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S. Schmutzhard, A. Jung, F. Hlawatsch:
"Minimum variance estimation for the sparse signal in noise model";
Talk: IEEE International Symposium on Information Theory (ISIT), St.Petersburg, Russische Föderation; 07-31-2011 - 08-05-2011; in: "IEEE Conf. Proceedings", (2011), 124 - 128.

We consider estimation of a sparse parameter vector from measurements corrupted by white Gaussian noise. Using the framework of reproducing kernel Hilbert spaces, we derive closed- form expressions of the Barankin bound, i.e., of the minimum locally achievable variance of any estimator with a prescribed bias function, including the unbiased case. We also derive the locally minimum variance (LMV) estimator that achieves the minimum variance, and a necessary and sufficient condition on the pre- scribed bias function for the existence of finite-variance estimators and, simultaneously, of the LMV estimator. Finally, we present a numerical comparison of the variance of the hard-thresholding estimator with the corresponding minimum achievable variance.

Sparsity, denoising, reproducing kernel Hilbert space, RKHS, Barankin bound, minimum variance estimation, unbiased estimation

http://publik.tuwien.ac.at/files/PubDat_203999.pdf