Natural images scale invariance and high-fidelity image restoration

One of the most striking properties of natural image statistics is their scale invariance. Intuitively, a natural image always contains the same contents of different scales and dually the same contents of same scale exist throughout scales of the image. Different from the previous scale invariance related work decomposing an image to its local band-pass filter components, this paper seeks a general model of the natural image paths distribution to describe the scale invariance in the visual world and then a novel strategy for high-fidelity image restoration is presented by characterizing nonlocal self-similarity of natural images throughout scales in a unified statistical manner, which offers a powerful mechanism of combining natural images scale invariance and nonlocal self-similarity simultaneously to ensure a more reliable and robust estimation. Extensive experiments on image restoration from partial random samples manifest that the proposed algorithm achieves significant performance improvements over the current state-of-the-art schemes.