FAST MULTIGRID TECHNIQUES IN TOTAL VARIATION-BASED IMAGE
                                RECONSTRUCTION

                               MARY ELLEN OMAN

Abstract.  Existing multigrid techniques are used to effect an effcient method
for reconstructing an image from noisy, blurred data.  Total Variation
minimization yields a nonlinear integro-differential equation which, when
discretized using cell-centered finite differences, yields a full matrix
equation.  A \fixed 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 m ultigrid scheme (due to Ewing and Shen) to invert the
differential operator.  With effective preconditioning, the method presented
requires O(n) operations.  Numerical results are given for a two-dimensional
example.