arXiv subjects

Zichao Wendy Di

Publications and source records attributed to Zichao Wendy Di.

At least 19 recordsLinked to original sources

arXiv2026

Stochastic Multigrid Method for Blind Ptychography

Blind ptychography reconstructs an object and a probe from diffraction measurements collected over overlapping scan regions. We introduce a reconstruction framework with two complementary operations. Local coordination adjusts the object and probe updates together at each scan position to account for their combined effect. Minibatch synthesis combines updates from a group of scan positions into common object and probe estimates. We provide a mathematical analysis of how these operations interact and incorporate coarse-grid corrections to refine the object at multiple spatial scales. In simulations spanning different scan overlaps and Poisson noise levels, the resulting stochastic multigrid method achieves the lowest final object and probe reconstruction errors among the compared methods in every tested case. Reconstructions of experimental test-pattern and integrated-circuit data demonstrate the method's practical applicability.

math.NA↗

arXiv2026

MAGPIE: Multilevel-Adaptive-Guided Solver for Ptychographic Phase Retrieval

We introduce MAGPIE (Multilevel-Adaptive-Guided Ptychographic Iterative Engine), a stochastic multigrid solver for the ptychographic phase-retrieval problem. The ptychographic phase-retrieval problem is inherently nonconvex and ill-posed. To address these challenges, we reformulate the original nonlinear and nonconvex inverse problem as the iterative minimization of a quadratic surrogate model that majorizes the original objective. This surrogate not only ensures favorable convergence properties but also generalizes the Ptychographic Iterative Engine (PIE) family of algorithms. By solving the surrogate model using a multigrid method, MAGPIE achieves substantial gains in convergence speed and reconstruction quality over traditional approaches.

math.NA↗

arXiv2026

Edge-Aligned Beam Placement in Scanning Probe Tomography via Reconstruction-Free Sequential Design of Experiments

In X-ray scanning probe tomography, reconstruction quality generally improves with larger numbers of projections. However, additional projections increase experiment costs, acquisition time, and the radiation dose imparted to the sample. One mitigation to these trade-offs is to adopt a sequential design of experiments, in which each subsequent measurement is determined as a function of previously acquired data in order to maximize information gain. In scanning probe tomography, a widely used heuristic to maximize information is to align beams with the edges of the sample. A key challenge, however, is that the true sample is unknown, so identifying edge-aligned beams typically requires reconstructing the sample based on available measurements. This work proposes a novel sequential design method that identifies edge-aligned measurements directly from the sinogram, bypassing any reconstruction, thereby improving computational efficiency and reducing the experimental design's susceptibility to reconstruction errors. Our method dynamically selects the next set of measurement beams by maximizing an acquisition function that balances exploration and exploitation over the domain of all possible measurements, improving reconstruction quality while reducing measurement redundancy.

physics.med-ph↗

arXiv2026

Simultaneous Drift Calibration and Reconstruction for Scanning-Probe X-Ray Tomography

Scanning-probe x-ray tomography is useful for imaging nanoscale structures of a sample. The image resolution, which can reach down to 10 nm by the increased brightness and coherence of the x-ray optics, however, is highly susceptible to experimental error. Failure to address these errors can lead to a smeared image and, in the worst case, to misinterpretation of the imaged object's structure. In this work, we present a novel optimization-based approach to calibrate a common yet challenging source of experimental error, the drifts of the scanning positions, while simultaneously reconstructing the object. This approach uses the coupled and complementary information from different measurements to enforce consistency between the measurements and the reconstruction. We illustrate the proposed approach on both synthetic and real tomography images and show its superior performance compared with reconstruction without explicit error calibration.

math.OC↗

arXiv2026

Acquisition Geometry-Assisted Whole-Group Localization of X-ray Fluorescence Maps in Optical Microscopy Images

X-ray fluorescence (XRF) microscopy maps elemental distributions, while optical microscopy can provide complementary morphological context. Localizing XRF fields of view (FOVs) in optical images is difficult because the two modalities differ in contrast mechanism and resolution. Most current workflows place each XRF tile independently, even when acquisition metadata already record the tiles' relative scan positions. This study formalizes XRF tile-group localization, in which one optical-frame placement is estimated for the whole group, constrained by acquisition geometry and quantified using group intersection-over-union (GroupIoU). In a controlled case study, independent localization failed with GroupIoU 0.000, whereas group localization achieved 0.931. Replacing the normalized cross-correlation (NCC) metric with mutual information (MI) gave nearly identical results, showing that the outcome is not specific to one local similarity metric. In another multiscale case study, using a coarse XRF survey scan to connect the fine-scale tile group to the optical image increased mean GroupIoU from 0.694 to 0.856. These case studies support using acquisition geometry as an explicit constraint when localizing related XRF tiles.

