基于跨尺度低秩约束的单幅图像盲超分辨率算法

Blind Single-Image Super-Resolution Algorithm Based on Cross-Scale Low Rank Prior

单幅图像盲超分辨率方法是在模糊核未知的情况下仅利用单幅低分辨率图像重建高分辨率图像,这是一个严重的欠定逆问题.超分辨率正则化方法通过正则化约束项引入附加信息,为低分辨率图像恢复或重建合理的高频成分.本文将跨尺度自相似性与低秩先验相结合,提出了一种基于跨尺度低秩约束的单幅图像盲超分辨率方法,采用联合建模的方法同时估计模糊核与高分辨率图像.利用高分辨率图像、低分辨率图像及其降采样图像之间的跨尺度自相似性,对于低分辨率图像中的图像块在降采样图像中搜索相似块,将该图像块在高分辨率重建图像中对应的父块与其相似块在低分辨率图像中对应的父块合并,构造跨尺度相似图像块组矩阵.由于低分辨率图像中的跨尺度相似图像块能够为重建图像块提供潜在的细节信息,因此对相似图像块组矩阵进行低秩约束,在迭代求解过程中迫使重建图像恢复高频成分,进而促使模糊核的估计更加准确.此外,低秩约束能够表示数据的全局结构,对噪声具有鲁棒性.在真实和模拟图像上的实验表明,本文的算法能够准确地估计模糊核,重建高分辨率图像的边缘和细节,优于现有的自监督盲超分辨率算法.

Blind single-image super-resolution refers to reconstructing the high-resolution image from a single low-resolution one with an unknown blur kernel,which is a severely ill-posed inverse problem.The additional information about the latent high-resolution image can be incorporated by adding the regularizer in order to recover or reconstruct rea-sonable high-frequency details for the low-resolution image.In this paper,we propose a blind super-resolution method based on the cross-scale low rank prior from a single low-resolution image,which alternates between updating the blur ker-nel and the high-resolution image by a jointly modeling approach.According to the self-similarity across the high-resolu-tion image,the low-resolution image and its down-sampled image,we search for similar patches from the down-sampled im-age for the low-resolution patch,and group into a matrix the cross-scale similar image patches consisting of the parents of the low-resolution patch and its similar patches in the high-resolution reconstructed image and the low-resolution image re-spectively.Since the cross-scale similar patches in the low-resolution image provide potential details for reconstructing the high-resolution image patches,the low rank matrix approximation applied to the cross-scale similar patches enforces the re-constructed image to recover more high-frequency details and thus promotes the accuracy of the kernel estimation during the iteration.In addition,the low rank regularization elegantly indicates the non-local structure of data inherently robust to noise.Experimental results on real and simulated images show that the proposed method can accurately estimate the blur kernel and reconstruct high-resolution image with sharp edges and fine details,which outperforms the existing blind super-resolution methods based on unsupervised learning.