Authors:
A. Dogandžić and K. Qiu
Reference:
in Proc. 43rd
Annu. Conf. Inform. Sci. Syst. , Baltimore, MD, Mar. 2009,
pp. 186-191.
Abstract:
We present an expansion-compression variance-component based method (ExCoV) for reconstructing sparse or compressible signals from noisy measurements. The measurements follow an underdetermined linear model, with noise covariance matrix known up to a constant. To impose sparse or compressible signal structure, we define high- and low-signal coefficients, where each high-signal coefficient is assigned its own variance, low-signal coefficients are assigned a common variance, and all the variance components are unknown. Our expansion-compression scheme approximately maximizes a generalized maximum likelihood (GML) criterion, providing an approximate GML estimate of the high-signal coefficient set and an empirical Bayesian estimate of the signal coefficients. We apply the proposed method to reconstruct signals from compressive samples, compare it with existing approaches, and demonstrate its performance via numerical simulations.
Paper (1.4 MB)
Matlab code (8 KB)
Here is the code for reproducing the results reported in this paper.
Please read the enclosed "Readme" file as well. If you use this code in your research and publications, please refer to this paper.
(Version 1.0)
Features of ExCoV:
ExCoV is automatic and does not need any convergence tolerance level or threshold. Therefore, using ExCoV is easy: just input
- the measurement column vector and
- the sensing matrix (number of measurements by the length of signal)
and ExCoV will do the rest. For more details on using ExCoV and running the demo, please refer to the readme file in the package.
ExCov performs particularly well (compared with competing approaches) in challenging scenarios where the noise is large or the number of measurements is small, see the numerical examples in the above paper.
We are currently working on large scale implemetations of ExCoV and will update this site when we are ready.
Illustrative Example:
The following videos show the reconstruction progress of our ExCoV algorithm. The sparse signal of length 512 contains 20 randomly placed binary spikes, taking values -1 and +1 with equal probability. We took 100 noisy measurements using a Gaussian sensing matrix with orthonormalized rows and zero-mean white Gaussian noise with variance 0.001.
The videos in the left and right panels are realizations of typical and atypical reconstructions performed by the ExCoV algorithm under the chosen simulation setup. The atypical reconstruction corresponds to a difficult case. The figure following the videos shows the signal estimates of various methods for the difficult case.
A twin page is available here.