Title :
On unbiased estimation of sparse vectors corrupted by Gaussian noise
Author :
Jung, Alexander ; Ben-Haim, Zvika ; Hlawatsch, Franz ; Eldar, Yonina C.
Author_Institution :
Inst. of Commun. & Radio-Freq. Eng., Vienna Univ. of Technol., Vienna, Austria
Abstract :
We consider the estimation of a sparse parameter vector from measurements corrupted by white Gaussian noise. Our focus is on unbiased estimation as a setting under which the difficulty of the problem can be quantified analytically. We show that there are infinitely many unbiased estimators but none of them has uniformly minimum mean-squared error. We then provide lower and upper bounds on the Barankin bound, which describes the performance achievable by unbiased estimators. These bounds are used to predict the threshold region of practical estimators.
Keywords :
Gaussian noise; acoustic noise; estimation theory; mean square error methods; sparse matrices; Barankin bound; practical estimators; sparse parameter vector; unbiased estimation; uniformly minimum mean-squared error; white Gaussian noise; Contracts; Gaussian noise; Noise measurement; Noise reduction; Parameter estimation; Performance analysis; Radio frequency; Signal to noise ratio; Upper bound; Wireless communication; Barankin bound; Cramér-Rao bound; Unbiased estimation; denoising; sparsity;
Conference_Titel :
Acoustics Speech and Signal Processing (ICASSP), 2010 IEEE International Conference on
Conference_Location :
Dallas, TX
Print_ISBN :
978-1-4244-4295-9
Electronic_ISBN :
1520-6149
DOI :
10.1109/ICASSP.2010.5495781