# On the Use of Structured Prior Models for Bayesian Compressive Sensing of Modulated Signals
## 3 Experimental Results
### Simulated Example
#### 3.1.3 Results
The strong assumption does not bring additional improvement to the results. It is worth to recall that this the test signal exhibits perfectly symmetrical support. However, this perfect symmetry may sometimes be altered in real applications. Therein, we recommend adopting the default choice of the weak assumption about the in-block symmetry of the support. In contrast, S&S-3A and S&S-3B generally yield less good results when compared to the other spike-and-slab models especially in low noise levels. This leads us to say that the strong assumption on the similarity of the support for the different carrier harmonic is not always advantageous. This can be explained by the relatively high shrinking power of such model that may be good to promote perfectly similar support, but which may not be adapted when modulations magnitudes are highly imbalanced. When comparing these different families of models, the results show that the performance of spike-and-slab models are poorer than those of continuous models in low to medium noise levels. For example, the SMG-block yields better results than its discrete version, namely S&S-1B, S&S-2B, and S&S-3B for the first four noise levels, while, for medium and high noise levels (for SNR \(<\) 6 dB), theses discrete models achieve similar or slightly better results than the SMG-block. We may explain this observation, as follows. The assumption regarding the support increases the shrinking behavior of the model. This is beneficial, as it allows for impressively reducing the background noise by shrinking the unwanted components that do not have their symmetrical part in the spectrum, at the cost of an over-shrinking of the small coefficients. In high noise levels, the reconstruction error is mainly dominated by the shrinking effect of background noise. While, in low noise levels, the effect of over-shrinking the small components is more dominant. This can also explain the small value of correlation in low compression rates that were observed for S&S-univ when compared to continuous univariate models in low noise levels. Another concern that may explain our observations is the muli-modality of the posterior for spike-and-slab models, which makes the inference task more challenging for them than for continuous models. Therefore, the authors recommend the default use of continuous models for signals sharing the same properties as this test signal (only few non-zero coefficients, with symmetrical spectrum support and unbalanced amplitudes). More specifically, we recommend the SMG-block, since it achieved better performance for all scenarios in our experiments. We now investigate the effect of presence of interfering components in the measured signal. Interfering components in real applications may come from external environment or simply other rotating components in the mechanical system, like fans, turbines, compressors, and so on. We simulate a small interfering sinusoidal signal \(s_{3}\) of frequency 0.13, and we add it to the test signal in addition to Gaussian noise. We investigate the shrinking behavior of the continuous models for a compression rate of 0.8 and for an initial signal-to-noise ration of 0 dB. Figure 7 shows zooms on the reconstructed spectra around frequency 0.13. We see that only the SMG-block succeeds in eliminating the interfering component. This can be also seen in the posterior marginal densities of the coefficient related to the interfering component. In fact, the additional symmetrical properties regarding the structure support included in SMG-block yield a marginal density, whose mass is concentrated at values near zero.