Graph-based regularization for color image demosaicking

We present a novel regularization framework for demosaicking by viewing image as smooth signal on a weighted graph. The restoration problem is formed as a minimization of variation of the signal on graph. As an initial step, we build a weight matrix which measures the similarity between every pair of pixels, from an estimate of the full color image. After that, a two-stage optimization is carried out: first, we assume that graph Laplacian is signal dependent and solve a non-quadratic problem by gradient descent; then, we pose a variational problem on graph with a static Laplacian, under the constraint of consistency with the available samples in each color component. Performance evaluation shows that our approach can improve the previous demosaicking methods both quantitively and visually, by alleviating the artifical effect. Moreover, the mapping from image to signal on graph provides a general method for image processing.