Restoration of clipped audio signals

Restoration of clipped (audio) signals is a challenging and very often ill-posed problem. Clipping refers to the truncation of the aplitude of a signal above and/or below a certain treshold (clipping level). Clipping can appear in the analog-to-digital conversion of a signal, during the recording of music with a suboptimal microphone or more generally, during data transmission. See the figure below for an example of a clipped audio signal. The problem of restoring the missing samples in a clipped signal is usually more challenging than the irregular sampling problem. The difficulty arises from following facts:

Missing samples are consecutive, resulting in possibly large missing data segments.
Missing samples and sampling energy of the signal in clipped areas are obviously intrinsically connected.
Typical regularization approaches that minimize the norm/seminorm of the signal fail (due to the reason above)
Fast algorithms are required if on-line processing is necessary

The algorithm I have developed for this purpose uses local and global informatiom and combines a statistical with a deterministic approach.

Here is an example for the restoration of a clipped audio signal:

You can download an example (I agree, it's not really a great song) in WAV-format here:
Unclipped signal (8 seconds, thanks to Earl Vickers for recording it)
Clipped signal
Restored signal

The original signal of the example above, the clipped version, and the restoration are displayed in the figure below. The restoration is not yet perfect (but better than existing patented algorithms). Click on the image to see a larger version.

The next figure shows the semgment of the signal above, which suffered most from clipping first together with the clipped signal (above) and then together with its restoration (below). Click on the image to see it in a better resolution.