Wavelet Inpainting Based on Tensor Diffusion

Due to the lossy transmission in the JPEG2000 image compression standard, the loss of wavelet coefficients heavily affects the quality of the received image. In this paper, we propose a novel wavelet inpainting model based on tensor diffusion (TDWI) to restore the missing or damaged wavelet coefficients. A hybrid model is built by combining structure-adaptive anisotropic regularization with wavelet representation. Its associated Euler-Lagrange equation is also given for analyzing its regularity performance. Owing to the matrix representation of the structure tensor in the regularization term, the shape of diffusion kernel changes adaptively according to the image features, including sharp edges, corners and homogeneous regions. Compared with existing wavelet inpainting models, the proposed one can control more adaptively and accurately the geometric regularity in the image and exhibits better robustness to noise. In addition, an effective and proper numerical scheme is adopted to improve the computation. Experimental results on a variety of loss scenarios are given to demonstrate the advantages of our proposed model.