Two supervised methods classify single-molecule patterns from X-ray imaging.
problem Classifying high-quality patterns from noisy, stochastic XFEL data.
method Supervised template-based learning methods: Eigen-Image and Log-Likelihood classifiers.
result Classifiers can find best-matched templates within milliseconds and parallelize for XFEL repetition rate.
New method for identifying phase shifts in XRD data.
problem Automating phase extraction from large XRD datasets.
method Nonnegative Matrix Factorization integrated with custom clustering.
result Robust determination of phase shifts and accurate phase diagrams.
Proposes EMG mixture model for spectroscopy data.
problem Modeling residuals in spectroscopy data with positive support.
method Exponentially-modified Gaussian mixture (EMG) model with expectation-maximization algorithm.
result EMG mixture outperforms existing models in spectroscopy applications.
Paper analyzes the phase retrieval problem in X-ray imaging.
problem Phase retrieval problem in X-ray imaging of amorphous samples.
method Analysis of well-posedness and development of experimental protocols.
result The phase retrieval problem is generally ill-posed.
DRNets combine deep learning and reasoning for complex tasks.
problem Solving complex tasks, especially in scientific discovery, with limited supervision.
method DRNets integrate logic and neural network optimization to encode structured latent spaces constrained by prior knowledge.
result DRNets outperform state-of-the-art models in scientific discovery tasks, recovering more precise crystal structures.
Extracts important peaks from XRD spectra using Attention mechanism.
problem Identifying significant peaks in XRD patterns for material properties.
method Convolutional neural network with Attention mechanism to analyze deep features.
result Selected lattice constant predicts cathodic material cell voltage.
Optical DNNet boosts accuracy with multiple frequency-channels.
problem Improving the accuracy of optical neural networks.
method Developed a novel optical diffractive deep neural network with multiple frequency-channels.
result Multiple frequency-channels significantly increase network accuracy.
Study on limits of recovering sparse variables from phaseless measurements.
problem Support recovery in phase retrieval model with noisy phaseless measurements.
method Information-theoretic analysis, considering discrete and Gaussian models, Gaussian measurement matrices.
result Sharp thresholds with near-matching constant factors for sparsity and signal-to-noise ratio in various scaling regimes.
We establish a link between Fourier optics and a recent construction from the machine learning community termed the kernel mean map. Using the Fraunhofer approximation, it identifies the kernel with the squared Fourier transform of the aperture. This allows us to use results about the invertibility of the kernel mean m…
COM finds shared minima in multiple cost functions.
problem Optimizing multiple cost functions with different local minima.
method Exploring common minima shared by all cost functions without metaheuristics.
result High success rate in finding correct crystal structures.
DeepFreak learns crystal diffraction patterns from synthetic and real images.
problem Classifying crystallography diffraction patterns.
method End-to-end CNN architecture (DeepFreak) for classification on DiffraNet dataset.
result Best model achieves 98.5% accuracy on synthetic images and 94.51% on real images.
New method uses image registration to recover complex signals from amplitude data.
problem Recovering complex-valued signals from amplitude measurements.
method Indirect registration using LDDMM formalism with exterior calculus.
result Algorithm performs well under various conditions including noise and topology.
Authors argue Lin's system is not a deep neural network.
problem Mischaracterization of Lin's system as a deep neural network.
method Lin's system uses a passive, strictly linear optical setup for pattern classification.
result Authors argue Lin's system is not a deep neural network.
This paper tackles non-convex phase retrieval with structured assumptions.
problem Phase retrieval with limited measurements and structure assumptions.
method Non-convex approaches with sample complexity guarantees.
result Sample-efficient recovery with structured signals/images.
In this paper, we investigate the geometric propagation and diffraction of singularities of solutions to the wave equation on manifolds with edge singularities.
Lecture notes on analysis tools for X-ray tomography.
problem Understanding X-ray tomography using mathematical analysis.
method Overview of analysis tools and ideas, minimal assumptions.
result Broad overview of analysis tools for X-ray tomography.
Sharp mapping properties and regularization for X-ray transform on disks of constant curvature.
problem Sharp mapping properties and regularization of X-ray transform.
method Derive functional relations and mapping properties using elliptic differential operators.
result Theoretical possibility of regularized inversions for X-ray transform.
CNNs trained on one hospital's x-rays perform poorly on x-rays from other hospitals.
problem Generalization of radiological deep learning models across different hospitals.
method Cross-sectional design using x-rays from three hospitals (NIH, Mount Sinai, Indiana).
result CNNs trained on one hospital's x-rays perform significantly worse on x-rays from other hospitals.
