Progressive image restoration through hybrid graph Laplacian regularization

In this paper, we propose a unified framework to perform progressive image restoration based on hybrid graph Laplacian regularized regression. We first construct a multi-scale representation of the target image by Laplacian pyramid, then progressively recover the degraded image in the scale space from coarse to fine so that the sharp edges and texture can be eventually recovered. On one hand, within each scale, a graph Laplacian regularization model represented by implicit kernel is learned which simultaneously minimizes the least square error on the measured samples and preserves the geometrical structure of the image data space by exploring non-local self-similarity. In this procedure, the intrinsic manifold structure is considered by using both measured and unmeasured samples. On the other hand, between two scales, the proposed model is extended to the parametric manner through explicit kernel mapping to model the inter-scale correlation, in which the local structure regularity is learned and propagated from coarser to finer scales. Experimental results on benchmark test images demonstrate that the proposed method achieves better performance than state-of-the-art image restoration algorithms.