Thursday, October 17, 2013

Implementation: EM-NN-AMP: Recovering Linearly-Constrained Non-Negative Sparse Signals

Following up on his recent ArXiv preprint (An Empirical-Bayes Approach to Recovering Linearly Constrained Non-Negative Sparse Signals) , Phil Schniter just sent me the following:

Hi Igor, 
My grad student Jeremy Vila created a nice website that summarizes our non-negative (NN) AMP work (which we call EM-NN-AMP) and presents concise Matlab examples of how to use it. Hopefully your readers will find it useful. The link is 

In particular, the examples presented there are:
1) Recovering a non-negative signal in noise. This also shows how to toggle between our three proposed algorithms: NNLS-AMP, EM-NNL-AMP, and EM-NNGM-AMP.
2) Recovering linearly constrained non-negative sparse signals in noise.
3) Recovering a NN satellite image from compressive linear (fast Hadamard) measurements.
4) Robustly recovering signals in the presence of outliers.
Phil Schniter

Thanks Phil  and Jeremy !

From the page:

Advantages of EM-NN-AMP
We highlight some of EM-NN-AMP's advantages below:
  • EM-NNL-AMP removes the need to hand tune for the NN LASSO problem.
  • State-of-the-art noiseless phase transitions of simplex-obeying sparse Dirichlet signals using EM-NNGM-AMP.
  • State-of-the-art noisy recovery of a NN image for all undersampling ratios using EM-NNGM-AMP.
  • Excellent performance on the portfolio optimization problem using the return-adjusted Markowitz mean-variance framework. When coupled with the additive white Laplacian noise model, performance improves further.
  • Very good complexity scaling with problem dimensions and can leverage fast operators such as FFTs.
Three tiny notes:

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