Combining Adaptive PDE and Wavelet Shrinkage in Image Denoising with Edge Enhancing Property

Partial differential equation (PDE) and wavelet shrinkage are two kinds of feature preserving regularized image recovery methods. In this paper, the equivalence of the two methods is discussed according to function space theory, and a new hybrid model combining adaptive PDE and wavelet shrinkage is proposed. In the new hybrid model, we use adaptive PDE with edge enhancing property. The regular coefficient of adaptive model is locally adjusted according to directional derivatives of image. Compared with traditional smoothing models, the new hybrid model has no Gibbs phenomena, smoothes image without staircasing, and enhances edge to preserve feature and texture of image. Both theoretical analysis and experiments have verified the validity o f the new model proposed in this paper.