Thursday, January 17, 2013

Compressed Sensing with Correlation Between Measurements and Noise - implementation -

Existing convex relaxation-based approaches to reconstruction in compressed sensing assume that noise in the measurements is independent of the measurements themselves. We consider the case of noise correlated with the compressed measurements and introduce a simple technique for improvement of compressed sensing reconstruction from such measurements.The technique is based on a linear model of the correlation of additive noise with the measurements. The modification of there construction algorithm based on this model is very simple and has negligible additional computational cost compared to standard reconstruction algorithms. The proposed technique reduces reconstruction error considerably in the case of correlated measurements and noise. Numerical experiments confirm the efficacy of the technique. The technique is demonstrated with application to low-rate quantization of compressed measurements, which is known to introduce correlated noise, and improvements in reconstruction error up to approximately 7 dB are observed for 1 bit/sample quantization.
The attendant code to replicate the figures is here.

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