Image Processing Reference
In-Depth Information
(b)
Fig. 7. Standard deviation of the errors in frequency and amplitude of sinusoids mixed by a
mixing matrix  with dimensions M x 1024 recovered using OMP/NLS as a function of the
small dimension M of the mixing matrix  for  = 10 -2 . The results are obtained from the
average of 100 independent calculations. (a) Frequency, (b) amplitude error.
Fig. 8. Standard deviation of the frequency and amplitude errors,  f (lower red curve) and  a
(upper green curve), as a function of  averaged over 20 different 4x1024 mixing matrices.
5.2 Signal composed of 2 sinusoids with 100:1 dynamic range
Noise also affects the ability of our algorithm to recover a small signal in the presence of a
large signal. Figs. 9 and 10 show  f and  a for a test case in which the amplitudes are given
by {1.0, 0.01}, M = 10, N =1024 and the frequencies are well separated. These results are for a
single realization of the mixing matrix and averaged over 20 realizations of the noise. Note
that as expected, the frequency and amplitude of the large-amplitude component are much
better recovered than those of the small-amplitude component. Knowledge of the
parameters of the small component essentially disappears for  greater than about 0.005.
Tests with the small amplitude equal to 0.001 and 0.0001 suggest that this threshold scales
with the amplitude of the small signal.
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