Invertible Low-Dimensional Modelling of X-ray Absorption Spectra for Potential Applications in Spectral X-ray Imaging

• URL: http://arxiv.org/abs/2307.04484v1
• Date: Mon, 10 Jul 2023 11:14:19 GMT
• Title: Invertible Low-Dimensional Modelling of X-ray Absorption Spectra for Potential Applications in Spectral X-ray Imaging
• Abstract summary: We propose a novel, non-linear model that combines a deep neural network autoencoder with an optimal linear model based on the Singular Value Decomposition (SVD) We demonstrate the advantages of our method over traditional models, especially when modelling X-ray absorption spectra that contain K-edges in the energy range of interest.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: X-ray interaction with matter is an energy-dependent process that is contingent on the atomic structure of the constituent material elements. The most advanced models to capture this relationship currently rely on Monte Carlo (MC) simulations. Whilst these very accurate models, in many problems in spectral X-ray imaging, such as data compression, noise removal, spectral estimation, and the quantitative measurement of material compositions, these models are of limited use, as these applications typically require the efficient inversion of the model, that is, they require the estimation of the best model parameters for a given spectral measurement. Current models that can be easily inverted however typically only work when modelling spectra in regions away from their K-edges, so they have limited utility when modelling a wider range of materials. In this paper, we thus propose a novel, non-linear model that combines a deep neural network autoencoder with an optimal linear model based on the Singular Value Decomposition (SVD). We compare our new method to other alternative linear and non-linear approaches, a sparse model and an alternative deep learning model. We demonstrate the advantages of our method over traditional models, especially when modelling X-ray absorption spectra that contain K-edges in the energy range of interest.

