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We consider the problem of differentiating a multivariable function specified by noisy data. We regularize the differentiation process by formulating it as an inverse problem with an integration operator as the forward model. Total-variation regularization avoids the noise amplification of finite-difference methods, while allowing for discontinuous solutions. Nonconvex generalizations of total variation, on the other hand, can lessen contrast loss and more faithfully preserve the geometry of image contours. We use an alternating directions, method of multipliers algorithm to provide greater efficiency, allowing rapid differentiation of images with millions of pixels. We apply our differentiation method to the phase wrapping problem of synthetic aperture radar interferometry.
This presentation is part of Minisymposium “MS37 - Sparse-based techniques in variational image processing (2 parts)”
organized by: Serena Morigi (Dept. Mathematics, University of Bologna) , Ivan Selesnick (New York University) , Alessandro Lanza (Dept. Mathematics, University of Bologna) .