Recently, convolutional neural networks (CNNs) achieve impressive results on remote sensing scene classification, which is a fundamental problem for scene semantic understanding. However, convolution, the most essential operation in CNNs, restricts the development of CNN-based methods for scene classification. Convolution is not efficient enough for high-resolution remote sensing images and limited in extracting discriminative features due to its linearity. Thus, there has been growing interest in improving the convolutional layer. The hardware implementation of the JPEG2000 standard relies on the lifting scheme to perform wavelet transform (WT). Compared with the convolution-based two-channel filter bank method of WT, the lifting scheme is faster, taking up less storage and having the ability of nonlinear transformation. Therefore, the lifting scheme can be regarded as a better alternative implementation for convolution in vanilla CNNs. This paper introduces the lifting scheme into deep learning and addresses the problems that only fixed and finite wavelet bases can be replaced by the lifting scheme, and the parameters cannot be updated through backpropagation. This paper proves that any convolutional layer in vanilla CNNs can be substituted by an equivalent lifting scheme. A lifting scheme-based deep neural network (LSNet) is presented to promote network applications on computational-limited platforms and utilize the nonlinearity of the lifting scheme to enhance performance. LSNet is validated on the CIFAR-100 dataset and the overall accuracies increase by 2.48% and 1.38% in the 1D and 2D experiments respectively. Experimental results on the AID which is one of the newest remote sensing scene dataset demonstrate that 1D LSNet and 2D LSNet achieve 2.05% and 0.45% accuracy improvement compared with the vanilla CNNs respectively.
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