Thursday, March 15, 2012

Sparse Signal Reconstruction from Quantized Noisy Measurements via GEM Hard Thresholding (and implementation)

Kun Qiu just sent me the following

Hi, Igor,
Aleksandar and I recently have the work “Sparse signal reconstruction from quantized noisy measurements via GEM hard thresholding” accepted by IEEE Trans. Signal Processing. Our GEM hard thresholding method reconstructs sparse signals from quantized measurements. The paper and the Matlab software package are posted at
Could you please post the above link of our work on the Nuit Blanche?

Sure Kun, not only will I post it but it will precedence over other posts because of the link to the implementation. Thanks! The paper is: Sparse Signal Reconstruction from Quantized Noisy Measurements via GEM Hard Thresholding by Kun. Qiu and  Aleksandar Dogandžić. The abstract reads:

We develop a generalized expectation-maximization (GEM) algorithm for sparse signal reconstruction from quantized noisy mea- surements. The measurements follow an underdetermined linear model with sparse regression coefficients, corrupted by additive white Gaussian noise having unknown variance. These measurements are quantized into bins and only the bin indices are used for reconstruction. We treat the unquantized measurements as the missing data and propose a GEM iteration that aims at maximizing the likelihood function with respect to the unknown parameters. Under mild conditions, our GEM iteration yields a convergent monotonically non-decreasing likelihood function sequence and the Euclidean distance between two consecutive GEM signal iterates goes to zero as the number of iterations grows. We compare the proposed scheme with the state-of-the-art convex relaxation method for quantized compressed sensing via numerical simulations.

The implementation is here.

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