IEEE Trans Image Process. 2015 Sep;24(9):2797-810. doi: 10.1109/TIP.2015.2431435.
Sparse representation has recently attracted enormous interests in the field of image restoration. The conventional sparsity-based methods enforce sparse coding on small image patches with certain constraints. However, they neglected the characteristics of image structures both within the same scale and across the different scales for the image sparse representation. This drawback limits the modeling capability of sparsity-based super-resolution methods, especially for the recovery of the observed low-resolution images. In this paper, we propose a joint super-resolution framework of structure-modulated sparse representations to improve the performance of sparsity-based image super-resolution. The proposed algorithm formulates the constrained optimization problem for high-resolution image recovery. The multistep magnification scheme with the ridge regression is first used to exploit the multiscale redundancy for the initial estimation of the high-resolution image. Then, the gradient histogram preservation is incorporated as a regularization term in sparse modeling of the image super-resolution problem. Finally, the numerical solution is provided to solve the super-resolution problem of model parameter estimation and sparse representation. Extensive experiments on image super-resolution are carried out to validate the generality, effectiveness, and robustness of the proposed algorithm. Experimental results demonstrate that our proposed algorithm, which can recover more fine structures and details from an input low-resolution image, outperforms the state-of-the-art methods both subjectively and objectively in most cases.
稀疏表示在图像恢复领域最近引起了极大的兴趣。传统的基于稀疏的方法在具有一定约束的小图像块上执行稀疏编码。然而，它们忽略了图像在同一尺度内和不同尺度之间的结构特征，用于图像稀疏表示。这种缺点限制了基于稀疏的超分辨率方法的建模能力，特别是对于观察到的低分辨率图像的恢复。在本文中，我们提出了一种结构调制稀疏表示的联合超分辨率框架，以提高基于稀疏的图像超分辨率的性能。所提出的算法为高分辨率图像恢复制定了约束优化问题。首先使用多步放大方案和岭回归来利用多尺度冗余进行高分辨率图像的初始估计。然后，梯度直方图保持作为图像超分辨率问题的稀疏建模的正则化项。最后，提供数值解来求解模型参数估计和稀疏表示的超分辨率问题。在图像超分辨率方面进行了广泛的实验，以验证所提出算法的通用性、有效性和鲁棒性。实验结果表明，我们提出的算法可以从输入的低分辨率图像中恢复更多的精细结构和细节，在大多数情况下，无论是主观上还是客观上，都优于最先进的方法。
