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Deep Block Transform for Autoencoders
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DOI：10.1109/LSP.2021.3082031.png)
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Abstract
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We discover that a trainable convolution layer with a stride over 1 and kernel >= stride is identical to a trainable block transform. A block transform is performed when we use a convolution layer with a stride >= 2 and a kernel >= the stride. For instance, if we use the same widths, such as a 2 x 2 convolution kernel and stride-2, there are no overlaps between sliding windows, so this layer operates a block transform on the partitioned 2 x 2 blocks. A block transform reduces the computational complexity due to a stride >= 2. To keep the original size, we apply a transposed convolution (stride = kernel >= 2), an adjoint operator of a forward block transform. Based on this relationship, we propose a trainable multi-scale block transform for autoencoders. The proposed method has an encoder consisting of two sequential convolutions with stride-2, a 2 x 2 kernel, and a decoder consisting of the encoder's two ad joint operators (transposed convolution). Clipping is used for nonlinear activations. Inspired by the zero-frequency element in the dictionary learning method, the proposed method uses DC values for residual learning. The proposed method shows high-resolution representations, whereas the stride-1 convolutional autoencoder with 3 x 3 kernels generates blurry images.
Keywords:
Block transform
image representation
autoencoder
convolutional neural network
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