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CORR
2011
Springer

Partially Linear Bayesian Estimation with Application to Sparse Approximations

8 years 10 days ago
Partially Linear Bayesian Estimation with Application to Sparse Approximations
—We address the problem of estimating a random vector X from two sets of measurements Y and Z, such that the estimator is linear in Y . We show that the partially linear minimum mean squared error (PLMMSE) estimator does not require knowing the joint distribution of X and Y in full, but rather only its second-order moments. This renders it of potential interest in various applications. We further show that the PLMMSE method is minimax-optimal among all estimators that solely depend on the second-order statistics of X and Y . Finally, we demonstrate our approach in the context of recovering a vector, which is sparse in a unitary dictionary, from two sets of noisy measurements. We show that in this setting PLMMSE estimation has a clear computational advantage, while its performance is comparable to state-of-the-art algorithms.
Tomer Michaeli, Daniel Sigalov, Yonina C. Eldar
Added 13 May 2011
Updated 13 May 2011
Type Journal
Year 2011
Where CORR
Authors Tomer Michaeli, Daniel Sigalov, Yonina C. Eldar
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