Fast Multigrid Techniques in Total Variation{based Image Reconstruction
نویسنده
چکیده
SUMMARY Existing multigrid techniques are used to eeect an eecient method for reconstructing an image from noisy, blurred data. Total Variation minimization yields a nonlinear integro-diierential equation which, when discretized using cell-centered-nite diierences, yields a full matrix equation. A xed point iteration is applied with the intermediate matrix equations solved via a preconditioned conjugate gradient method which utilizes multi-level quadrature (due to Brandt and Lubrecht) to apply the integral operator and a multigrid scheme (due to Ewing and Shen) to invert the diierential operator. With eeective preconditioning, the method presented seems to require O(n) operations. Numerical results are given for a two-dimensional example.
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