Noise-resistant structure-preserving multiscale image decomposition

Abstract

A challenge for current edge-preserving image decompositions is to deal with noisy images. Gradient- or magnitude difference-based techniques regard the noise boundary as edges, while the local extrema-based method suffers from averaging noisy envelops. We introduce local anisotropy derived from nonlinear local structure tensor to differentiate edges from fine-scale details and noises. Providing low smoothness weights to the places with large local anisotropy rather than a large gradient under the improved weighted least squares optimization framework, we present a noise-resistant, structure-preserving smoothing operator. By either progressively or recursively applying this operator we construct our structure-preserving multiscale image decomposition. Based on the key property of our algorithm, noise resistance, we compare our results with existing edge-preserving image decomposition methods and demonstrate the effectiveness and robustness of our structure-preserving decompositions in the context of image restoration, noisy image abstraction, and noisy image dehazing.