Algorithms for Audio Decomposition Using Mixed Norms

Manuscript

"Algorithms for Audio Decomposition Using Mixed Norms", İ. Bayram, Ö. D. Akyıldız, August, 2012. [.pdf]

Software

The file PDToolbox.zip contains Matlab implementations of the experiments in the manuscript.

Experiments

Below are some results from the manuscript.

Restoration Experiment

The original signal is an old recording of a kaval tune. The signal contains artifacts due to recording.
Two attempts to clean the signal are made.
First, we denoise the signal using mixed norms.
Second, the restoration is performed by separating the artifacts and the tune of interest. See the manuscript for details.

Original Signal , Denoised Signal , Restored Signal .

Separation of Ney and Darbuka

Mixture signal (Ney + Darbuka)

Analysis Prior : Ney , Darbuka

Synthesis Prior : Ney , Darbuka

Heuristic Scheme : Ney , Darbuka

Further Results

Another Old Recording

The signal is an excerpt from "Taxim Zeybekiko". The signal contains crackles and our aim is to suppress them using the decomposition formulation. This problem could be regarded as a variation of the denoising problem discussed above. Notice that although the noise in this signal (i.e., crackles) is different in nature from the noise in the phonogram signal, it is also far from being Gaussian.

Mixture Signal

Spectrogram of the Mixture Signal

Below are the component separation results with the analysis and synthesis prior formulations. The same parameters as in the Restoration Experiment above are used (see the Matlab Code).

Analysis Prior : Tonal Component , Transient Component

Synthesis Prior : Tonal Component , Transient Component

Heuristic Scheme : Tonal Component , Transient Component

The spectrograms for the components obtained by the analysis prior formulation :

The spectrograms for the components obtained by the synthesis prior formulation :

The spectrograms for the components obtained by the heuristic scheme :

Separation of Percussion

Here, we are mainly interested in the capability of the model to separate the drums. Notice that this is not necessarily what tonal and transient component analysis aims to achieve.