Regularity results for geodesic X-ray transform on nonsmooth manifolds
problem Geodesic X-ray transform on nonsmooth simple manifolds
method Symbol smoothing arguments and pseudodifferential operators with low regularity symbols
result Improved injectivity results for Lp functions Paper shows invertibility of tensor X-ray transform on certain manifolds.
problem Invertibility of tensor X-ray transform on asymptotically conic manifolds.
method Used 1-cusp pseudodifferential operator algebra and modified solenoidal gauge condition.
result Invertibility of tensor X-ray transform up to natural obstruction.
Local X-ray transform works well near boundaries in hyperbolic spaces.
problem Injectivity of X-ray transform near boundaries for hyperbolic metrics.
method Local injectivity proof for geodesic X-ray transform on asymptotically hyperbolic manifolds.
result Local injectivity near a boundary point for X-ray transform in dimensions 3 and higher, up to O(ρ5). Study characterizes X-ray transform kernel for periodic slabs and related manifolds.
problem Characterizing the kernel of X-ray transform for tensor fields on periodic slabs.
method Characterization of the kernel for L2-regular m-tensors on [0,1]imesTn. result Kernel characterization extends to more general manifolds, including the Möbius strip.
Functions with constant geodesic X-ray transform are restricted to manifolds with specific geometrical properties.
problem Existence of functions with constant geodesic X-ray transform on manifolds.
method Analyzing the geometrical properties of manifolds based on the existence of such functions.
result Functions with constant geodesic X-ray transform impose specific geometrical restrictions on the manifold.
Study shows X-ray transform injectivity for hyperbolic manifolds.
problem Recovering metrics from boundary measurements on hyperbolic manifolds.
method Injectivity of X-ray transform in several cases.
result Injectivity of X-ray transform proven for asymptotically hyperbolic manifolds.
Study shows stability in X-ray transform on specific hyperbolic manifolds.
problem Stability of X-ray transform on asymptotically hyperbolic manifolds.
method Constructed a parametrix for the normal operator in 0-pseudodifferential calculus.
result Showed a stability estimate for the X-ray transform.
Study X-ray transform on Anosov manifolds with improved stability estimates.
problem Analyzing the geodesic X-ray transform on Anosov manifolds.
method Refined Livsic theorem for Anosov flows, new quantitative finite time Livsic theorem.
result New stability estimates for the X-ray transform.
Deep learning tackles X-ray noise without clean data.
problem Lack of clean X-ray images for deep learning denoising.
method Uses Stein's Unbiased Risk Estimator (SURE) to train a deep neural network.
result SURE-based approach effectively denoises X-ray images.
CheXNet detects pneumonia from chest X-rays better than radiologists.
problem Detecting pneumonia from chest X-rays with high accuracy.
method 121-layer convolutional neural network trained on ChestX-ray14 dataset.
result CheXNet outperforms radiologists on F1 metric.
Study X-ray transform on conic spaces, proving injectivity under certain conditions.
problem Injectivity of geodesic X-ray transform on conic metrics.
method Injectivity under non-trapping and no conjugate point assumptions.
result Injectivity of geodesic X-ray transform for asymptotically conic metrics.
Injectivity of X-ray transform on solenoidal tensors proven for certain manifolds.
problem Injectivity of X-ray transform on solenoidal tensors on manifolds with hyperbolic trapped set.
method Proof of equivalence principle concerning injectivity and surjectivity of operators on symmetric solenoidal tensors.
result Injectivity of X-ray transform on solenoidal tensors of any order for surfaces with hyperbolic trapped set.
Injective X-ray transform on Heisenberg group for regular functions.
problem Injectivity of X-ray transform on sub-Riemannian manifolds.
method Group Fourier Transform and analysis of taming metrics.
result Sufficiently regular functions on Heisenberg group are determined by their line integrals.
Paper proves injectivity of non-abelian X-ray transform on certain spaces.
problem Injectivity of non-abelian X-ray transform on asymptotically hyperbolic spaces.
method Gauge equivalence for unitary connections and skew-Hermitian Higgs fields.
result Injectivity result for non-abelian X-ray transform over skew-Hermitian Higgs fields.
