Joint generalized singular value decomposition and tensor decomposition for image super-resolution

The existing methods for performing the super-resolution of the three-dimensional images are mainly based on the simple learning algorithms with the low computational powers and the complex deep learning neural network-based learning algorithms with the high computational powers. However, these methods are based on the prior knowledge of the images and require a large database of the pairs of the low-resolution images and the corresponding high-resolution images. To address this difficulty, this paper proposes a method based on the joint generalized singular value decomposition and tensor decomposition for performing the super-resolution. Here, it is not required to know the prior knowledge of the pairs of the low-resolution images and the corresponding high-resolution images. First, an image is represented as a tensor. Compared to the three-dimensional singular spectrum analysis, the spatial structure of the local adjacent pixels of the image is retained. Second, both the generalized singular value decomposition and the Tucker decomposition are applied to the tensor to obtain two low-resolution tensors. It is worth noting that the correlation between these two low-resolution tensors is preserved. Also, these two decompositions achieve the exact perfect reconstruction. Finally, the high-resolution image is reconstructed. Compared to the de-Hankelization of the three-dimensional singular spectrum analysis, the required computational complexity of the reconstruction of our proposed method is much lower. The computer numerical simulation results show that our proposed method achieves a higher peak signal-to-noise ratio than the existing methods.