In this work, we consider a radar system where the antenna elements are arbitrarily distributed in space with several hundred wavelengths away. We call such a radar system distributed aperture radar system. We assume that the system is operating in multi-pathing environment, such as an urban area. We present methods for designing clutter rejecting waveforms and for reconstruction of reflectivit...

In Krylov-based iterative methods, the computation of an orthonormal basis of the Krylov space is a key issue in the algorithms because the many scalar products are often a bottleneck in parallel distributed environments. Using GMRES, we present a comparison of four variants of the Gram-Schmidt process on distributed memory machines. Our experiments are carried on an application in astrophysics...

BACKGROUND Left ventricular size and shape are important for quantifying cardiac remodeling in response to cardiovascular disease. Geometric remodeling indices have been shown to have prognostic value in predicting adverse events in the clinical literature, but these often describe interrelated shape changes. We developed a novel method for deriving orthogonal remodeling components directly fro...

We characterize the class of probability measures for which the multiplicative renormalization method can be applied for the function h(x) = 1 √ 1−x to obtain orthogonal polynomials. It turns out that this class consists of only uniform probability measures on intervals and probability measures being supported by one or two points. 1. Multiplicative Renormalization Method Let μ be a probability...

Let there be given a probability measure μ on the unit circle T of the complex plane and consider the inner product induced by μ. In this paper we consider the problem of orthogonalizing a sequence of monomials {zk}k, for a certain order of the rk ∈ Z, by means of the Gram-Schmidt orthogonalization process. This leads to a basis of orthonormal Laurent polynomials {ψk}k. We show that the matrix ...

Constrained orthogonal polynomials have been recently introduced in the study of the HohenbergKohn functional to provide basis functions satisfying particle number conservation for an expansion of the particle density. More generally, we define block orthogonal (BO) polynomials which are orthogonal, with respect to a first Euclidean inner product, to a given i-dimensional subspace Ei of polynom...

The standard ratio of spatial resolution between bands for high resolution satellites is 1:4, which is typical when combining images obtained from the same sensor. However, the cost of simultaneously purchasing a set of panchromatic and multispectral images is still relatively high. There is therefore a need to develop methods of data fusion of very high resolution panchromatic imagery with low...