma}_{p,q} (N)$ and Triebel-Lizorkin spaces $\dot{\mathbf{F}}^{\sigma}_{p,q} (N)$ on an arbitrary homogeneous group $N$ for the full range of parameters $p, q \in (0, \infty]$ and $\sigma \in \mathbb{R}$. Among others, it is shown that these spaces are independent of the choice of the Littlewood-Paley decomposition and that they admit characterizations in terms of continuous maximal functions and molecular frame decompositions. The defined spaces include as special cases various classical function spaces, such as Hardy spaces on homogeneous groups and homogeneous Sobolev spaces and Lipschitz spaces associated to sub-Laplacians on stratified groups.

math.FA↗
arXiv2024

Wide-Field, High-Resolution Reconstruction in Computational Multi-Aperture Miniscope Using a Fourier Neural Network

Traditional fluorescence microscopy is constrained by inherent trade-offs among resolution, field-of-view, and system complexity. To navigate these challenges, we introduce a simple and low-cost computational multi-aperture miniature microscope, utilizing a microlens array for single-shot wide-field, high-resolution imaging. Addressing the challenges posed by extensive view multiplexing and non-local, shift-variant aberrations in this device, we present SV-FourierNet, a novel multi-channel Fourier neural network. SV-FourierNet facilitates high-resolution image reconstruction across the entire imaging field through its learned global receptive field. We establish a close relationship between the physical spatially-varying point-spread functions and the network's learned effective receptive field. This ensures that SV-FourierNet has effectively encapsulated the spatially-varying aberrations in our system, and learned a physically meaningful function for image reconstruction. Training of SV-FourierNet is conducted entirely on a physics-based simulator. We showcase wide-field, high-resolution video reconstructions on colonies of freely moving C. elegans and imaging of a mouse brain section. Our computational multi-aperture miniature microscope, augmented with SV-FourierNet, represents a major advancement in computational microscopy and may find broad applications in biomedical research and other fields requiring compact microscopy solutions.

physics.optics↗
arXiv2024

EventLFM: Event Camera integrated Fourier Light Field Microscopy for Ultrafast 3D imaging

Ultrafast 3D imaging is indispensable for visualizing complex and dynamic biological processes. Conventional scanning-based techniques necessitate an inherent trade-off between acquisition speed and space-bandwidth product (SBP). Emerging single-shot 3D wide-field techniques offer a promising alternative but are bottlenecked by the synchronous readout constraints of conventional CMOS systems, thus restricting data throughput to maintain high SBP at limited frame rates. To address this, we introduce EventLFM, a straightforward and cost-effective system that overcomes these challenges by integrating an event camera with Fourier light field microscopy (LFM), a state-of-the-art single-shot 3D wide-field imaging technique. The event camera operates on a novel asynchronous readout architecture, thereby bypassing the frame rate limitations inherent to conventional CMOS systems. We further develop a simple and robust event-driven LFM reconstruction algorithm that can reliably reconstruct 3D dynamics from the unique spatiotemporal measurements captured by EventLFM. Experimental results demonstrate that EventLFM can robustly reconstruct fast-moving and rapidly blinking 3D fluorescent samples at kHz frame rates. Furthermore, we highlight EventLFM's capability for imaging of blinking neuronal signals in scattering mouse brain tissues and 3D tracking of GFP-labeled neurons in freely moving C. elegans. We believe that the combined ultrafast speed and large 3D SBP offered by EventLFM may open up new possibilities across many biomedical applications.

physics.optics↗
arXiv2023

Robust single-shot 3D fluorescence imaging in scattering media with a simulator-trained neural network

Imaging through scattering is a pervasive and difficult problem in many biological applications. The high background and the exponentially attenuated target signals due to scattering fundamentally limits the imaging depth of fluorescence microscopy. Light-field systems are favorable for high-speed volumetric imaging, but the 2D-to-3D reconstruction is fundamentally ill-posed, and scattering exacerbates the condition of the inverse problem. Here, we develop a scattering simulator that models low-contrast target signals buried in heterogeneous strong background. We then train a deep neural network solely on synthetic data to descatter and reconstruct a 3D volume from a single-shot light-field measurement with low signal-to-background ratio (SBR). We apply this network to our previously developed Computational Miniature Mesoscope and demonstrate the robustness of our deep learning algorithm on scattering phantoms with different scattering conditions. The network can robustly reconstruct emitters in 3D with a 2D measurement of SBR as low as 1.05 and as deep as a scattering length. We analyze fundamental tradeoffs based on network design factors and out-of-distribution data that affect the deep learning model's generalizability to real experimental data. Broadly, we believe that our simulator-based deep learning approach can be applied to a wide range of imaging through scattering techniques where experimental paired training data is lacking.

eess.SP↗
arXiv2022

Fourier multipliers for Hardy spaces on graded Lie groups

In this paper, we investigate the $H^p(G) \rightarrow L^p(G)$, $0< p \leq 1$, boundedness of multiplier operators defined via group Fourier transform on a graded Lie group $G$, where $H^p(G)$ is the Hardy space on $G$. Our main result extends those obtained in [Colloq. Math. \textbf{165} (2021), 1--30], where the $L^1(G)\rightarrow L^{1,\infty}(G)$ and $L^p(G) \rightarrow L^p(G)$, $1< p <\infty$, boundedness of such Fourier multiplier operators were proved.

