Improved Gabor transform and group sparse representation for ancient mural inpainting

Sparse representation has been highly successful in various tasks related to image processing and computer vision. For ancient mural image inpainting, traditional group sparse representation models usually lead to structure blur and line discontinuity due to the construction of similarity group solely based on the Euclidean distance and the randomness of dictionary initialization. To address the aforementioned issues, an improved curvature Gabor transform and group sparse representation (CGabor-GSR) model for ancient Dunhuang mural inpainting is proposed. To begin with, mutual information is introduced to weight the Euclidean distance, and then the weighted Euclidean distance acts as a new standard of similarity group. Subsequently, to mitigate the randomness of dictionary initialization, a curvature Gabor wavelet transform is proposed to extract the features and initialize the feature dictionary with dimension reduction based on principal component analysis (PCA). Ultimately, singular value decomposition (SVD) and split Bregman iteration (SBI) can be used to resolve the CGabor-GSR model to reconstruct the mural images. Experimental results on Dunhuang mural inpainting demonstrate tha the proposed CGabor-GSR achieves a better performance than compared algorithms in both objective and visual evaluation.