Low rank recovery based image interpolation using local and nonlocal modeling

Linear representation models are effective to represent the correlation in image interpolation. However, linear models usually lack constraints of the representation coefficient. In this paper, we propose a low rank matrix recovery based image interpolation to reinforce the sparsity of representation coefficient implicitly. Since both the local and nonlocal correlation is pervasive in natural images, we exploit such correlations by incorporating the local and nonlocal modeling, which fully utilizes the redundancy in images and improves the representation ability of our model. By minimizing the sum of the rank of data matrices which reflect the linear relationship among local patch pixels and nonlocal similar patch pixels, a precise low rank approximation of the missing pixels is obtained according to the low rank matrix recovery theory. A Split Bregman based minimization algorithm is developed to efficiently solve the low rank recovery problem. Extensive experimental results indicate the proposed method outperforms the traditional methods in both the objective and subjective visual quality.