Piecewise affine sparse representation via edge preserving image smoothing

We show a new image editing method, which can obtain the sparse representation of images. The previous methods obtain the sparse image representation by using first-order smooth prior with l0-norm. A type of incorrect structure will be preserved due to the so called staircasing effects, which usually occur in the region where the image changes gradually. In this paper, we propose the model formed with the data fidelity and the new regularization preserving the gradient at the salient edges and penalizing the magnitude of second-order derivative at all of the other pixels. To obtain the sparse representation, we iteratively minimize the model. In each iteration, the salient edges are re-extracted and the weight of regularization becomes larger than previous. Our iterating smoothing scheme yields the sparse representation, and avoids the incorrect structure caused by staircasing. The experiments illustrate our method outperforms the state of the arts.