Image Processing Reference
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Fig. 6. Fraction of failed recoveries as a function of the small dimension of the mixing matrix
M. The red curve is with the weighting matrix defined by eq. (7). The green curve has the
weighting matrix set to the identity matrix.
5. Results for sparse sinusoids with noise
5.1 Signal composed of a single sinusoid with noise
Figs. 7 (a) and (b) show the error in the recovery of a single-frequency, unity amplitude
signal as a function of the small dimension M of an M x1024 mixing matrix Φ with  = 10 -2
for 100 realizations of the noise. As M increases the standard deviations of the errors in both
frequency and amplitude,  f and  a , decrease as expected since more measurements are
made to average a given noise level. The decrease of about a factor of 3 in  f and  a for a
factor of 10 increase in M is consistent with estimates based on SNR (Shaw and Valley, 2010;
Davenport et al., 2006). Fig. 8 shows  f and  a as a function of s averaged over 20 different
4x1024 mixing matrices. Both  f and  a are proportional to  with  a about 2 to 3 orders of
magnitude larger than  f .
(a)
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