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Classification for degraded images having various levels of degradation is very important in practical applications. This paper proposes a convolutional neural network to classify degraded images by using a restoration network and an ensemble learning. The results demonstrate that the proposed network can classify degraded images over various levels of degradation well. This paper also reveals how the image-quality of training data for a classification network affects the classification performance of degraded images., Comment: Accepted by the 27th IEEE International Conference on Image Processing (ICIP 2020)