IEEE Trans Image Process - Hessian Schatten-norm regularization for linear inverse problems.

Tópicos

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Resumo

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, they avoid the staircase effect, a common artifact of TV-based reconstructions, and perform well for a wide range of applications. To solve the corresponding optimization problems, we propose an algorithm that is based on a primal-dual formulation. A fundamental ingredient of this algorithm is the projection of matrices onto Schatten norm balls of arbitrary radius. This operation is performed efficiently based on a direct link we provide between vector projections onto lq norm balls and matrix projections onto Schatten norm balls. Finally, we demonstrate the effectiveness of the proposed methods through experimental results on several inverse imaging problems with real and simulated data.

Resumo Limpo

introduc novel famili invari convex nonquadrat function employ deriv regular solut illpos linear invers imag problem propos regular involv schatten norm hessian matrix comput everi pixel imag can view secondord extens popular totalvari tv seminorm sinc satisfi invari properti meanwhil take advantag secondord deriv avoid staircas effect common artifact tvbase reconstruct perform well wide rang applic solv correspond optim problem propos algorithm base primaldu formul fundament ingredi algorithm project matric onto schatten norm ball arbitrari radius oper perform effici base direct link provid vector project onto lq norm ball matrix project onto schatten norm ball final demonstr effect propos method experiment result sever invers imag problem real simul data

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