Convolutional neural network (CNN)-based single image super-resolution (SR) methods have achieved superior performance on some discrete-scaling factors, including 2, 3, and 4. However, the scaling factors for SR should be continuous and not discrete in practical applications. Previous CNN-based SR models usually yield poor results for non-integer-scaling factors and are sometimes even worse than results derived from the conventional bicubic method. To extend CNN-based SR models to continuous scale, this paper proposes a multiple-scaling-based SR (MSSR) method that combines an integer-scaling-factor SR and once or twice non-integer-scaling-factor SR without retraining networks. For a non-integer-scaling factor, the MSSR method first computes an optimal integer-scaling factor according to the data similarity and choose the corresponding pre-trained model for the next stage. Then, an existing CNN-based model is used to perform the integer-scaling-factor SR. Finally, the output is scaled to the target size. The proposed MSSR method can extend a variety of existing CNN-based SR models from discrete to continuous-scaling factors. Experimental results with six CNN-based SR models demonstrated that the MSSR method could effectively improve the performance of existing CNN-based SR models for continuous-scaling-factor SR without retraining networks. Furthermore, the comparison with a magnification-arbitrary method, called Meta-SR, shows that the proposed MSSR method usually outperforms Meta-SR for scaling factors greater than or equal to 2. INDEX TERMS Convolutional neural network, image interpolation, super-resolution.

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