Blind image super-resolution (BISR) aims to reconstruct a high-resolution image from its low-resolution counterpart degraded by unknown blur kernel and noise. Many deep neural network based methods have been proposed to tackle this challenging problem without considering the image degradation model. However, they largely rely on the training sets and often fail to handle images with unseen blur kernels during inference. Deep unfolding methods have also been proposed to perform BISR by utilizing the degradation model. Nonetheless, the existing deep unfolding methods cannot explicitly solve the data term of the unfolding objective function, limiting their capability in blur kernel estimation. In this work, we propose a novel unfolded deep kernel estimation (UDKE) method, which, for the first time to our best knowledge, explicitly solves the data term with high efficiency. The UDKE based BISR method can jointly learn image and kernel priors in an end-to-end manner, and it can effectively exploit the information in both training data and image degradation model. Experiments on benchmark datasets and real-world data demonstrate that the proposed UDKE method could well predict complex unseen non-Gaussian blur kernels in inference, achieving significantly better BISR performance than state-of-the-art. The source code of UDKE is available at: https://github.com/natezhenghy/UDKE.
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