  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.
