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A novel regularised image super-resolution algorithm is proposed, building on the emerging cosparse or analysis sparse prior models, which are important complementary alternatives to the widely used synthesis sparse counterpart. Moreover, to achieve adaptivity to the varying local structures of natural images, the patch space is partitioned into meaningful subspaces by clustering and learn analysis sub-dictionary for each cluster are partitioned, which are performed online and iteratively based solely on the current available image information, for maximum generality and flexibility. In addition, non-local feature self-similarity is incorporated for further reconstruction quality enhancement. Experimental results show that the proposed approach gives favourable results with respect to the state-of-the-art methods.

The latent variable prior of the variational autoencoder (VAE) often utilizes a standard Gaussian distribution because of the convenience in calculation, but has an underfitting problem. This paper proposes a variational autoencoder with optimizing Gaussian mixture model priors. This method utilizes a Gaussian mixture model to construct prior distribution, and utilizes the Kullback-Leibler (KL) distance between posterior and prior distribution to implement an iterative optimization of the prior distribution based on the data. The greedy algorithm is used to solve the KL distance for defining the approximate variational lower bound solution of the loss function, and for realizing the VAE with optimizing Gaussian mixture model priors. Compared with the standard VAE method, the proposed method obtains state-of-the-art results on MNIST, Omniglot, and Frey Face datasets, which shows that the VAE with optimizing Gaussian mixture model priors can learn a better model.

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