  Clipping or saturation in audio signals is a very common problem in signal
processing, for which, in the severe case, there is still no satisfactory
solution. In such case, there is a tremendous loss of information, and
traditional methods fail to appropriately recover the signal. We propose a
novel approach for this signal restoration problem based on the framework of
Iterative Hard Thresholding. This approach, which enforces the consistency of
the reconstructed signal with the clipped observations, shows superior
performance in comparison to the state-of-the-art declipping algorithms. This
is confirmed on synthetic and on actual high-dimensional audio data processing,
both on SNR and on subjective user listening evaluations.