Related papers

• Free Decompression with Algebraic Spectral Curves [45.17701640697655]
  Free decompression (FD) is a recently proposed method for extrapolating spectral information across matrix sizes.<n>This paper recasts FD as an evolution along spectral curves which can be readily integrated.<n>We demonstrate the efficacy of our framework on models of interest in modern machine learning.
  arXiv  Detail & Related papers  (2026-05-05T11:03:48Z)
• Variational Autoencoder with Normalizing flow for X-ray spectral fitting [0.0]
  Black hole X-ray binaries (BHBs) can be studied with spectral fitting to provide physical constraints on accretion in extreme gravitational environments.<n>We introduce a probabilistic model, utilizing a variational autoencoder with a normalizing flow, trained to adopt a physical latent space.
  arXiv  Detail & Related papers  (2026-01-12T11:28:40Z)
• Modeling X-ray photon pile-up with a normalizing flow [0.0]
  The analysis of bright X-ray sources is complicated by so-called pile-up, which results from high incident photon flux.<n>We present a machine learning solution to this problem, using a simulation-based inference framework that allows us to estimate posterior distributions of physical source parameters from piled-up eROSITA data.<n>We show that a normalizing flow produces better-constrained posterior densities than traditional mitigation techniques, as more data can be leveraged.
  arXiv  Detail & Related papers  (2025-11-14T20:46:32Z)
• Direct Dual-Energy CT Material Decomposition using Model-based Denoising Diffusion Model [105.95160543743984]
  We propose a deep learning procedure called Dual-Energy Decomposition Model-based Diffusion (DEcomp-MoD) for quantitative material decomposition.<n>We show that DEcomp-MoD outperform state-of-the-art unsupervised score-based model and supervised deep learning networks.
  arXiv  Detail & Related papers  (2025-07-24T01:00:06Z)
• A theoretical framework for overfitting in energy-based modeling [5.1337384597700995]
  We investigate the impact of limited data on training pairwise energy-based models for inverse problems aimed at identifying interaction networks. We dissect training trajectories across the eigenbasis of the coupling matrix, exploiting the independent evolution of eigenmodes. We show that finite data corrections can be accurately modeled through random matrix theory calculations.
  arXiv  Detail & Related papers  (2025-01-31T14:21:02Z)
• Latent Space Energy-based Neural ODEs [73.01344439786524]
  This paper introduces a novel family of deep dynamical models designed to represent continuous-time sequence data. We train the model using maximum likelihood estimation with Markov chain Monte Carlo. Experiments on oscillating systems, videos and real-world state sequences (MuJoCo) illustrate that ODEs with the learnable energy-based prior outperform existing counterparts.
  arXiv  Detail & Related papers  (2024-09-05T18:14:22Z)
• SMILE: Zero-Shot Sparse Mixture of Low-Rank Experts Construction From Pre-Trained Foundation Models [85.67096251281191]
  We present an innovative approach to model fusion called zero-shot Sparse MIxture of Low-rank Experts (SMILE) construction. SMILE allows for the upscaling of source models into an MoE model without extra data or further training. We conduct extensive experiments across diverse scenarios, such as image classification and text generation tasks, using full fine-tuning and LoRA fine-tuning.
  arXiv  Detail & Related papers  (2024-08-19T17:32:15Z)
• Time dependent Vibrational Electronic Coupled Cluster (VECC) theory for non-adiabatic nuclear dynamics [0.0]
  A time-dependent vibrational electronic coupled-cluster approach is proposed to simulate photoelectron/ UV-VIS absorption spectra. A detailed derivation of the equations of motion and a motivation of the ansatz is presented. To illustrate the capabilities the VECC method is also applied successfully to a large vibronic model for hexahelicene.
  arXiv  Detail & Related papers  (2023-12-02T20:53:22Z)
• Geometric Neural Diffusion Processes [55.891428654434634]
  We extend the framework of diffusion models to incorporate a series of geometric priors in infinite-dimension modelling. We show that with these conditions, the generative functional model admits the same symmetry.
  arXiv  Detail & Related papers  (2023-07-11T16:51:38Z)
• Capturing dynamical correlations using implicit neural representations [85.66456606776552]
  We develop an artificial intelligence framework which combines a neural network trained to mimic simulated data from a model Hamiltonian with automatic differentiation to recover unknown parameters from experimental data. In doing so, we illustrate the ability to build and train a differentiable model only once, which then can be applied in real-time to multi-dimensional scattering data.
  arXiv  Detail & Related papers  (2023-04-08T07:55:36Z)
• Learning to Bound: A Generative Cram\'er-Rao Bound [25.739449801033846]
  We introduce a novel approach to approximate the Cram'er-Rao bound (CRB) using data-driven methods. We model the distribution of the measurements and obtain an approximation of the CRB, which we call Generative Cram'er-Rao Bound (GCRB)
  arXiv  Detail & Related papers  (2022-03-07T20:31:53Z)
• Kernel Methods and Multi-layer Perceptrons Learn Linear Models in High Dimensions [25.635225717360466]
  We show that for a large class of kernels, including the neural kernel of fully connected networks, kernel methods can only perform as well as linear models in a certain high-dimensional regime. More complex models for the data other than independent features are needed for high-dimensional analysis.
  arXiv  Detail & Related papers  (2022-01-20T09:35:46Z)
• Regularization by Denoising Sub-sampled Newton Method for Spectral CT Multi-Material Decomposition [78.37855832568569]
  We propose to solve a model-based maximum-a-posterior problem to reconstruct multi-materials images with application to spectral CT. In particular, we propose to solve a regularized optimization problem based on a plug-in image-denoising function. We show numerical and experimental results for spectral CT materials decomposition.
  arXiv  Detail & Related papers  (2021-03-25T15:20:10Z)
• Hessian Eigenspectra of More Realistic Nonlinear Models [73.31363313577941]
  We make a emphprecise characterization of the Hessian eigenspectra for a broad family of nonlinear models. Our analysis takes a step forward to identify the origin of many striking features observed in more complex machine learning models.
  arXiv  Detail & Related papers  (2021-03-02T06:59:52Z)
• Hybrid modeling: Applications in real-time diagnosis [64.5040763067757]
  We outline a novel hybrid modeling approach that combines machine learning inspired models and physics-based models. We are using such models for real-time diagnosis applications.
  arXiv  Detail & Related papers  (2020-03-04T00:44:57Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.