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Communication Dans Un Congrès Année : 2005

Spectrum Interpolation and Extrapolation by Means of Total Variation Minimization

Résumé

Resolution enhancement of digital images may be seen has a ill-posed inverse problem. Formulated in the Fourier domain the problem consists in spectral extrapolation, where low-frequencies are known in a fraction of the image spectrum and where high-frequencies have to be guessed in accordance with the human visual system. A similar situation occurs in computerized tomography, where the inversion of the discrete Radon transform leads to a spectral interpolation, from a polar to a Cartesian grid. We present a constrained total variation minimization framework that can be applied both for spectrum interpolation and extrapolation and, therefore, which solves the two problems above. The total variation semi-norm allows to reconstruct a realistic image, with sharp edges and without oscillation, while the constraint space ensures that the reconstructed image fulfills the conditions settled by the observed data. In this conference, we will also see that the two mains drawbacks traditionally associated to total variation algorithms (slowness of the iterative process and incomplete fit to the human visual system leading some loss of details) may be easily bypassed.
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Dates et versions

hal-00907681 , version 1 (21-11-2013)

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  • HAL Id : hal-00907681 , version 1

Citer

Jacques Froment. Spectrum Interpolation and Extrapolation by Means of Total Variation Minimization. International Conference on Superresolution Imaging - Theory, Algorithms and Applications, Aug 2005, Hong Kong SAR China. ⟨hal-00907681⟩
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