Wavelet Pooling CNN

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It is generally the case that Convolution Neural Networks (CNNs) out perform vector-based deep learning techniques. As such, the fundamentals of CNNs are good candidates to be innovated in order to improve said performance. The pooling layer is one of these fundamentals, and although various methods exist ranging from deterministic and simple: max pooling and average pooling, to probabilistic: mixed pooling and stochastic pooling, all these methods employ a neighborhood approach to the sub-sampling which, albeit fast and simple, can produce artifacts such as blurring, aliasing, and edge halos (Parker et al., 1983).

This paper introduces a novel pooling method based on the discrete wavelet transform. Specifically, it uses a second-level wavelet decomposition for the sub-sampling. This method, instead of nearest neighbor interpolation, uses a sub-band method that the authors claim produces less artifacts and represents the underlying features more accurately. Therefore, if pooling is viewed as a lossy process, the reason for employing a wavelet approach is to try to minimize this loss.