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.

• Type: Journal
• Year: 2011
• Where: CORR
• Authors: Tomer Michaeli, Daniel Sigalov, Yonina C. Eldar
• Keywords: Clear Computational Advantage, CORR 2011, Education, Estimators, Second-order Moments