This paper develops methods for recovering high-resolution images from low-resolution images by combining ideas inspired by sparse coding, such as compressive sensing techniques, with super-resolution neural networks. Sparse coding leverages the existence of bases in which signals can be sparsely represented, and herein we use such ideas to improve the performance of super-resolution convolutional neural networks (CNN). In particular, we propose an improved model in which CNNs are used for super-resolution in the frequency domain, and we demonstrate that such an approach improves the performance of image super-resolution neural networks. In addition, we indicate that instead of numerous deep layers, a shallower architecture in the frequency domain is sufficient for many types of image super-resolution problems.
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