X-ray free-electron lasers (XFELs) are the only sources currently able to produce bright few-fs pulses with tunable photon energies from 100 eV to more than 10 keV. Due to the stochastic SASE operating principles and other technical issues the output pulses are subject to large fluctuations, making it necessary to char…
X-rays are commonly performed imaging tests that use small amounts of radiation to produce pictures of the organs, tissues, and bones of the body. X-rays of the chest are used to detect abnormalities or diseases of the airways, blood vessels, bones, heart, and lungs. In this work we present a stochastic attention-based…
Large dataset study improves chest x-ray analysis.
problem Improving accuracy in recognizing thorax diseases from chest x-rays.
method Training and evaluating deep convolutional neural networks (CNNs) on a large dataset (473k images).
result DualNet architecture shows improved performance in recognizing chest x-ray findings.
Deep-learning method estimates bone 3D structure from X-ray images.
problem Estimating bone 3D structure from X-ray images.
method Triplet loss-trained neural network selecting closest 3D bone shape from predefined set.
result Average RMS distance of 1.08 mm between predicted and true shapes.
X-ray transform on H-type groups solved, revealing function injectivity.
problem Injectivity in sub-Riemannian geometry.
method Fourier Slice Theorem adapted to H-type groups.
result Integrable functions on H-type groups are uniquely determined by their integrals over geodesics.
New method eliminates domain size restrictions for X-ray transform inversion.
problem Injectivity and stability of X-ray transform in convex domains.
method Semiclassical analysis to invert X-ray transform without small domain assumptions.
result Elimination of domain size restrictions for injectivity and stability.
Study improves deep learning chest X-ray models by incorporating lateral views.
problem Lack of lateral views in training datasets limits deep learning performance.
method Used PadChest dataset with multiple views to explore merging methods.
result Incorporating lateral views increases model performance for 32 labels.
Study proper sampling for X-ray transforms on simple surfaces.
problem Proper discretizing and sampling issues related to geodesic X-ray transforms on simple surfaces.
method Provide minimal sampling rates for faithful reconstruction, quantify sampling quality, and predict artifacts.
result Minimal sampling rates and artifact prediction for geodesic X-ray transforms on simple surfaces.
Paper uses deep learning to suppress bones on chest X-rays.
problem Improving pathologies classification by suppressing bones on chest X-rays.
method Conditional Generative Adversarial Network (GAN) and Haar 2D wavelet decomposition.
result Achieves state-of-the-art performance on bone suppression.
FRODO method rejects out-of-distribution chest x-ray images with high accuracy.
problem Rejecting out-of-distribution samples in medical image analysis.
method Uses feature activations and Mahalanobis distance to measure distribution mismatch.
result Achieves an AUC score of 0.99 in classifying chest x-ray images as in or out of distribution.
New proof of injectivity for broken non-abelian X-ray transform in Minkowski space.
problem Injectivity of broken non-abelian X-ray transform in Minkowski space.
method Stability estimate considering gauge, light-sink connections, Bayesian inversion.
result Consistent recovery of light-sink connections from noisy data.
Paper solves injectivity of X-ray transform on surfaces.
problem Injectivity of non-Abelian X-ray transform on surfaces.
method Factorization theorem for Loop Groups, energy methods, scalar holomorphic integrating factors.
result Extends results to arbitrary Lie groups.
Enhanced X-ray polarimetry with deep learning for better exposure times.
problem Improving sensitivity of X-ray telescopic observations with imaging polarimeters.
method A weighted maximum likelihood combination of predictions from a deep ensemble of ResNet convolutional neural networks trained on Monte Carlo event simulations.
result Improves effective exposure times by ~45% for power-law source spectra.
Study X-ray transform on manifolds, desingularize, and improve mapping properties.
problem Characterize mapping properties of X-ray transform and its adjoint on manifolds with strictly convex boundary.
method Use b-fibrations, desingularize, and apply Melrose's Pushforward Theorem to analyze polyhomogeneous functions.
result Improved mapping properties of X-ray transform and its adjoint, recovering sharp results.
Unique continuation for X-ray transforms of one-forms with partial data.
problem Proving unique continuation for X-ray transforms of one-forms with limited data.
method Proved unique continuation for the normal operator of X-ray transforms of one-forms, leading to partial data results.
result Unique continuation for X-ray transforms of one-forms with partial data.
Study shows certain manifolds uniquely determined by X-ray data.
problem Determining manifolds from X-ray data.
method Injectivity of X-ray transform over symmetric solenoidal 2-tensors.
result Smooth compact manifolds with strictly convex boundary, no conjugate points, and hyperbolic trapped set are locally marked boundary rigid.