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The discrete tomographic reconstruction problem is generally considered for binary image. In this work, we consider the reconstruction of an image with more than two grey levels and compare two reconstruction methods. The first one is based on a classical TV regularization and the second one is a level-set regularization method. In this second method, the discrete tomographic problem is formulated...
In this work, we use stochastic diffusion equations to improve the reconstruction of binary tomography cross-sections obtained from a small number of projections. A first reconstruction image is obtained with the Total Variation regularization method. The reconstruction is then refined with stochastic approaches. This method is applied to a noisy bone cross-section with 10 projection angles. The main...
In this work, we propose a stochastic level-set method to reconstruct binary tomography cross-sections from few projections. A first reconstruction image is obtained with a level-set regularization method. The reconstruction is then refined with a stochastic partial differential equation based on a Stratanovitch formulation. The reconstruction results are compared with the ones obtained with the classical...
In this work, we propose a stochastic level-set method to reconstruct binary tomography cross-sections from a small number of projections. A first reconstruction image is obtained with a deterministic level-set regularization method. The reconstruction is then refined with a stochastic partial differential equation based on a Stratanovitch formulation. The methods are tested on a slice of bone microstructure...
In this work, we study a new reconstruction method for binary tomography cross-sections of the bone microstructure. The binary cross-sections are obtained from a small number of projections and the binary tomography problem is formulated as a non linear inverse problem. Stable solution are obtained with level-set methods and a Bounded Variation-Sobolev regularization of the level set function. The...
The in-line X-ray phase contrast imaging technique relies on the measurement of the Fresnel diffraction intensity patterns associated to a phase shift induced by the object. The simultaneous recovery of the phase and of the absorption is an ill-posed nonlinear inverse problem. If the object is made up of several homogeneous materials, the absorption and the phase are proportional in each material...
Phase retrieval from Fresnel diffraction patterns is a nonlinear ill-posed inverse problem of paramount importance in various areas of applied physics. Recently a new non-linear iterative algorithm based on a Landweber method with an analytic calculation of the Frechet derivative adjoint has been proposed. In this work, we refine this scheme by introducing Fienup projectors in the algorithm. The new...
Several methods of phase retrieval for in line phase tomography have already been investigated based on the linearization of the relation between the phase shift induced by the object and the diffracted intensity. They use the Transport Intensity Equation (TIE) or the Contrast Transfer Function (CTF), or mixed approaches. In this work, we present a non linear iterative approach using the Frechet derivative...
The present paper is devoted to a comparison between time- resolved fluorescence diffuse optical tomography and continuous wave fluorescence diffuse optical tomography. Both of these techniques aim at reconstructing 3D biodistribution of fluorescent markers embedded in biological tissues. The study is restricted in the time domain to the exploitation of the first three temporal moments of measurements...
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