We propose a convolutional neural network (CNN) architecture for image classification based on subband decomposition of the image using wavelets. The proposed architecture decomposes the input image spectra into multiple critically sampled subbands, extracts features using a single CNN per subband, and finally, performs classification by combining the extracted features using a fully connected layer. Processing each of the subbands by an individual CNN, thereby limiting the learning scope of each CNN to a single subband, imposes a form of structural regularization. This provides better generalization capability as seen by the presented results. The proposed architecture achieves best-in-class performance in terms of total multiply-add-accumulator operations and nearly best-in-class performance in terms of total parameters required, yet it maintains competitive classification performance. We also show the proposed architecture is more robust than the regular full-band CNN to noise caused by weight-and-bias quantization and input quantization.