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Noisy low resolution (LR) images are always obtained in real applications, but many existing image magnification algorithms can not get good result from a noisy LR image. We propose a two-step image magnification algorithm to solve this problem. The proposed algorithm takes the advantages of both regularization-based method and learning-based method. The first step is based on total variation (TV) regularization and the second step is based on sparse representation. In the first step, we add a constraint on the TV regularization model to magnify the LR image and at the same time to suppress the noise in it. In the second step, we propose an order-changed dictionary training algorithm to train the dictionaries which is dominated by texture details. Experimental results demonstrate that the proposed algorithm performs better than many other algorithms when the noise is not serious. The proposed algorithm can also provide better visual quality on natural LR images.

Noisy image magnification with total variation regularization and order-changed dictionary learning