Regularity for solutions of the total variation denoising problem

The main purpose of this paper is to prove a local Holder regularity result for the solutions of the total variation based denoising problem assuming that the datum is locally Holder continuous. We also prove a global estimate on the modulus of continuity of the solution in convex domains of R and some extensions of this result for the total variation minimization flow.

[1]  A. Chambolle,et al.  Anisotropic curvature-driven ow of convex sets , 2004 .

[2]  T. O’Neil.  Geometric Measure Theory , 2002 .

[3]  Michael G. Crandall,et al.  GENERATION OF SEMI-GROUPS OF NONLINEAR TRANSFORMATIONS ON GENERAL BANACH SPACES, , 1971 .

[4]  H. Brezis.  Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert , 1973 .

[5]  M. Novaga,et al.  The Total Variation Flow in RN , 2002 .

[6]  L. Rudin,et al.  Nonlinear total variation based noise removal algorithms , 1992 .

[7]  U. Massari,et al.  Successioni convergenti di ipersuperfici di curvatura media assegnata , 1975 .

[8]  L. Ambrosio,et al.  Functions of Bounded Variation and Free Discontinuity Problems , 2000 .

[9]  F. Almgren,et al.  Curvature-driven flows: a variational approach , 1993 .

[10]  Luigi Ambrosio.  Corso introduttivo alla teoria geometrica della misura ed alle superfici minime , 1997 .

[11]  M. Novaga,et al.  Explicit Solutions of the Eigenvalue Problem $div \left(\frac Du\vert Du \vert \right)=u$ in $R^2$ , 2005 .

[12]  C. Ballester,et al.  The Dirichlet Problem for the Total Variation Flow , 2001 .

[13]  Regularity for minimal boundaries in Rn¶with mean curvature in Ln , 1998 .

[14]  P. Lions,et al.  Image recovery via total variation minimization and related problems , 1997 .

[15]  P. Bassanini,et al.  Elliptic Partial Differential Equations of Second Order , 1997 .

[16]  V. Caselles,et al.  Parabolic Quasilinear Equations Min-imizing Linear Growth Functionals , 2004 .

[17]  G. Anzellotti,et al.  Pairings between measures and bounded functions and compensated compactness , 1983 .

[18]  Vicent Caselles,et al.  Explicit Solutions of the Eigenvalue Problem -div(Du/|Du|)=u in R2 , 2005, SIAM J. Math. Anal..

[19]  Eduardo Gonzalez,et al.  The mean curvature of a set of finite perimeter , 1987 .

[20]  Ronald F. Gariepy.  FUNCTIONS OF BOUNDED VARIATION AND FREE DISCONTINUITY PROBLEMS (Oxford Mathematical Monographs) , 2001 .

[21]  Antonin Chambolle,et al.  The Discontinuity Set of Solutions of the TV Denoising Problem and Some Extensions , 2007, Multiscale Model. Simul..

[22]  Umberto Massari,et al.  Frontiere orientate di curvatura media assegnata in $L^P$ , 1975 .

[23]  I. Tamanini.  Boundaries of Caccioppoli sets with Hölder-continuois normal vector. , 1982 .

[24]  Gene H. Golub,et al.  A Nonlinear Primal-Dual Method for Total Variation-Based Image Restoration , 1999, SIAM J. Sci. Comput..

[25]  Umberto Massari,et al.  Esistenza e regolarità delle ipersuperfici di curvatura media assegnata in Rn , 1974 .

[26]  A. Chambolle,et al.  A characterization of convex calibrable sets in , 2005 .