Abstract-Synthetic aperture radar (SAR) images are disturbed by a multiplicative noise depending on the signal (the ground reflectivity) due to the radar wave coherence. Images have a strong variability from one pixel to another reducing essentially the efficiency of the algorithms of detection and classification. In this study, we propose to filter this noise with a multiresolution analysis of the image. The wavelet coefficient of the reflectivity is estimated with a Bayesian model, maximizing the a posteriori probability density function. The different probability density function are modeled with the Pearson system of distributions. The resulting filter combines the classical adaptive approach with wavelet decomposition where the local variance of high-frequency images is used in order to segment and filter wavelet coefficients.Index Terms-Adaptive filtering, synthetic aperture radar (SAR), speckle, wavelet.

Processing simultaneous bathymetry and backscatter data, multibeam echosounders (MBESs) show promising abilities for remote seafloor characterization. High-frequency MBESs provide a good horizontal resolution, making it possible to distinguish fine details at the water-seafloor interface. However, in order to accurately measure the seafloor influence on the backscattered energy, the recorded sonar data must first be processed and cleared of various artifacts generated by the sonar system itself. Such a preprocessing correction procedure along with the assessment of its validity limits is presented here and applied to a 95-kHz MBES (Simrad EM1000) data set. Beam pattern effects, uneven array sensitivities, and inaccurate normalization of the ensonified area are removed to make possible further quantitative analysis of the corrected backscatter images. Unlike low-frequency data where the average backscattered energy proves to be the only relevant feature for discriminating the nature of the seafloor, high-frequency MBES backscatter images exhibit visible texture patterns. This additional information involves different statistical distributions of the backscattered amplitudes obtained from various seafloor types. Non-Rayleigh statistics such as-distributions are shown to fit correctly the skewed distributions of experimental high-frequency data. Apart from the effect of the seafloor micro-roughness, a statistical model makes clear a correlation between the amplitude statistical distributions and the signal incidence angle made available by MBES bathymetric abilities. Moreover, the model enhances the effect of the first derivative of the seafloor backscattering strength upon statistical distributions near the nadir and at high incidence angles. The whole correction and analysis process is finally applied to a Simrad EM 1000 data set.

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In order to improve the resolution of seismic images, a blind deconvolution of seismic traces is necessary, since the source wavelet is not known and cannot be considered as a stationary signal. The reflectivity sequence is modeled as a Gaussian mixture, depending on three parameters (high and low reflector variances and reflector density), on the wavelet impulse response, and on the observation noise variance. These parameters are unknown and must be estimated from the recorded trace, which is the reflectivity convolved with the wavelet, plus noise. Two methods are compared in this paper for the parameter estimation. Since we are considering an incomplete data problem, we first consider maximum likelihood estimation by means of a stochastic expectation maximization (SEM) method. Alternatively, proper prior distributions can be specified for all unknown quantities. Then, a Bayesian strategy is applied, based on a Monte Carlo Markov Chain (MCMC) method. Having estimated the parameters, one can proceed to the deconvolution. A maximum posterior mode (MPM) criterion is optimized by means of an MCMC method. The deconvolution capability of these procedures is checked first on synthetic signals and then on the seismic data of the IFREMER ESSR4 campaign, where the wavelet duration blurs the reflectivity, and on the SMAVH high-resolution marine seismic data.

A method is presented for automatic analysis of the P-wave, based on lead II of a 12-lead standard ECG, in resting conditions during a routine examination for the detection of patients prone to atrial fibrillation (AF), one of the most prevalent arrhythmias. First, the P-wave was delineated, and this was achieved in two steps: the detection of the QRS complexes for ECG segmentation, using a wavelet analysis method, and a hidden Markov model to represent one beat of the signal for P-wave isolation. Then, a set of parameters to detect patients prone to AF was calculated from the P-wave. The detection efficiency was validated on an ECG database of 145 patients, including a control group of 63 people and a study group of 82 patients with documented AF. A discriminant analysis was applied, and the results obtained showed a specificity and a sensitivity between 65% and 70%.