to be expressible in closed form, the D-LMMSE ones are provably robust to communication or quantization noise and both are particularly simple to implement when the data model is linear-Gaussian. For decentralized tracking applications, distributed Kalman filtering and smoothing algorithms are derived for any

frames are similar to the current pixel one wishes to denoise. Thus, denoising by an averaging process can use many more pixels than just the ones on a single trajectory. This observation leads to use for movies a recently introduced denoising method, the NL-means algorithm. This static 3D algorithm

estimator) as input. Simulation results of a MIMO HSDPA system show that the tap-wise LMMSE estimator with instantaneous channel autocorrelation estimation yields performance gains of up to 0.85 dB over a correlation-based channel estimator. Even larger gains can be achieved with improved channel

in the superresolved signal. We also provide three efficient implementation schemes of the LMMSE estimate, one of which specialized for 1D applications. These methods constitute a natural generalization of several well known single-image recovery algorithms, such as spline interpolation, to the multichannel SR setting

in the superresolved signal. We also provide three efficient implementation schemes of the LMMSE estimate, one of which specialized for 1D applications. These methods constitute a natural generalization of several well known single-image recovery algorithms, such as spline interpolation, to the multichannel SR setting

isometric structure reduces the intersymbol interference generated within each relay. The gain over i.i.d. codes in terms of spectral efficiency is analyzed for both the LMMSE and the ML receivers under the assumption of frequency-flat quasi-static fading. In this setting, the spectral efficiency is a

Abstract—We address the problem of Bayesian estimation where the statistical relation between the signal and measure-ments is only partially known. We propose modeling partial Bayesian knowledge by using an auxiliary random vector called instrument. The statistical relations between the instrument and the signal, and between the instrument and the measurements, are known. However, the joint probability function of the signal and measurements is unknown. Two types of statistical relations are considered, corresponding to second-order moment and complete distribution function knowledge. We propose two approaches for estimation in partial knowledge scenarios. The first is based on replacing the orthogonality principle by an oblique counterpart, and is proven to coincide with the method of instrumental variables from statistics, although developed in a different context. The second is based on a worst-case design strategy and is shown to be advantageous in many aspects. We provide a thorough analysis showing in which situations each of the methods is preferable and propose a non-parametric method for approximating the estimators from a set of examples. Finally, we demonstrate our approach in the context of enhancement of facial images that have undergone unknown degradation and image zooming. Index Terms—Bayesian estimation, minimax regret, partial knowledge, instrumental variables, nonparametric regression. I.

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