Comparison of Model Orders for OMP and LoCOMP with Interference Adaptation

Continuing on with my experiments (see here, and here) with LoCOMP, I now have some model performance comparisons between LoCOMP and OMP using interference adaptation.
The plots below show the model orders (decomposition iteration) for a given signal-to-residual-energy ratio (SRR), \(20\log_{10} ||\vx||/||\vr||\), as a function of the interference weighting \(\gamma\) used in the atom selection. (I hold the weighting constant, which I don’t think is ideal.) The three signals used are shown here.


nsparsity.jpg
The black and gray lines are from models produced by OMPIA, and the red lines are from models produced by LoCOMPIA. At low SRRs we see small differences between the model orders; but as the models grow, their behaviors become drastically different. For Attack, we can see differences of over 20 atoms at 60 dB. (Where there are breaks in the lines, the algorithm experienced problems with a nearly singular matrix, thus breaking the monotonicity in the residual energy decay; thus, I have removed these data points.) For Bimodal, the maximum differences are over 50 atoms at 60 dB in the range \(\gamma \in [0.15, 0.23]\). For this signal, LoCOMP appears to be much less sensitive to the interference weighting than OMP. For Sine we don’t see much difference, but it is unusual that both algorithms were have so much trouble with singular matrices — which I take it to mean that my implementation might not be operating accurately at the edges of the signal. However, at lower SRRs we see that the lower-order models result in both cases for \(\gamma > 0.5\) than without interference adaptation \(\gamma = 0\).

In summary, I am confident from all of my experiments that LoCOMP generates signal models that are comparable to those generated by OMP even though it involves a local optimization, and not a global one. LoCOMP also appears more amenable than OMP to using the characteristics of the developing model to influence the atom selection (i.e., interference). My next experiments will involve real audio signals instead of these rather artificial ones. This means it is time for me to dive into MPTK and find a way to implement interference adaptation.

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