Section: New Results

Reconstruction of Speech signal from its Unpredictable Points Manifold

Participants : Vahid Khanagha, Khalid Daoudi, Oriol Pont, Hussein Yahia.

Local Predictability Exponents (LPEs) can be used to classify a given signal's samples according to their predictability. In particular, the Unpredictable Points Manifold, the subset of less predictable points can be formed as the ensemble of points having the least value of singularity exponents. We call these exponents the Local Predictability Exponents since they are are computed according to a procedure based on the evaluation of the degree of reconstruction at a given point. We demonstrate in the case of Speech signal that LPEs are key quantities related to predictability in the framework of reconstructible systems: it is possible to reconstruct the whole Speech signal by applying a reconstruction kernel to the UPM. This provides a strong indication of the importance of the UPM, already demonstrated for other types of complex signals. Experiments show that a UPM containing a small number of the points provides very good perceptual reconstruction quality. In summary following steps have been taken:

• Using the LPEs to form the UPM for Speech signal and coping with the implementation issues in particular case of Speech signal.

• Successful reconstruction of Speech signal from the UPM. The performance was measured using objective measures of reconstruction quality.

• Detailed study of geometrical implications of the points in UPM, and proposition of a new multiscale measure, to be used in estimation procedure of exponents, which is more appropriate for speech analysis. In fact, the same quality of reconstruction is achieved with a quite smaller UPM.

• Development of a very simple compression algorithm (8-bit differential nonuniform quantizer) which overperforms the traditional DPCM coding method.

Related Publication: [15] .