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Table of Contents

                            List of Figures
Introduction
Radon transform over generalized Cormack curves
	Review of Radon transform
		Standard Radon transform
		Cormack's class of curves and Radon transform
		Extension to others kind of curves in the plane
	Inverse Radon transform over generalized Cormack curves
		Definition and forward problem
		Inversion formulae
	SVD and FBP for A defined over C1
	Some examples of curves
	Conclusion
Applications in Compton scattering tomography
	Basis of conventional and Compton scattering tomographies
		Ionising radiation : interactions with matter
		Conventional tomography
		Motivations behind Compton scattering tomography (CST)
	CST modality based on CART1
		Working principle
		Norton's inversion method
		Definition of the CART1 and of its adjoint
		Modeling of the image formation process
		Associated inversion formulae
	Novel CST modality based on CART2
		Working principle
		Definition of the CART2 and of its adjoint
		Modeling of image formation process
		Associated inversion formulae
	Novel CST modality based on CART3
		Working principle
		Defintion of the CART3 and of its adjoint
		Suited sampling for CART3
		Associated inversion formulae
	Implementation methods for different equations
		Image formation
		Noisy data
		Image reconstruction
	Simulation Results
	Conclusion
A new concept of bimodality in Compton scattering tomography
	Attenuation correction algorithms
		Detection of the contours of the attenuating medium
		Constant attenuation factor correction
		Attenuation correction with a given heterogeneous attenuation map
	Generalized Iterative Pre-Correction algorithm (GIPC)
		Presentation of the algorithm
		Application for inverting the attenuated CART2
	A novel bimodal system based on scattered radiation
		A new concept
		Theory
		Correction algorithm description
		Simulation studies
		Results
	Conclusion
Conclusion and Perspectives
Bibliography