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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.

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., Comment: Machine Learning and the Physical Sciences Workshop at NeurIPS 2024, 7 pages, 4 figures

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.

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., Comment: 8 pages, 4 figures

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.

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.

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., Comment: Accepted at the Fourth Workshop on Machine Learning for Physical Sciences, NeurIPS 2021

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.

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.

With more satellite and model precipitation data becoming available, new analytical methods are needed that can take advantage of emerging data patterns to make well informed predictions in many hydrological applications. We propose a new strategy where we extract precipitation variability patterns and use correlation map to build the resulting density map that serves as an input to centroidal Voronoi tessellation construction that optimizes placement of precipitation gauges. We provide results of numerical experiments based on the data from the Alto-Adige region in Northern Italy and Oklahoma and compare them against actual gauge locations. This method provides an automated way for choosing new gauge locations and can be generalized to include physical constraints and to tackle other types of resource allocation problems.

Tomography can be used to reveal internal properties of a 3D object using any penetrating wave. Advanced tomographic imaging techniques, however, are vulnerable to both systematic and random errors associated with the experimental conditions, which are often beyond the capabilities of the state-of-the-art reconstruction techniques such as regularizations. Because they can lead to reduced spatial resolution and even misinterpretation of the underlying sample structures, these errors present a fundamental obstacle to full realization of the capabilities of next-generation physical imaging. In this work, we develop efficient and explicit recovery schemes of the most common experimental error: movement of the center of rotation during the experiment. We formulate new physical models to capture the experimental setup, and we devise new mathematical optimization formulations for reliable inversion of complex samples. We demonstrate and validate the efficacy of our approach on synthetic data under known perturbations of the center of rotation.