In the blind equalization problem, one can recently observe that the sought unknown filter can be performed from the sole knowledge of second order statistics of the received signal. According to this fact, a powerful algorithm which is the socalled subspace method has been developed. The subspace method was previously described in rational spaces framework which seemed to be unappropriated. In...

By analyzing how one obtains the Stone space of the reduced product of an indexed collection of Boolean algebras from the Stone spaces of those algebras, we derive a topological construction, the "reduced coproduct", which makes sense for indexed collections of arbitrary Tichonov spaces. When the filter in question is an ultrafilter, we show how the "ultracoproduct" can be obtained from the usu...

In this paper, a new nonlinear wavelet identification structure is proposed for high noise resistive soft sensors. This method uses proposedPolynomial Nonlinear Auto Regressive Exogenous Model, which can be solved with linear Gaussian Least Square Method, alongside the Averaging Wavelet Method (AWM) filter. AWM uses the approximation spaces for analyzing the signals and reduce the noise by a me...

We study the optimal input-output stabilization of discrete time-invariant linear systems in Hilbert spaces by output injection. We show that a necessary and sufficient condition for this problem to be solvable is that the transfer function has a left factorization over H-infinity. Another equivalent condition is that the filter Riccati equation (of an arbitrary realization) has a solution (in ...

We study the optimal input-output stabilization of discrete time-invariant linear systems in Hilbert spaces by output injection. We show that a necessary and sufficient condition for this problem to be solvable is that the transfer function has a left factorization over H-infinity. Another equivalent condition is that the filter Riccati equation (of an arbitrary realization) has a solution (in ...

In this paper, we propose an original approach for sequential non-parametric density estimation defined in high-dimensional state spaces using the particle filtering framework. By exploiting conditional independences in the state space, we propose to swap independent subparticle sets to generate new sets that better sample this space. We integrate this approach into two versions of particle fil...

In this paper, we propose an original approach for sequential non-parametric density estimation defined in highdimensional state spaces using the particle filtering framework. By exploiting conditional independences in the state space, we propose to swap independent particle subsets to generate new sets that better sample this space. We integrate this approach into two versions of particle filt...

This is a survey paper on estimates for the topological degree and related topics which cover from characterizations of Sobolev spaces to Jacobian determinant, and non-local filter problems in Image Processing. These results are obtained jointly with Bourgain and Brezis. Several open questions are mentioned.

This paper introduces the effective speckle reduction of synthetic aperture radar (SAR) images using inner product spaces in undecimated wavelet domain. There are two major areas in projection onto span algorithm where improvement can be made. First is the use of undecimated wavelet transformation instead of discrete wavelet transformation. And second area is the use of smoothing filter namely ...