Hessian Schatten-Norm Regularization for Linear Inverse Problems

@article{Lefkimmiatis2013HessianSR,
  title={Hessian Schatten-Norm Regularization for Linear Inverse Problems},
  author={Stamatios Lefkimmiatis and John Paul Ward and Michael Unser},
  journal={IEEE Transactions on Image Processing},
  year={2013},
  volume={22},
  pages={1873-1888}
}
We introduce a novel family of invariant, convex, and non-quadratic functionals that we employ to derive regularized solutions of ill-posed linear inverse imaging problems. The proposed regularizers involve the Schatten norms of the Hessian matrix, which are computed at every pixel of the image. They can be viewed as second-order extensions of the popular total-variation (TV) semi-norm since they satisfy the same invariance properties. Meanwhile, by taking advantage of second-order derivatives… CONTINUE READING
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