Recovery of Sparse Signals with Cyclic Matching Pursuit and Compressive Measurements: Now With Orthogonal Least Squares

Yesterday I presented some results of CMP recovering compressively sensed sparse signals. Over the night I ran them again, but this time with orthogonal least squares (OLS) and cyclic orthogonal least squares (COLS) — which is presented in my paper discussed here.

RecoveryProbability.jpg
For the same experimental conditions previously, above we can clearly see that all greedy cousins to MP begin to fail at nearly the same sparsity of 0.14, but COLS “fails better” than all the others — almost 10% better recovery at a sparsity of 0.35. Still, I wouldn’t want my banking information recovered like so. Below we see the mean ell2 norm of the approximation error. We see that COLS provides less mean error than the others. (The curve for OLS had a bunch of NaNs, so I don’t know what is going on there. I predict it will be a bit east of the CMP line, and north of the COLS line.)

ell2normerror.jpg
Now, I wonder if CMP and COLS can be further improved by reconsidering multiple atoms at the same time instead of one?

Try this at home! Feel free to reproduce my results with
this MATLAB code. It is much more simple than the code presented here since I am not considering complex multiscale time-frequency dictionaries.

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