Introducing oriented Laplacian diffusion into a variational decomposition model.

The decomposition model proposed by Osher, Solé and Vese in 2003 (the OSV model) is known for its good denoising performance. This performance has been found to be due to its higher weighting of lower image frequencies in the H -1-norm modeling the noise component in the model. However, the OSV model tends to also move high-frequency texture into this noise component. Diffusion with an oriented Laplacian for oriented texture is introduced in this paper, in lieu of the usual Laplacian operator used to solve the OSV model, thereby significantly reducing the presence of such texture in the noise component. Results obtained from the proposed oriented Laplacian model for test images with oriented texture are given, and compared to those from the OSV model as well as the Mean Curvature model (MCM). In general, the proposed oriented Laplacian model yields higher signal-to-noise ratios and visually superior denoising results than either the OSV or the MCM models. We also compare the proposed method to a non-local means model and find that although the proposed method generally yields slightly lower signal-to-noise ratios, it generally gives results of better perceptual visual quality.

Decorrelating the structure and texture components of a variational decomposition model.

The observation has been made by Aujol and Gilboa that the cartoon and texture components of the decomposition of an image should not be correlated, as they are generated from independent processes. They use this observation in order to choose an optimal fidelity parameter lambda for the decomposition process. However, this determination can be quite inefficient since a wide range of parameters lambda must be searched through before an estimated optimal parameter can be found. In the present paper, we take a different approach, in which the cartoon and texture components are explicitly decorrelated by adding a decorrelation term to the energy functional of the decomposition model of Osher, SolE, and Vese (the OSV model). Decomposition results of improved quality over those from the OSV model are obtained, as quantified by a series of new decomposition quality measures, with cartoon and texture information better separated into their respective components. A new derivation of the OSV model is developed which maintains the texture subcomponents g(1) and g(2) so that discrimination results similar to those from other decomposition models (e.g., from the model of Vese and Osher and Improved Edge Segregation) may be obtained. This derivation is extended to the proposed model, for which discrimination results are obtained in a substantially smaller number of iterations.