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--- research:tomography:start [2015/03/22 20:05]
aneufeld created
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-    *  **__Phase Transitions and Cosparse Tomographic Recovery of Compound Solid Bodies from Few Projections__** *
-{{ research:3d_ellipses.png?250x125}}
-Compared to the well known Nyquist-Shannon sampling theorem, which allows a signal to be accurately reconstructed only if there are twice more measurements available than the sampling rate at which the signal was acquired, compressive sensing (CS) has been advocated as a sparsity promoting approach, able to obtain accurate reconstructions from a few linear, but random and non-adaptive measurements.
-In this paper, we investigate conditions for unique signal recovery based on sparse and cosparse signal models. Moreover, we present a relation between image co-/sparsity and sufficient number of tomographic measurements for exact recovery similar to the settings in CS.
-** Publication:**
-[IPABIB,Denitiu2014a]
-   *  **__An Entropic Perturbation Approach to TV-Minimization for Limited-Data Tomography__**
-{{ research:Mma_ellipses.png?230x115}}
-We address the problem of reconstructing compound solid bodies from few tomographic projections by regularizing the sparse Anisotropic Total Variation cost function subject to equality constraints, through the addition of a penalized separable nonlinear function. We rely on convex optimization
-tools, i.e. duality, to reach an objective function that can efficiently be solved using methodologies from unconstrained optimization. Numerical results validate the theory for large-scale recovery problems of integer-valued functions that exceed the capacity of commercial MOSEK software.
-{{ research:plots.png?230x105}}
-** Publication:**
-[IPABIB,Denitiu2014]