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Source estimation from several noisy observations, each of which are corrupted with additive independent noise is arguably among the most fundamental problems in estimation theory. Estimating multiple independent sources, corrupted by identical noise realization is important in various communication applications. It is well-known for both cases that when all sources and noises are Gaussian, linear...
When is optimal estimation linear? It is well known that when a Gaussian source is contaminated with Gaussian noise, a linear estimator minimizes the mean square estimation error. This paper analyzes, more generally, the conditions for linearity of optimal estimators. Given a noise (or source) distribution, and a specified signal-to-noise ratio (SNR), we derive conditions for existence and uniqueness...
It is well-known that, when a multivariate Gaussian source is contaminated with Gaussian noise, a linear estimator minimizes the mean square estimation error, irrespective of the covariance matrices of both source and noise. This paper analyzes the conditions for linearity of optimal estimators for general source and noise distributions over vector spaces. Given a noise (or source) distribution, we...
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