IEEE Trans Image Process - Hessian-based norm regularization for image restoration with biomedical applications.

Tópicos

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Resumo

We present nonquadratic Hessian-based regularization methods that can be effectively used for image restoration problems in a variational framework. Motivated by the great success of the total-variation (TV) functional, we extend it to also include second-order differential operators. Specifically, we derive second-order regularizers that involve matrix norms of the Hessian operator. The definition of these functionals is based on an alternative interpretation of TV that relies on mixed norms of directional derivatives. We show that the resulting regularizers retain some of the most favorable properties of TV, i.e., convexity, homogeneity, rotation, and translation invariance, while dealing effectively with the staircase effect. We further develop an efficient minimization scheme for the corresponding objective functions. The proposed algorithm is of the iteratively reweighted least-square type and results from a majorization-minimization approach. It relies on a problem-specific preconditioned conjugate gradient method, which makes the overall minimization scheme very attractive since it can be applied effectively to large images in a reasonable computational time. We validate the overall proposed regularization framework through deblurring experiments under additive Gaussian noise on standard and biomedical images.

Resumo Limpo

present nonquadrat hessianbas regular method can effect use imag restor problem variat framework motiv great success totalvari tv function extend also includ secondord differenti oper specif deriv secondord regular involv matrix norm hessian oper definit function base altern interpret tv reli mix norm direct deriv show result regular retain favor properti tv ie convex homogen rotat translat invari deal effect staircas effect develop effici minim scheme correspond object function propos algorithm iter reweight leastsquar type result majorizationminim approach reli problemspecif precondit conjug gradient method make overal minim scheme attract sinc can appli effect larg imag reason comput time valid overal propos regular framework deblur experi addit gaussian nois standard biomed imag

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