IEEE Trans Image Process - Higher degree total variation (HDTV) regularization for image recovery.

Tópicos

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Resumo

We introduce novel image regularization penalties to overcome the practical problems associated with the classical total variation (TV) scheme. Motivated by novel reinterpretations of the classical TV regularizer, we derive two families of functionals involving higher degree partial image derivatives; we term these families as isotropic and anisotropic higher degree TV (HDTV) penalties, respectively. The isotropic penalty is the L(1) - L(2) mixed norm of the directional image derivatives, while the anisotropic penalty is the separable L(1) norm of directional derivatives. These functionals inherit the desirable properties of standard TV schemes such as invariance to rotations and translations, preservation of discontinuities, and convexity. The use of mixed norms in isotropic penalties encourages the joint sparsity of the directional derivatives at each pixel, thus encouraging isotropic smoothing. In contrast, the fully separable norm in the anisotropic penalty ensures the preservation of discontinuities, while continuing to smooth along the linelike features; this scheme thus enhances the linelike image characteristics analogous to standard TV. We also introduce efficient majorize-minimize algorithms to solve the resulting optimization problems. The numerical comparison of the proposed scheme with classical TV penalty, current second-degree methods, and wavelet algorithms clearly demonstrate the performance improvement. Specifically, the proposed algorithms minimize the staircase and ringing artifacts that are common with TV and wavelet schemes, while better preserving the singularities. We also observe that anisotropic HDTV penalty provides consistently improved reconstructions compared with the isotropic HDTV penalty.

Resumo Limpo

introduc novel imag regular penalti overcom practic problem associ classic total variat tv scheme motiv novel reinterpret classic tv regular deriv two famili function involv higher degre partial imag deriv term famili isotrop anisotrop higher degre tv hdtv penalti respect isotrop penalti l l mix norm direct imag deriv anisotrop penalti separ l norm direct deriv function inherit desir properti standard tv scheme invari rotat translat preserv discontinu convex use mix norm isotrop penalti encourag joint sparsiti direct deriv pixel thus encourag isotrop smooth contrast fulli separ norm anisotrop penalti ensur preserv discontinu continu smooth along linelik featur scheme thus enhanc linelik imag characterist analog standard tv also introduc effici majorizeminim algorithm solv result optim problem numer comparison propos scheme classic tv penalti current seconddegre method wavelet algorithm clear demonstr perform improv specif propos algorithm minim staircas ring artifact common tv wavelet scheme better preserv singular also observ anisotrop hdtv penalti provid consist improv reconstruct compar isotrop hdtv penalti

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