cs.CV↗

arXiv2026

XRF-to-Optical Field-of-View Localization with Vision Language Models

Registering images acquired with different microscopy modalities is essential for relating complementary measurements of the same specimen. In correlative X-ray fluorescence (XRF) and optical microscopy, the XRF map often covers only a small region of an optical image acquired from the same or an adjacent tissue section. Field-of-view (FOV) localization is necessary but can be difficult when appearance and structure differ across modalities. Here we evaluate training-free vision language model (VLM) localization on two datasets representing same-section high-correspondence and adjacent-section low-correspondence imaging. We test unconstrained and metadata-constrained search and compare VLMs with geometric controls, classical template matching, and two alternative training-free approaches (DINOv2 and multiGradICON). Direct VLM prompting produced content-dependent spatial signals but was not reliable alone. Classical matching was most accurate when cross-modal structure was preserved but failed in the low-correspondence collection. A proposal-and-verify workflow used repeated VLM predictions as candidates and image-based similarity to select the final location. This workflow recovered useful localization in the low-correspondence regime.

cs.CV↗

arXiv2026

A Joint Variational Framework for Multimodal X-ray Ptychography and Fluorescence Reconstruction

Recovering high-resolution structural and compositional information from coherent X-ray measurements involves solving coupled, nonlinear, and ill-posed inverse problems. Ptychography reconstructs a complex transmission function from overlapping diffraction patterns, while X-ray fluorescence provides quantitative, element-specific contrast at lower spatial resolution. We formulate a joint variational framework that integrates these two modalities into a single nonlinear least-squares problem with shared spatial variables. This formulation enforces cross-modal consistency between structural and compositional estimates, improving conditioning and promoting stable convergence. The resulting optimization couples complementary contrast mechanisms (i.e., phase and absorption from ptychography, elemental composition from fluorescence) within a unified inverse model. Numerical experiments on simulated data demonstrate that the joint reconstruction achieves faster convergence, sharper and more quantitative reconstructions, and lower relative error compared with separate inversions. The proposed approach illustrates how multimodal variational formulations can enhance stability, resolution, and interpretability in computational X-ray imaging.

math.NA↗

arXiv2025

Structured Column Subset Selection for Bayesian Optimal Experimental Design

We consider optimal experimental design (OED) for Bayesian inverse problems, where the experimental design variables have a certain multiway structure. Given $d$ different experimental variables with $m_i$ choices per design variable $1 \le i\le d$, the goal is to select $k_i \le m_i$ experiments per design variable. Previous work has related OED to the column subset selection problem by mapping the design variables to the columns of a matrix $\mathbf{A}$. However, this approach is applicable only to the case $d=1$ in which the columns can be selected independently. We develop an extension to the case where the design variables have a multi-way structure. Our approach is to map the matrix $\mathbf{A}$ to a tensor and perform column subset selection on mode unfoldings of the tensor. We develop an algorithmic framework with three different algorithmic templates, and randomized variants of these algorithms. We analyze the computational cost of all the proposed algorithms and also develop greedy versions to facilitate comparisons. Numerical experiments on four different applications -- time-dependent inverse problems, seismic tomography, X-ray tomography, and flow reconstruction -- demonstrate the effectiveness and scalability of our methods for structured experimental design in Bayesian inverse problems.

math.NA↗

arXiv2025

FIRM: Federated Image Reconstruction using Multimodal Tomographic Data

We propose a federated algorithm for reconstructing images using multimodal tomographic data sourced from dispersed locations, addressing the challenges of traditional unimodal approaches that are prone to noise and reduced image quality. Our approach formulates a joint inverse optimization problem incorporating multimodality constraints and solves it in a federated framework through local gradient computations complemented by lightweight central operations, ensuring data decentralization. Leveraging the connection between our federated algorithm and the quadratic penalty method, we introduce an adaptive step-size rule with guaranteed sublinear convergence and further suggest its extension to augmented Lagrangian framework. Numerical results demonstrate its superior computational efficiency and improved image reconstruction quality.

