Identification of time-varying systems using multiresolution wavelet models

Identification of linear and nonlinear time-varying systems is investigated and a new wavelet model identification algorithm is introduced. By expanding each time-varying coefficient using a multiresolution wavelet expansion, the time-varying problem is reduced to a time invariant problem and the identification reduces to regressor selection and parameter estimation. Several examples are included to illustrate the application of the new algorithm

Multiscale identification of spatio-temporal dynamical systems using a wavelet multiresolution analysis

In this paper, a new algorithm for the multiscale identification of spatio-temporal dynamical systems is derived. It is shown that the input and output observations can be represented in a multiscale manner based on a wavelet multiresolution analysis. The system dynamics at some specific scale of interest can then be identified using an orthogonal forward leastsquares algorithm. This model can then be converted between different scales to produce predictions of the system outputs at different scales. The method can be applied to both multiscale and conventional spatio-temporal dynamical systems. For multiscale systems, the method can generate a parsimonious and effective model at a coarser scale while considering the effects from finer scales. Additionally, the proposed method can be used to improve the performance of the identification when measurements are noisy. Numerical examples are provided to demonstrate the application of the proposed new approach

Astronomical Data Analysis and Sparsity: from Wavelets to Compressed Sensing

Wavelets have been used extensively for several years now in astronomy for many purposes, ranging from data filtering and deconvolution, to star and galaxy detection or cosmic ray removal. More recent sparse representations such ridgelets or curvelets have also been proposed for the detection of anisotropic features such cosmic strings in the cosmic microwave background. We review in this paper a range of methods based on sparsity that have been proposed for astronomical data analysis. We also discuss what is the impact of Compressed Sensing, the new sampling theory, in astronomy for collecting the data, transferring them to the earth or reconstructing an image from incomplete measurements.Comment: Submitted. Full paper will figures available at http://jstarck.free.fr/IEEE09_SparseAstro.pd

Identification of partial differential equation models for a class of multiscale spatio-temporal dynamical systems

In this paper, the identification of a class of multiscale spatio-temporal dynamical sys-tems, which incorporate multiple spatial scales, from observations is studied. The proposed approach is a combination of Adams integration and an orthogonal least squares algorithm, in which the multiscale operators are expanded, using polynomials as basis functions, and the spatial derivatives are estimated by finite difference methods. The coefficients of the polynomials can vary with respect to the space domain to represent the feature of multiple scales involved in the system dynamics and are approximated using a B-spline wavelet multi-resolution analysis (MRA). The resulting identified models of the spatio-temporal evolution form a system of partial differential equations with different spatial scales. Examples are provided to demonstrate the efficiency of the proposed method

A new class of multiscale lattice cell (MLC) models for spatio-temporal evolutionary image representation

Spatio-temporal evolutionary (STE) images are a class of complex dynamical systems that evolve over both space and time. With increased interest in the investigation of nonlinear complex phenomena, especially spatio-temporal behaviour governed by evolutionary laws that are dependent on both spatial and temporal dimensions, there has been an increased need to investigate model identification methods for this class of complex systems. Compared with pure temporal processes, the identification of spatio-temporal models from observed images is much more difficult and quite challenging. Starting with an assumption that there is no apriori information about the true model but only observed data are available, this study introduces a new class of multiscale lattice cell (MLC) models to represent the rules of the associated spatio-temporal evolutionary system. An application to a chemical reaction exhibiting a spatio-temporal evolutionary behaviour, is investigated to demonstrate the new modelling framework

Locally adaptive image denoising by a statistical multiresolution criterion

We demonstrate how one can choose the smoothing parameter in image denoising by a statistical multiresolution criterion, both globally and locally. Using inhomogeneous diffusion and total variation regularization as examples for localized regularization schemes, we present an efficient method for locally adaptive image denoising. As expected, the smoothing parameter serves as an edge detector in this framework. Numerical examples illustrate the usefulness of our approach. We also present an application in confocal microscopy

A review of RFI mitigation techniques in microwave radiometry

Radio frequency interference (RFI) is a well-known problem in microwave radiometry (MWR). Any undesired signal overlapping the MWR protected frequency bands introduces a bias in the measurements, which can corrupt the retrieved geophysical parameters. This paper presents a literature review of RFI detection and mitigation techniques for microwave radiometry from space. The reviewed techniques are divided between real aperture and aperture synthesis. A discussion and assessment of the application of RFI mitigation techniques is presented for each type of radiometer.Peer ReviewedPostprint (published version