  This paper introduces a defense approach against end-to-end adversarial
attacks developed for cutting-edge speech-to-text systems. The proposed defense
algorithm has four major steps. First, we represent speech signals with 2D
spectrograms using the short-time Fourier transform. Second, we iteratively
find a safe vector using a spectrogram subspace projection operation. This
operation minimizes the chordal distance adjustment between spectrograms with
an additional regularization term. Third, we synthesize a spectrogram with such
a safe vector using a novel GAN architecture trained with Sobolev integral
probability metric. To improve the model's performance in terms of stability
and the total number of learned modes, we impose an additional constraint on
the generator network. Finally, we reconstruct the signal from the synthesized
spectrogram and the Griffin-Lim phase approximation technique. We evaluate the
proposed defense approach against six strong white and black-box adversarial
attacks benchmarked on DeepSpeech, Kaldi, and Lingvo models. Our experimental
results show that our algorithm outperforms other state-of-the-art defense
algorithms both in terms of accuracy and signal quality.