math.CA↗
arXiv2022

Deep-learning-augmented Computational Miniature Mesoscope

Fluorescence microscopy is essential to study biological structures and dynamics. However, existing systems suffer from a tradeoff between field-of-view (FOV), resolution, and complexity, and thus cannot fulfill the emerging need of miniaturized platforms providing micron-scale resolution across centimeter-scale FOVs. To overcome this challenge, we developed Computational Miniature Mesoscope (CM$^2$) that exploits a computational imaging strategy to enable single-shot 3D high-resolution imaging across a wide FOV in a miniaturized platform. Here, we present CM$^2$ V2 that significantly advances both the hardware and computation. We complement the 3$\times$3 microlens array with a new hybrid emission filter that improves the imaging contrast by 5$\times$, and design a 3D-printed freeform collimator for the LED illuminator that improves the excitation efficiency by 3$\times$. To enable high-resolution reconstruction across the large imaging volume, we develop an accurate and efficient 3D linear shift-variant (LSV) model that characterizes the spatially varying aberrations. We then train a multi-module deep learning model, CM$^2$Net, using only the 3D-LSV simulator. We show that CM$^2$Net generalizes well to experiments and achieves accurate 3D reconstruction across a $\sim$7-mm FOV and 800-$μ$m depth, and provides $\sim$6-$μ$m lateral and $\sim$25-$μ$m axial resolution. This provides $\sim$8$\times$ better axial localization and $\sim$1400$\times$ faster speed as compared to the previous model-based algorithm. We anticipate this simple and low-cost computational miniature imaging system will be impactful to many large-scale 3D fluorescence imaging applications.

physics.optics↗
arXiv2021

Continuous characterizations of inhomogeneous Besov and Triebel-Lizorkin spaces associated to non-negative self-adjoint operators

Let $(M,ρ,μ)$ be a metric measure space satisfying the doubling, reverse doubling and non-collapsing conditions, and $\mathscr{L}$ be a self-adjoint operator on $L^2 (M, dμ)$ whose heat kernel $p_t (x,y)$ satisfy the small-time Gaussian upper bound, Hölder continuity and Markov property. In this paper, we give characterizations of inhomogeneous "classical" and "non-classical" Besov and Triebel-Lizorkin spaces associated to $\mathscr{L}$ in terms of continuous Littlewood-Paley and Lusin area functions defined by the heat semigroup, for complete range of indices. This extends related classical results for Besov and Triebel-Lizorkin spaces on $\mathbb{R}^n$ to more general setting, and extends corresponding results in [Trans. Amer. Math Soc. 367 (2015), 121-189] to complete range of indices.

math.CA↗
arXiv2020

Marcinkiewicz multipliers associated with the Kohn Laplacian on the Shilov boundary of the product domain in $\mathbb C ^{2n}$

Let $M^{(k)}$, $k=1,2,\ldots, n$, be the boundary of an unbounded polynomial domain $Ω^{(k)}$ of finite type in $\mathbb C ^2$, and let $\Box_b^{(k)}$ be the Kohn Laplacian on $M^{(k)}$. In this paper, we study multivariable spectral multipliers $m(\Box_b^{(1)},\ldots, \Box_b^{(n)})$ acting on the Shilov boundary $\widetilde{M}=M^{(1)} \times\cdots\times M^{(n)}$ of the product domain $Ω^{(1)}\times\cdots\times Ω^{(n)}$. We show that if a function $F(λ_1, \ldots ,λ_n)$ satisfies a Marcinkiewicz-type differential condition, then the spectral multiplier operator $m(\Box_b^{(1)}, \ldots, \Box_b^{(n)})$ is a product Calderón--Zygmund operator of Journé type.

math.CV↗
arXiv2017

Equivalence of Littlewood-Paley square function and area function characterizations of weighted product Hardy spaces associated to operators

Let $L_{1}$ and $L_{2}$ be non-negative self-adjoint operators acting on $L^{2}(X_{1})$ and $L^{2}(X_{2})$, respectively, where $X_{1}$ and $X_{2}$ are spaces of homogeneous type. Assume that $L_{1}$ and $L_{2}$ have Gaussian heat kernel bounds. This paper aims to study some equivalent characterizations of the weighted product Hardy spaces $H^{p}_{w,L_{1},L_{2}}(X_{1}\times X_{2})$ associated to $L_{1}$ and $L_{2}$, for $p \in (0, \infty)$ and the weight $w$ belongs to the product Muckenhoupt class $A_{\infty}(X_{1} \times X_{2})$. Our main result is that the spaces $H^{p}_{w,L_{1},L_{2}}(X_{1}\times X_{2})$ introduced via area functions can be equivalently characterized by Littlewood-Paley $g$-functions, Littlewood-Paley $g^{\ast}_{λ_{1}, λ_{2}}$-functions, and Peetre type maximal functions, without any further assumptions beyond the Gaussian upper bounds on the heat kernels of $L_{1}$ and $L_{2}$. Our results are new even in the unweighted product setting.

math.CA↗