Joint detection - estimation from time-scale and time-frequency designs.

Summary The work summarized in this thesis has developed two joint detection-estimation methods applying a Bernoulli-Gaussian deconvolution algorithm (dbg) after a study of the specificities of the representations that are the multiresolution analysis and the short term fourier transform (tfct). The first method realizes a dbg in a non-Gaussian environment. The use of multiresolution analysis is justified by the Gaussianizing effect induced by a linear filtering from the projections on each scale via the hole algorithm. A dbg algorithm is then applied on these scales. These different results are then merged thanks to the redundancy of information from one scale to another. We obtain a new version of the dbg algorithm as an alternative to the original one when the additive noise is non-Gaussian such as the poissononian noise for example. The 2nd method performs an instantaneous frequency estimation (fi). This one is based on a conjecture that gives the tfct a convolutional structure between a kernel (depending on the time-frequency atom (tf) used during the tfct computation) and tf attributes such as fi and group delays. The latter 2 are assumed to be composite point-continuous processes (chirps). This structure allows two dual convolutional models on each of the temporal and frequency marginals. After an initial step of identification of the tf kernel, we propose a 3-step procedure. Step 1 uses a goniometry function to detect the main tf angles of the signal. For each of these angles, we then have a tf atom adapted to the associated linear chirp and the convolutional model to consider. Step 2 consists in performing the dbg on each tfct. Step 3 allows to obtain the fi by merging the different results. This Bayesian formulation has allowed us to obtain a powerful method for estimating these frequencies, bringing a gain of about 10 db compared to classical methods.