CMP in MPTK: Third Results

In a previous entry, I compared our results with those produced by my own implementation of CMP in MATLAB — which did not suffer from the bug because it computes the optimal amplitude and phases in a slow way with matrix inverses. Now, with the new corrected code, I have produced the following results.
Just for comparison, here are the residual energy decays of my previous experiments, detailed in my paper on CMP with time-frequency dictionaries.

Now, with the corrections, I observe the decays. The “MPold” decay is that produced by the uncorrected MPTK.
“MP” shows that of the new code.
Only in Attack and Sine do we see much difference;
and at times in Sine the previous version of MPTK beats the corrected version. (Such is the behavior of greedy algorithms. I will write a Po’D about this soon.)
Anyhow, the decays of CMP-\(\ell\) (where the number denotes the largest number of possible cycles of refinement, but I suspend refinement cycles when energyAfter/energyBefore > 0.999), comports with the decays I see in my MATLAB implementation (see above).
So, now I am comfortable moving on.

Below we see the decays and cycle refinements for three different CMPs for these four signals. (Note the change in the y axes.) Bimodal appears to benefit the most in the short term from the refinement cycles, after which improvement is sporadic.
The modeling of Sine has a flurry of improvements.
It is interesting to note that as \(\ell\) increases, we do not necessarily see better models with respect to the residual energy. For instance, for Attack, the residual energy for CMP-1 beats the others.

And briefly back to the glockenspiel signal, below we see the decays and improvements
using a multiscale Gabor dictionary (up to atoms with scale 512 samples).


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