Abstract
The total variation minimization method for deblurring noisy data is shown to be effective in dramatically increasing the resolution in a modified gradient approach to index of refraction reconstruction from measured scattered field data. Numerical evidence is presented which shows that by including the total variation in the functional to be minimized the reconstructions of piecewise constant profiles are considerably sharpened. The stability of the modified gradient method with respect to noise is apparently also enhanced. Furthermore, the presence of the total variation does not appear to adversely effect the established effectiveness of the modified gradient method in reconstructing smooth profiles.
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