Geometrical method for non-negative source separation : Application to dynamic PET imaging and mass spectrometry
type: Distribution
access URL: https://theses.hal.science/tel-00859690
format: HTML
issued: 2026-05-09T19:53:58.971267
modified: 2026-05-09T19:53:58.943763

test_moissonnage_selune
type: Agent

Geometrical method for non-negative source separation : Application to dynamic PET imaging and mass spectrometry
type: Dataset
contact point: Organization
  fn: CCSD
keyword: spiotherengineering-sciences-physicsother
keyword: theses
keyword: infoeu-reposemanticsdoctoralthesis
keyword: simplicial-cone
keyword: dynamic-pet-imaging
keyword: separation-aveugle-de-sources
keyword: ouverture-dun-cone-spectrometrie-de-masse-imagerie-tep-dynamique
keyword: geometrical-approach
keyword: cone-simplicial
keyword: mass-spectrometry
keyword: positivity-constraint
keyword: contrainte-de-positivite
keyword: scatter-plot
keyword: aperture
keyword: methode-geometrique
keyword: nuage-de-points
keyword: blind-sources-separation
landing page: https://theses.hal.science/tel-00859690
description: This thesis addresses the problem of non-negative blind source separation (i.e. positive or zero quantities). The situation of linear instantaneous mixtures of non-negative sources occurs in many problems of signal and image processing, such as decompositions of signals measured by a spectrometer (mass spectra, Raman spectra, infrared spectra), decomposition of images (medical, multi-spectral and hyperspectral) or estimating of the activity of a radionuclide. In these problems, the sources are inherently non-negative and this property should be preserved during their estimation, in order to get physical meaning components. Most of existing non-negative blind source separation methods require ``strong" assumptions on sources (such as mutual independence, local dominance or total additivity), which are not always satisfied in practice. In this work, we propose a new geometrical method for separating non-negative sources. The mixing matrix and the sources are estimated by finding the minimum aperture simplicial cone containing the scatter plot of mixed data. The proposed method does not require the mutual independence of the sources, neither their decorrelation, nor their local dominance, or their total additivity. One condition is necessary and sufficient: the positive orthant must be the unique minimum aperture simplicial cone cone containing the scatter plot of the sources. The proposed algorithm is successfully evaluated in two different problems of non-negative sources separation. In the first situation, we perform the separation of mass spectra measured at the output of a liquid chromatograph to identify and quantify the different metabolites (small molecules) present in the urine of rats treated with phenobarbital . In the second situation, we estimate the different pharmacokinetics compartments of the radiotracer [18F]-FDG in human brain, from a set of 3D PET images of this organ, without blood sampling. Among these pharmacokinetics, arterial input function is …
identifier: NNT: 2012GRENT098
issued: 2026-05-09T19:53:58.962977
language: fr
modified: 2026-05-09T19:53:58.962981