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Linear Regression With a Sparse Parameter Vector

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2 Author(s)
Larsson, E.G. ; Sch. of Electr. Eng., R. Inst. of Technol., Stockholm ; Selen, Y.

We consider linear regression under a model where the parameter vector is known to be sparse. Using a Bayesian framework, we derive the minimum mean-square error (MMSE) estimate of the parameter vector and a computationally efficient approximation of it. We also derive an empirical-Bayesian version of the estimator, which does not need any a priori information, nor does it need the selection of any user parameters. As a byproduct, we obtain a powerful model ("basis") selection tool for sparse models. The performance and robustness of our new estimators are illustrated via numerical examples

Published in:

Signal Processing, IEEE Transactions on  (Volume:55 ,  Issue: 2 )