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Selecte topics in integral geometry Gelfand, I. M. ; Gindikin, S. G. ; Graev, M. I. | American Mathematical Society 2003

Ouvrage

V

- 170 p.
ISBN 978-0-8218-2932-5

Translations of mathematical monographs , 0220

Localisation : Collection 1er étage

géométrie intégrale # transformation de Radon # transformation de Fourier # analyse harmonique # transformation de John # transformation de Minkowski-Funk # espace hyperbolique # transformation horosphérique

53C65 ; 42A38 ; 44A12 ; 60D05 ; 60E05 ; 60E10 ; 92C55

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Ressources Electroniques

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ord.htm?list=link&xRecord=19240015146910682979" class='linkstyle1'>11-06 ; 81-06

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Optimization and data analysis in biomedical informatics.
Selected papers based on the presentations at the workshop
Toronto # June 11-12, 2010
Pardalos, Panos M. ; Coleman, Thomas F. ; Xanthopoulos, Petros | Springer;The Fields Institute for Research in Mathematical Sciences 2012

Congrès

y

- viii; 198 p.
ISBN 978-1-4614-4132-8

Fields institute communications , 0063

Localisation : Collection 1er étage

optimisation # informatique biomédicale # imagerie biomédicale # programmation

92-06 ; 92C55 ; 62P10 ; 68U99 ; 90C90 ; 00B25

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Wavelet-based multifractal analysis of dynamic infrared thermograms and X-ray mammograms to assist in early breast cancer diagnosis Arneodo, Alain | CIRM H

Multi angle

y

Special events;30 Years of Wavelets

Breast cancer is the most common type of cancer among women and despite recent advances in the medical field, there are still some inherent limitations in the currently used screening techniques. The radiological interpretation of X-ray mammograms often leads to over-diagnosis and, as a consequence, to unnecessary traumatic and painful biopsies. First we use the 1D Wavelet Transform Modulus Maxima (WTMM) method to reveal changes in skin temperature dynamics of women breasts with and without malignant tumor. We show that the statistics of temperature temporal fluctuations about the cardiogenic and vasomotor perfusion oscillations do not change across time-scales for cancerous breasts as the signature of homogeneous monofractal fluctuations. This contrasts with the continuous change of temperature fluctuation statistics observed for healthy breasts as the hallmark of complex multifractal scaling. When using the 2D WTMM method to analyze the roughness fluctuations of X-ray mammograms, we reveal some drastic loss of roughness spatial correlations that likely results from some deep architectural change in the microenvironment of a breast tumor. This local breast disorganisation may deeply affect heat transfer and related thermomechanics in the breast tissue and in turn explain the loss of multifractal complexity of temperature temporal fluctuations previously observed in mammary glands with malignant tumor. These promising findings could lead to the future use of combined wavelet-based multifractal processing of dynamic IR thermograms and X-ray mammograms to help identifying women with high risk of breast cancer prior to more traumatic examinations. Besides potential clinical impact, these results shed a new light on physiological changes that may precede anatomical alterations in breast cancer development.

Keywords: breast cancer - X-ray mammography - infrared thermography - multifractal analysis - wavelet transform - wavelet transform modulus maxima method
Breast cancer is the most common type of cancer among women and despite recent advances in the medical field, there are still some inherent limitations in the currently used screening techniques. The radiological interpretation of X-ray mammograms often leads to over-diagnosis and, as a consequence, to unnecessary traumatic and painful biopsies. First we use the 1D Wavelet Transform Modulus Maxima (WTMM) method to reveal changes in skin ...

92-08 ; 92C50 ; 92C55

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Direct and inverse biomechanical modeling of the heart Chapelle, Dominique | CIRM H

Multi angle

y

Research talks

The heart undergoes some highly complex multi-scale multi-physics phenomena that must be accounted for in order to adequately model the biomechanical behavior of the complete organ. In this respect, a major focus of our work has been on formulating modeling ingredients that satisfy the most crucial thermomechanical requirements - in particular as regards energy balances - throughout the various forms of physical and scale-related couplings. This has led to a "beating heart" model for which some experimental and clinical validations have already been obtained. Concurrently, with the objective of building "patient-specific" heart models, we have investigated some original approaches inspired from data assimilation concepts to benefit from the available clinical data, with a particular concern for medical imaging. By combining the two fundamental sources of information represented by the model and the data, we are able to extract some most valuable quantitative knowledge on a given heart, e.g. as regards some uncertain constitutive parameter values characterizing a possible pathology, with important perspectives in diagnosis assistance. In addition, once the overall uncertainty has been adequately controlled via this adjustment process, the model can be expected to become "predictive", hence should provide clinically-relevant quantitative information, both in the current state of the patient and under various scenarii of future evolutions, such as for therapy planning. The heart undergoes some highly complex multi-scale multi-physics phenomena that must be accounted for in order to adequately model the biomechanical behavior of the complete organ. In this respect, a major focus of our work has been on formulating modeling ingredients that satisfy the most crucial thermomechanical requirements - in particular as regards energy balances - throughout the various forms of physical and scale-related couplings. This ...

92C10 ; 92C55 ; 74H15

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Geometric tomography Gardner, Richard J. | Cambridge University Press 1995

Ouvrage

V

- 424 p.
ISBN 978-0-521-45126-0

Encyclopedia of mathematics and its applications , 0058

Localisation : Collection 1er étage

corps d'intersection # corps de projection # differentiabilité # dualité polaire # ensemble étoilé # estimation de fonction de projection ou de section # fonction corde # fonction de section # fonction radiale # fonction support # inégalité de Alexandrov-Fenchel # inégalité de Brunn-Minkowski # inégalité de volume # mesure de volumes mélangés ou d'aires mélangées # mesure et intégration # métrique de Hausdorff # problème équicordal # projection et fonction de projection # rayons X de point # rayons X parallèles de corps convexes plans # rayons X parallèles à n dimensions # tomographie géométrique # transformation # transformée intégrale corps d'intersection # corps de projection # differentiabilité # dualité polaire # ensemble étoilé # estimation de fonction de projection ou de section # fonction corde # fonction de section # fonction radiale # fonction support # inégalité de Alexandrov-Fenchel # inégalité de Brunn-Minkowski # inégalité de volume # mesure de volumes mélangés ou d'aires mélangées # mesure et intégration # métrique de Hausdorff # problème équicordal # projection ...

44A12 ; 65R10 ; 92C05 ; 92C55

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Applied problems of Radon transform Gindikin, Simon | American Mathematical Society 1994

Ouvrage

V

- 261 p.
ISBN 978-0-8218-7508-7

American mathematical society translations series 2 , 0162

Localisation : Collection 1er étage

algoritme # analyse numérique # calcul de convolution singulière # calcul numérique # réconstruction d'algorithme # tomographie # transformation d'intégrale # transformation de Radon # transformée d'intégrale # équation d'intégrale

44-02 ; 44A12 ; 65R10 ; 92C55

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