math.OC↗

arXiv2024

Integrating Generative and Physics-Based Models for Ptychographic Imaging with Uncertainty Quantification

Ptychography is a scanning coherent diffractive imaging technique that enables imaging nanometer-scale features in extended samples. One main challenge is that widely used iterative image reconstruction methods often require significant amount of overlap between adjacent scan locations, leading to large data volumes and prolonged acquisition times. To address this key limitation, this paper proposes a Bayesian inversion method for ptychography that performs effectively even with less overlap between neighboring scan locations. Furthermore, the proposed method can quantify the inherent uncertainty on the ptychographic object, which is created by the ill-posed nature of the ptychographic inverse problem. At a high level, the proposed method first utilizes a deep generative model to learn the prior distribution of the object and then generates samples from the posterior distribution of the object by using a Markov Chain Monte Carlo algorithm. Our results from simulated ptychography experiments show that the proposed framework can consistently outperform a widely used iterative reconstruction algorithm in cases of reduced overlap. Moreover, the proposed framework can provide uncertainty estimates that closely correlate with the true error, which is not available in practice. The project website is available here.

eess.IV↗

arXiv2024

Homomorphic data compression for real time photon correlation analysis

The construction of highly coherent x-ray sources has enabled new research opportunities across the scientific landscape. The maximum raw data rate per beamline now exceeds 40 GB/s, posing unprecedented challenges for the online processing and offline storage of the big data. Such challenge is particularly prominent for x-ray photon correlation spectroscopy (XPCS), where real time analyses require simultaneous calculation on all the previously acquired data in the time series. We present a homomorphic compression scheme to effectively reduce the computational time and memory space required for XPCS analysis. Leveraging similarities in the mathematical expression between a matrix-based compression algorithm and the correlation calculation, our approach allows direct operation on the compressed data without their decompression. The lossy compression reduces the computational time by a factor of 10,000, enabling real time calculation of the correlation functions at kHz framerate. Our demonstration of a homomorphic compression of scientific data provides an effective solution to the big data challenge at coherent light sources. Beyond the example shown in this work, the framework can be extended to facilitate real-time operations directly on a compressed data stream for other techniques.

math.NA↗

arXiv2024

Imaging 3D Chemistry at 1 nm Resolution with Fused Multi-Modal Electron Tomography

Measuring the three-dimensional (3D) distribution of chemistry in nanoscale matter is a longstanding challenge for metrological science. The inelastic scattering events required for 3D chemical imaging are too rare, requiring high beam exposure that destroys the specimen before an experiment completes. Even larger doses are required to achieve high resolution. Thus, chemical mapping in 3D has been unachievable except at lower resolution with the most radiation-hard materials. Here, high-resolution 3D chemical imaging is achieved near or below one nanometer resolution in a Au-Fe$_3$O$_4$ metamaterial, Co$_3$O$_4$ - Mn$_3$O$_4$ core-shell nanocrystals, and ZnS-Cu$_{0.64}$S$_{0.36}$ nanomaterial using fused multi-modal electron tomography. Multi-modal data fusion enables high-resolution chemical tomography often with 99\% less dose by linking information encoded within both elastic (HAADF) and inelastic (EDX / EELS) signals. Now sub-nanometer 3D resolution of chemistry is measurable for a broad class of geometrically and compositionally complex materials.

physics.comp-ph↗

arXiv2023

Imaging Atomic-Scale Chemistry from Fused Multi-Modal Electron Microscopy

Efforts to map atomic-scale chemistry at low doses with minimal noise using electron microscopes are fundamentally limited by inelastic interactions. Here, fused multi-modal electron microscopy offers high signal-to-noise ratio (SNR) recovery of material chemistry at nano- and atomic- resolution by coupling correlated information encoded within both elastic scattering (high-angle annular dark field (HAADF)) and inelastic spectroscopic signals (electron energy loss (EELS) or energy-dispersive x-ray (EDX)). By linking these simultaneously acquired signals, or modalities, the chemical distribution within nanomaterials can be imaged at significantly lower doses with existing detector hardware. In many cases, the dose requirements can be reduced by over one order of magnitude. This high SNR recovery of chemistry is tested against simulated and experimental atomic resolution data of heterogeneous nanomaterials.

