Team

Signal Images Physique

Team manager : Jocelyn CHANUSSOT, Cornel IOANA

Research Areas

The analysis of transient phenomena represents today an axis in full expansion, both from an application standpoint and from the theoretical point of view. On the theoretical side, transient signal characterization poses great challenges issued mainly from their representation with a reduced number of samples. This fact restricts the use of techniques developed in the context of quasi-stationary signals because these techniques are not necessarily adapted for the representation of signals characterized by a reduced number of points. Traditionally, the multiresolution analysis provides interesting elements for transient detection, but the results are influenced by the choice of the adequate wavelet, as well as adequate resolution levels. In this context, the main contribution of this axis will be concentrated around the construction of new representation spaces for transient signals. This will rely on the fusion signal and system parameters. More precisely, two research directions will be jointly addressed.

The first concerns a new approach for transient signal analysis and emerges from the analysis of complex functions. In this approach, regardless of its origin, a transient signal exhibits phase singularities that will be characterized analytically using the bias of Cauchy's Integral Theory. The strong point of the idea is describing the phase singularities via complex plane integration using the signal's samples. Existing research to this day show the benefits of this approach (generally names complex time distribution). However, certain issues must be solved in order to guarantee its generic character, especially the analytic continuation problem that is difficult to solve and requires an extensive research work. More precisely, the complex time signal samples are obtained using the Fourier decomposition which proves insufficient. Other decomposition basis will be considered in order to guarantee a precise and robust description of phase singularities. Another contribution to this axis will be the multicomponent context.

The second axis is represented by a systemic vision of transient signal occurrence. Specifically, staring from the general remark that a transint represents a change in the system's state, the system's evolution analysis (via phase diagrams for example) will represent an additional information regarding the generation of transient phenomena. Considering this information could, on one hand, contribute to complex plane transient characterization (first axis), as inferring system evolution notions allows the optimization of transient representation issued form the phase singularities. On the other hand, this systemic view, backed up by an adequate representation of the phase, can lead to a generic methodology concerning a large class of application.

The two axis provide new transient analysis spaces, highlighting the specific phase recurrences for each studied transient phenomena. The adaptation and study of these representations for acoustic and electromagnetic transient classes will be considered.

The specific mission of this research axis is to develop a general model adapted for the analysis of a large class of signals issued from various natural phenomena. This model relies on the analytic characterization of the signal's instantaneous phase law using slow varying time - frequency functions, separated by transients (i.e. phase singularities). In order to fine tune this model, we define the general ambiguity function. This concept reiterates firstly on the slow varying components using polynomial phase functions. The polynomial coefficients are estimated using the high order ambiguity function. Regarding this aspect, an important task will be carried out in order to render this concept more robust to interference. An interesting method will be the delay axis warping.

The second generalized ambiguity function component will be related to the analysis of phase law components. The general methodology relies on the complex time distributions that try to characterize the transients in the complex plane (based on Cuachy's theory).An initial application for the generalized ambiguity function will be the construction of waveforms robust to the Doppler Effect. This application concept, in relation with current and future collaborations with Arizona State University/SenSip, consists in evaluating the deformations induced by the Doppler effect specific to each propagation path done by the generalized ambiguity function components warping. The innovation part is the generalization, via the Mellin transform. This ensures a good estimation and consequently a good robustness of the emitted waveform in a given dynamic context. Another aspect related to the generalized ambiguity function is represented by its use in the analysis of phase singularities (current and future collaboration with EDF R&D). Finally, we envision using the concept of the generalized ambiguity function in a passive configuration for analyzing signals coming from marine mammals.

On the theoretical side, the innovation is represented by the tools for representing generalized ambiguity function signals: high order ambiguity function and complex time distributions. This will allow for a sparse representation of different natural signals.

The analysis of geophysical signals by their transient nature is a rich research subject, recurrent in the laboratory, especially inside the SIGMAPHY team. During the last 5 years, this theme was oriented towards the multicomponent data and towards adapting the wave separating techniques to this type of transient signals. In this directions, we work to adapt and apply fast source separation techniques for transient multi component signals, because the latest developments in terms of source separation in the time or frequency domain for an under determined and/or sparse problem appear promising. We intend to show that these new techniques can be particularly interesting for polarized transients characterization and analysis and for sparse events source separation (the separation of thermometric sources for example). Simultaneously, a study is directed towards highlighting the capability of these separation techniques in underground imaging for foundation reconnaissance. The validation of these techniques will allow us to refine the direct problems related to underground imaging.

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