Digital Signal Processing Reference
In-Depth Information
successfully tested for all major operating systems, under MATLAB 6.x and MAT-
LAB 7.x. GMCALab is distributed for noncommercial use.
9.6.2 Reproducible Experiment
Figure 9.9 illustrates the results provided by the script
sparse noisy
, which applies the fast GMCA Algorithm 35 to a BSS problem with
examples.m
N
s
=
10 noisy channels, and SNR = 10 dB. The mixing matrix is
randomly generated with entries independent and identically distributed
4 sources,
N
c
=
∼N
(0
,
1).
The fast GMCA was applied using the OWT dictionary.
9.7 SUMMARY
In this chapter, the role of sparsity and morphological diversity was highlighted to
solve the blind source separation problem. On the basis of these key ingredients, a
fast algorithmic approach coined GMCA was described, together with variations
to solve several problems, including BSS. The conclusions that one has to keep
in mind are essentially twofold: first, sparsity and morphological diversity lead to
enhanced separation quality, and second, the GMCA algorithm takes better advan-
tage of sparsity, yielding better and robust-to-noise separation. When the number of
sources is unknown, a GMCA-based method was described to objectively estimate
the correct number of sources. The results are given that illustrate the reliability
of morphospectral sparsity regularization. In a wider framework, GMCA is shown
to provide an effective basis for solving classical multichannel restoration problems
such as color image inpainting.
Nonetheless, this exciting field of sparse BSS still has many interesting open
problems. Among them, one may cite, for instance, the extension to the underdeter-
mined case with more sources than channels and the theoretical guarantees of the
sparsity-regularized BSS problem.
