Data-Driven Multi-scale Non-local Wavelet Frame Construction and Image Recovery

By assuming that images of interest can be sparsely modelled by some transform, the sparsity-based regularization has been one promising approach for solving many ill-posed inverse problems in image recovery. One often-used type of systems for sparsifying images is wavelet tight frames, which can efficiently exploit the sparse nature of local intensity variations of images. However, existing wavelet frame systems lack the capability of exploiting another important image prior, i.e., the self-recursion of local image structures in both spatial and scale domain. Such a self-recursion prior of image structures has led to many powerful non-local image restoration schemes with impressive performance. This paper aims at developing a scheme for constructing a non-local wavelet frame or wavelet tight frame that is adaptive to the input image. The proposed multi-scale non-local wavelet frame allows the resulting regularization simultaneously exploits both the sparse prior of local variations of image intensity and the global self-recursive prior of image structures in spatial domain and across scales. Based on the proposed construction scheme, a powerful regularization method is developed for solving image deconvolution problem. The experiments showed that the results from the proposed regularization method are compared favorably against that from several popular image restoration methods.