This paper presents reduced-rank linearly constrained minimum variance (LCMV) beamforming algorithms based on joint iterative optimization of filters. The proposed reduced-rank scheme is based on a constrained joint iterative optimization of filters according to the minimum variance criterion. The proposed optimization procedure adjusts the parameters of a projection matrix and an adaptive redu...

This chapter presents reduced-rank linearly constrained minimum variance (LCMV) algorithms based on the concept of joint iterative optimization of parameters. The proposed reduced-rank scheme is based on a constrained robust joint iterative optimization (RJIO) of parameters according to the minimum variance criterion. The robust optimization procedure adjusts the parameters of a rank-reduction ...

We consider the problem of approximating an affinely structured matrix, for example a Hankel matrix, by a low-rank matrix with the same structure. This problem occurs in system identification, signal processing and computer algebra, among others. We impose the low-rank by modeling the approximation as a product of two factors with reduced dimension. The structure of the low-rank model is enforc...

We consider the problem of approximating an affinely structured matrix, for example a Hankel matrix, by a low-rank matrix with the same structure. This problem occurs in system identification, signal processing and computer algebra, among others. We impose the low-rank by modeling the approximation as a product of two factors with reduced dimension. The structure of the low-rank model is enforc...

Using a non-uniformly distributed aperture radar system for forming a SAR image will result in data correlations between the SAR image resolution cells. Thus, this requires that a more robust filter than the Matched Filter, i.e. the MMSE or Wiener Filter to be used in the receiver processing. As the Wiener Filter involves a computationally expensive matrix inverse operation, it can be avoided b...

It is proved that, for the following classes of groups, ?, the reduced group C-algebra C (?) has stable rank 1: (i) hyperbolic groups which are either torsion{free and non{elementary or which are cocom-pact lattices in a real, noncompact, simple, connected Lie group of real rank 1 having trivial center; (ii) amalgamated free products of groups, ? = G 1 H G 2 , where H is nite and there is g 0 2...

This paper proposes a new approach to linearly-constrained adaptive filtering, where successive Householder transformations are incorporated in the algorithm update equation in order to reduce computational complexity and coefficienterror norm. We show the derivation of two new algorithms, namely the unnormalized and the normalized Householdertransform constrained LMS algorithms (HCLMS and NHCL...

Let V ∈ R be a nonnegative matrix. The nonnegative matrix factorization (NNMF) problem consists of finding nonnegative matrix factors W ∈ R and H ∈ R such that V ≈ WH. Lee and Seung proposed two algorithms which find nonnegative W and H such that ‖V −WH‖F is minimized. After examining the case in which r = 1 about which a complete characterization of the solution is possible, we consider the ca...

High-dimensional time-series data from a wide variety of domains, such as neuroscience, are being generated every day. Fitting statistical models to such data, to enable parameter estimation and time-series prediction, is an important computational primitive. Existing methods, however, are unable to cope with the high-dimensional nature of these data, due to both computational and statistical r...

A selection of these reports is available in PostScript form at the Faculty's anonymous ftp-Abstract The Kalman lter algorithm can be used for many data assimilation problems. For large systems, that arise from discretizing partial diierential equations, the standard algorithm has huge computational and storage requirements. This makes direct use infeasible for many applications. In addition nu...