—We address the problem of linear minimum meansquared error (LMMSE) estimation under constraints on the lter or the estimated signal. We develop a general formula that leads to closed form solutions for a wide class of constrained LMMSE problems. The results are applicable to both nite dimensional problems as well as to the Wiener ltering setup, in which in nitely-many measurements are availabl...

Non-Bayesian parameter estimation under parametric constraints is encountered in numerous applications in signal processing, communications, and control. Mean-squared-error (MSE) lower bounds are widely used as performance benchmarks and for system design. The well-known constrained Cramér-Rao bound (CCRB) is a lower bound on the MSE of estimators that satisfy some unbiasedness conditions. In m...

The Weiss–Weinstein bound (WWB) provides a lower limit on the mean-squared error (MSE) achievable by an estimator of an unknown random parameter. In this correspondence, it is shown that some previously proposed simplified versions of the bound do not always hold for constrained parameters, i.e., parameters whose distribution has finite support. These simplifications can produce results which a...

The paper aims at contrasting two different ways of incorporating a-priori information in parameter estimation, i.e. hard-constrained and soft-constrained estimation. Hardconstrained estimation can be interpreted, in the Bayesian framework, as Maximum A-posteriori Probability (MAP) estimation with uniform prior distribution over the constraining set, and amounts to a constrained Least-Squares (...

Constrained adaptive filtering algorithms inculding constrained least mean square (CLMS), constrained affine projection (CAP) and constrained recursive least squares (CRLS) have been extensively studied in many applications. Most existing constrained adaptive filtering algorithms are developed under mean square error (MSE) criterion, which is an ideal optimality criterion under Gaussian noises....

In recent years, many approaches to differentially privately publish histograms have been proposed. Several approaches rely on constructing tree structures in order to decrease the error when answer large range queries. In this paper, we examine the factors affecting the accuracy of hierarchical approaches by studying the mean squared error (MSE) when answering range queries. We start with one-...

It is well known that compression of very large images (e.g. medical imaging, microscopy, satellite images) requires stripebased or tiling processing. In some applications, the transmission of compressed data is performed through a rate constrained channel. Thus, rate allocation and control procedures have to be used to fit the channel characteristics. On the contrary, most of applications requ...

We consider distributed estimation of a Gaussian source in a heterogenous bandwidth constrained sensor network, where the source is corrupted by independent multiplicative and additive observation noises, with incomplete statistical knowledge of the multiplicative noise. For multi-bit quantizers, we derive the closed-form mean-square-error (MSE) expression for the linear minimum MSE (LMMSE) est...