Efficient Wiener filtering without preconditioning

We present a new approach to calculate the Wiener filter solution of general data sets. It is trivial to implement, flexible, numerically absolutely stable, and guaranteed to converge. Most importantly, it does not require an ingenious choice of preconditioner to work well. The method is capable of taking into account inhomogeneous noise distributions and arbitrary mask geometries. It iteratively builds up the signal reconstruction by means of a messenger field, introduced to mediate between the different preferred bases in which signal and noise properties can be specified most conveniently. Using cosmic microwave background (CMB) radiation data as a showcase, we demonstrate the capabilities of our scheme by computing Wiener filtered WMAP7 temperature and polarization maps at full resolution for the first time. We show how the algorithm can be modified to synthesize fluctuation maps, which, combined with the Wiener filter solution, result in unbiased constrained signal realizations, consistent with the observations. The algorithm performs well even on simulated CMB maps with Planck resolution and dynamic range.Comment: 5 pages, 2 figures. Submitted to Astronomy and Astrophysics. Replaced to match published versio

Cold Flows and Large Scale Tides

Several studies have indicated that the local cosmic velocity field is rather cold, in particular in the regions outside the massive, virialized clusters of galaxies. If our local cosmic environment is taken to be a representative volume of the Universe, the repercussion of this finding is that either we live in a low-$\Omega$ Universe and/or that the galaxy distribution is a biased reflection of the underlying mass distribution. Otherwise, the pronounced nature of the observed galaxy distribution would be irreconcilable with the relatively quiet flow of the galaxies. Here we propose a different view on this cosmic dilemma, stressing the fact that our cosmic neighbourhood embodies a region of rather particular dynamical properties, and henceforth we are apt to infer flawed conclusions with respect to the global Universe. Suspended between two huge mass concentrations, the Great Attractor region and the Perseus-Pisces chain, we find ourselves in a region of relatively low density yet with a very strong tidal shear. This tidal field induces a local velocity field with a significant large-scale bulk flow but a low small-scale velocity dispersion. By means of constrained realizations of our local Universe, consisting of Wiener-filtered reconstructions inferred from the Mark III catalogue of galaxy peculiar velocities in combination with appropriate spectrally determined fluctuations, we study the implications for our local velocity field. We find that we live near a local peak in the distribution of the cosmic Mach number, $|v_{bulk}|/\sigma_v$, and that our local cosmic niche is located in the tail of the Mach number distribution function.Comment: Contribution to `Evolution of Large Scale Structure', MPA/ESO Conference, August 1997, eds. A. Banday & R. Sheth, Twin Press. 5 pages of LaTeX including 3 postscript figures. Uses tp.sty and psfi

Blind adaptive constrained reduced-rank parameter estimation based on constant modulus design for CDMA interference suppression

This paper proposes a multistage decomposition for blind adaptive parameter estimation in the Krylov subspace with the code-constrained constant modulus (CCM) design criterion. Based on constrained optimization of the constant modulus cost function and utilizing the Lanczos algorithm and Arnoldi-like iterations, a multistage decomposition is developed for blind parameter estimation. A family of computationally efficient blind adaptive reduced-rank stochastic gradient (SG) and recursive least squares (RLS) type algorithms along with an automatic rank selection procedure are also devised and evaluated against existing methods. An analysis of the convergence properties of the method is carried out and convergence conditions for the reduced-rank adaptive algorithms are established. Simulation results consider the application of the proposed techniques to the suppression of multiaccess and intersymbol interference in DS-CDMA systems

Coherent Quantum Filtering for Physically Realizable Linear Quantum Plants

The paper is concerned with a problem of coherent (measurement-free) filtering for physically realizable (PR) linear quantum plants. The state variables of such systems satisfy canonical commutation relations and are governed by linear quantum stochastic differential equations, dynamically equivalent to those of an open quantum harmonic oscillator. The problem is to design another PR quantum system, connected unilaterally to the output of the plant and playing the role of a quantum filter, so as to minimize a mean square discrepancy between the dynamic variables of the plant and the output of the filter. This coherent quantum filtering (CQF) formulation is a simplified feedback-free version of the coherent quantum LQG control problem which remains open despite recent studies. The CQF problem is transformed into a constrained covariance control problem which is treated by using the Frechet differentiation of an appropriate Lagrange function with respect to the matrices of the filter.Comment: 14 pages, 1 figure, submitted to ECC 201