Geodesic
A comparison of multilevel methods for total variation regularization
Electronic transactions on numerical analysis, Tome 6 (1997), pp. 255-270
We consider numerical methods for solving problems involving total variation (TV) regularization for semidefinite quadratic minimization problems minu Ku - z 2 arising from illposed inverse problems. Here K is a 2 compact linear operator, and z is data containing inexact or partial information about the "true" u. TV regularization entails adding to the objective function a penalty term which is a scalar multiple of the total variation of u; this term formally appears as (a scalar times) the L1 norm of the gradient of u. The advantage of this regularization is that it improves the conditioning of the optimization problem while $not penalizing discontinuities$ in the reconstructed image. This approach has enjoyed significant success in image denoising and deblurring, laser interferometry, electrical tomography, and estimation of permeabilities in porus media flow models.
Classification : 65N55, 35R30, 65F10
Keywords: total variation, regularization, multilevel methods, inverse problems 
@article{ETNA_1997__6__a1,
     author = {Vassilevski,  P.S. and Wade,  J.G.},
     title = {A comparison of multilevel methods for total variation regularization},
     journal = {Electronic transactions on numerical analysis},
     pages = {255--270},
     year = {1997},
     volume = {6},
     zbl = {0888.65135},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_1997__6__a1/}
}
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%A Wade,  J.G.
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%J Electronic transactions on numerical analysis
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Vassilevski,  P.S.; Wade,  J.G. A comparison of multilevel methods for total variation regularization. Electronic transactions on numerical analysis, Tome 6 (1997), pp. 255-270. http://geodesic.mathdoc.fr/item/ETNA_1997__6__a1/