Efficient Computation of MSE Lower Bounds via Matching Pursuit

Abstract

The classes of large-error bounds that are based on the covariance inequality, in both Bayesian and non-Bayesian approaches, are characterized as projection-based bounds. Tightening of bounds in these classes involves high computational complexity due to multidimensional optimization procedure. Consequently, projection-based large-error bounds have little popularity, while small-error bounds are frequently preferred, although they are not necessarily tight. In this letter, we first introduce a unified formulation for Bayesian and non-Bayesian projection-based lower bounds and set a general framework, which allows for their approximation via a greedy-based method. This framework is then used to propose the use of optimized orthogonal matching pursuit approach for computing projection-based large-error bounds. We analyze the complexity of the proposed algorithm and show that it is significantly lower than the complexity of the conventional approach. Finally, we apply the algorithm for the problem of multitone estimation and show that for fixed computational resources, the Weiss–Weinstein bound implemented with the proposed algorithm, provides a tighter bound compared to conventional approaches.