Deep Learning with Sparse Representations for Biomedical Signals

In a deep convolutional neural network (DCNN), an input signal is filtered using convolution to obtain its features. The filter characteristics govern the nature of the feature space inside the DCNN. Defining these filters based on the knowledge of the signal characteristics gives us some control in modelling the feature space. A wavelet filter bank in a similar setting produces a multiresolution distribution of these features, providing a sparse representation of the input signal features inside the DCNN. Learning such sparse representations is simpler and it leads to stable and explainable models. Naturally occurring biomedical signals contain patterns that often require identification for critical applications. This paper presents two successful unification of multiresolution analysis (MRA) with machine learning for biomedical signals. The first uses continuous wavelet transform (CWT) with a DCNN classifier to identify fetal electrocardiogram (fECG) from non-invasive fECG recordings. In the second, a discrete wavelet transform (DWT) filter bank embedded in a DCNN encoder-decoder architecture successfully generates brain masks for skull-stripping in brain MR images. The skull-stripped brain volume is further segmented into grey matter (GM) and white matter (WM) regions using Haar DWT and K-means. Unifying MRA in DCNNs reduces the model complexity without compromising performance in both cases.