Trainable signal encoders that are robust against noise

Within the deep learning paradigm, finite impulse response (FIR) filters are often used to encode audio signals, yielding flexible and adaptive feature representations. We show that a stabilization of FIR filterbanks with fixed filter lengths (convolutional layers with 1-D filters) by means of their condition number leads to encoders that are optimally robust against noise and can be inverted with perfect reconstruction by their transposes. To maintain their flexibility as regular neural network layers we implement the stabilization via a computationally efficient regularizing term in the objective function of the learning problem. In this way, the encoder keeps its expressive power and is optimally stable and noise-robust throughout the whole learning procedure. We show in a denoising task where noise is additionally present in the encoder representation of the signals, that the proposed stabilization of the trainable filterbank encodings is decisive for increasing the signal-to-noise ratio of the denoised signals significantly compared to a model with a naively trained encoder.