Variational decomposition has been widely used in image denoising, however, it can’t distinguish texture from noise well. Replacing the fixed parameter in the (BV, G) decomposition with a monotone increasing sequence, and iteratively taking the residual of the previous step as the input to decompose, we propose a multiscale variational decomposition model in this paper. Unlike the fixed-scale decomposition, the new model can decompose the input image into a sum of a series of features with different scales. So, texture can be distinguished from noise. In addition, we prove the nontrivial property and the convergence of this multiscale decomposition, and introduce a hybrid iteration algorithm that combines the first-order primal–dual algorithm with the gradient decent method to numerically solve the multiscale decomposition model. Numerical results validate the effectiveness of the proposed model. Furthermore, we apply this multiscale decomposition for image hierarchical restoration. Compared with the classical hierarchical (BV, L 2) decomposition, hierarchical wavelet decomposition and fixed-scale (BV, G) decomposition, our model has better performance for both synthetic and real images in terms of PSNR and MSSIM. 
Multiscale variational decomposition and its application for image hierarchical restoration