Nonnegative signal reconstruction from compressive samples

via a difference map ECME algorithm

K. Qiu and A. Dogandžić

in *Proc. IEEE Workshop on Statistical Signal
Processing*, Nice, France, Jun. 2011, pp. 561-564.

**Abstract:
**We develop an approximate maximum
likelihood (ML) scheme for reconstructing nonnegative sparse signals
from compressive samples. The measurements follow an underdetermined
linear model, where the regression vector is modeled as the sum of
an unknown deterministic nonnegative signal with sparse transform
coefficients and a zero-mean white Gaussian component with an unknown variance. We first derive an expectation-conditional maximization either (ECME) algorithm that aims at maximizing the likelihood function with respect to the unknown parameters and then employ a difference map iteration to approximate the maximization (M) step of the ECME iteration. We compare the proposed and existing large-scale sparse signal reconstruction methods via numerical simulations and demonstrate that, by exploiting both the nonnegativity of the underlying image and the sparsity of its wavelet coefficients, we can reconstruct this image using a significantly smaller number of measurements than the existing methods.

**Matlab code:****
** The Matlab codes for the difference map ECME (DM-ECME) methods proposed in the paper. All the simulation results reported in the above paper can be reproduced from the package. Please read the enclosed readme file as well. If you use this code in your research and publications, please refer to this paper. The package is only tested on PCs running Windows and should be able to run on other platforms if the appropriate wavelet toolbox is downloaded from the Rice wavelet toolbox .

(Version 1.0, last updated Jun. 17, 2011)