Summary: In this paper, we propose a new model for image restoration and image decomposition into cartoon and texture, based on the total variation minimization of {\it L. I. Rudin}, {\it S. Osher} and {\it E. Fatemi} [Physica D 60, No. 1--4, 259--268 (1992;

Zbl 0780.49028)] and on oscillatory functions, which follows results of {\it Y. Meyer} [“Oscillating pattern in image processing and nonlinear evolution equations” (2001;

Zbl 0987.35003)]. This paper also continues the ideas introduced by the authors in a previous work on image decomposition models into cartoon and texture [{\it L. A. Vese} and {\it S. Osher}, J. Sci. Comput. 19, No. 1--3, 553--572 (2003;

Zbl 1034.49039)]. Indeed, by an alternative formulation, an initial image $f$ is decomposed here into a cartoon part $u$ and a texture or noise part $v$. The $u$ component is modeled by a function of bounded variation, while the $v$ component is modeled by an oscillatory function, bounded in the norm dual to $\vert \cdot \vert_{H^1_0}$. After some transformation, the resulting PDE is of fourth order, involving the Laplacian of the curvature of level lines. Finally, image decomposition, denoising, and deblurring numerical results are shown.