Fundamentals of statistical signal processing: estimation theory
Fundamentals of statistical signal processing: estimation theory
Multi-frame compression: theory and design
Signal Processing - Special section on signal processing technologies for short burst wireless communications
Asymptotic achievability of the Cramér-Rao bound for noisy compressive sampling
IEEE Transactions on Signal Processing
Compressed sensing of analog signals in shift-invariant spaces
IEEE Transactions on Signal Processing
Robust recovery of signals from a structured union of subspaces
IEEE Transactions on Information Theory
Time-delay estimation from low-rate samples: a union of subspaces approach
IEEE Transactions on Signal Processing
Coherence-based performance guarantees for estimating a sparse vector under random noise
IEEE Transactions on Signal Processing
Just relax: convex programming methods for identifying sparse signals in noise
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Image Denoising Via Sparse and Redundant Representations Over Learned Dictionaries
IEEE Transactions on Image Processing
Coherence-based performance guarantees for estimating a sparse vector under random noise
IEEE Transactions on Signal Processing
| Hi-index | 35.69 |
The goal of this contribution is to characterize the best achievable mean-squared error (MSE) in estimating a sparse deterministic parameter from measurements corrupted by Gaussian noise. To this end, an appropriate definition of bias in the sparse setting is developed, and the constrained Cramér-Rao bound (CRB) is obtained. This bound is shown to equal the CRB of an estimator with knowledge of the support set, for almost all feasible parameter values. Consequently, in the unbiased case, our bound is identical to the MSE of the oracle estimator. Combined with the fact that the CRB is achieved at high signal-to-noise ratios signal-to-noise ratio (SNRs) by the maximum likelihood technique, our result provides a new interpretation for the common practice of using the oracle estimator as a gold standard against which practical approaches are compared.