physics.comp-ph↗

arXiv2023

Autonomous Electron Tomography Reconstruction with Machine Learning

Modern electron tomography has progressed to higher resolution at lower doses by leveraging compressed sensing methods that minimize total variation (TV). However, these sparsity-emphasized reconstruction algorithms introduce tunable parameters that greatly influence the reconstruction quality. Here, Pareto front analysis shows that high-quality tomograms are reproducibly achieved when TV minimization is heavily weighted. However, in excess, compressed sensing tomography creates overly smoothed 3D reconstructions. Adding momentum to the gradient descent during reconstruction reduces the risk of over-smoothing and better ensures that compressed sensing is well behaved. For simulated data, the tedious process of tomography parameter selection is efficiently solved using Bayesian optimization with Gaussian processes. In combination, Bayesian optimization with momentum-based compressed sensing greatly reduces the required compute time$-$an 80% reduction was observed for the 3D reconstruction of SrTiO$_3$ nanocubes. Automated parameter selection is necessary for large scale tomographic simulations that enable the 3D characterization of a wider range of inorganic and biological materials.

physics.med-ph↗

arXiv2023

Simultaneous Reconstruction and Uncertainty Quantification for Tomography

Tomographic reconstruction, despite its revolutionary impact on a wide range of applications, suffers from its ill-posed nature in that there is no unique solution because of limited and noisy measurements. Therefore, in the absence of ground truth, quantifying the solution quality is highly desirable but under-explored. In this work, we address this challenge through Gaussian process modeling to flexibly and explicitly incorporate prior knowledge of sample features and experimental noises through the choices of the kernels and noise models. Our proposed method yields not only comparable reconstruction to existing practical reconstruction methods (e.g., regularized iterative solver for inverse problem) but also an efficient way of quantifying solution uncertainties. We demonstrate the capabilities of the proposed approach on various images and show its unique capability of uncertainty quantification in the presence of various noises.

stat.AP↗

arXiv2022

Physics-Inspired Unsupervised Classification for Region of Interest in X-Ray Ptychography

X-ray ptychography allows for large fields to be imaged at high resolution at the cost of additional computational expense due to the large volume of data. Given limited information regarding the object, the acquired data often has an excessive amount of information that is outside the region of interest (RoI). In this work we propose a physics-inspired unsupervised learning algorithm to identify the RoI of an object using only diffraction patterns from a ptychography dataset before committing computational resources to reconstruction. Obtained diffraction patterns that are automatically identified as not within the RoI are filtered out, allowing efficient reconstruction by focusing only on important data within the RoI while preserving image quality.

eess.IV↗

arXiv2021

Uncertainty quantification for ptychography using normalizing flows

Ptychography, as an essential tool for high-resolution and nondestructive material characterization, presents a challenging large-scale nonlinear and non-convex inverse problem; however, its intrinsic photon statistics create clear opportunities for statistical-based deep learning approaches to tackle these challenges, which has been underexplored. In this work, we explore normalizing flows to obtain a surrogate for the high-dimensional posterior, which also enables the characterization of the uncertainty associated with the reconstruction: an extremely desirable capability when judging the reconstruction quality in the absence of ground truth, spotting spurious artifacts and guiding future experiments using the returned uncertainty patterns. We demonstrate the performance of the proposed method on a synthetic sample with added noise and in various physical experimental settings.

stat.ML↗

arXiv2021

Low-Rank Tensor Regression for X-Ray Tomography

Tomographic imaging is useful for revealing the internal structure of a 3D sample. Classical reconstruction methods treat the object of interest as a vector to estimate its value. Such an approach, however, can be inefficient in analyzing high-dimensional data because of the underexploration of the underlying structure. In this work, we propose to apply a tensor-based regression model to perform tomographic reconstruction. Furthermore, we explore the low-rank structure embedded in the corresponding tensor form. As a result, our proposed method efficiently reduces the dimensionality of the unknown parameters, which is particularly beneficial for ill-posed inverse problem suffering from insufficient data. We demonstrate the robustness of our proposed approach on synthetic noise-free data as well as on Gaussian noise-added data.

stat.AP↗