Spatial Frequency Loss for Learning Convolutional Autoencoders

This paper presents a learning method for convolutional autoencoders (CAEs) for extracting features from images. CAEs can be obtained by utilizing convolutional neural networks to learn an approximation to the identity function in an unsupervised manner. The loss function based on the pixel loss (PL) that is the mean squared error between the pixel values of original and reconstructed images is the common choice for learning. However, using the loss function leads to blurred reconstructed images. A method for learning CAEs using a loss function computed from features reflecting spatial frequencies is proposed to mitigate the problem. The blurs in reconstructed images show lack of high spatial frequency components mainly constituting edges and detailed textures that are important features for tasks such as object detection and spatial matching. In order to evaluate the lack of components, a convolutional layer with a Laplacian filter bank as weights is added to CAEs and the mean squared error of features in a subband, called the spatial frequency loss (SFL), is computed from the outputs of each filter. The learning is performed using a loss function based on the SFL. Empirical evaluation demonstrates that using the SFL reduces the blurs in reconstructed images.