In this paper, signal-adaptive parametric models based on overcomplete dictionaries of time-frequency atoms are considered for high quality low bit-rate parametric audio coding. There are a variety of frameworks for deriving overcomplete signal expansions, which differ in the structure of the dictionary and the manner in which dictionary atoms are selected for the expansion. Psychoacoustic-adapted matching pursuits are accomplished for extracting sinusoidal components using an harmonic dictionary, while energy-adapted matching pursuits are carried out for transients modelling with a wavelet-based dictionary. First, transients are detected, modelled (with wavelet functions) and removed from the original audio signal, leaving a residue. Then, sinusoids are modelled using complex exponential functions and removed from the initial residue, leaving a noise-like signal. This final residue is modelled taking advantage of the good time-frequency location of the wavelet transform and considering psychoacoustic principles. An M-depth Wavelet Transform is first applied to the residue. Energy of each wavelet sub-band is then computed, and finally a Time Noise Shaping (TNS) process is applied to each one, which involves a parametric model for the noise-like signal. The resulting multi-part model (Sines + Transients + Noise) is efficiently applied by taking into account psycho-acoustical information for audio coding purposes. The combination of these all ideas results in nearly transparent parametric audio coding at binary rates close to 16kbps for most of the CD-quality one channel audio signals considered for testing. Listening tests allow us to say that our coder achieves better results than MPEG-4 AAC at very low bit rates (close to 16kbps).
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