Compound tetrolet sparsity and total variation regularization for image restoration
Liqian Wang, Liang Xiao, Zhihui Wei · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2011
Image restoration is one of the most classical problems in image processing. The main issue of image restoration is deblurring as well as preserving the fine details. In order to restore the high quality image, we propose a compound regularization method which combines the tetrolet-based sparsity and a new weighted adaptive total variation (ATV). Tetrolet transform is a geometric adaptive Haar-type wavelet transform. It finds the optimal partition to fit the local image structures and the tetrolet coefficients can capture the textures and details information in different image scales. ATV adds two directional gradient operators into the original anisotropic TV. It not only seeks the intensity continuity horizontally and vertically, but also seeks the intensity continuity diagonally. Combining the tetrolet-based sparsity and ATV together, our model can restore the local structures and details by the tetrolet-based sparsity regularization while suppress the noise and recover piecewise smooth images with sharp edges along four directions by the ATV regularization. For solving the minimizing problem, we propose an algorithm which consists of the variable splitting method and the Dual Douglas-Rachford splitting method. The Experimental results demonstrate the efficiency of our image restoration method for preserving the structure details and the sharp edges of image.