For ECG interpretation, the detection and delineation of P and T waves are challenging tasks. This paper proposes sequential Bayesian methods for simultaneous detection, threshold-free delineation, and waveform estimation of P and T waves on a beat-to-beat basis. By contrast to state-of-the-art methods that process multiple-beat signal blocks, the proposed Bayesian methods account for beat-to-beat waveform variations by sequentially estimating the waveforms for each beat. Our methods are based on Bayesian signal models that take into account previous beats as prior information. To estimate the unknown parameters of these Bayesian models, we first propose a block Gibbs sampler that exhibits fast convergence in spite of the strong local dependencies in the ECG signal. Then, in order to take into account all the information contained in the past rather than considering only one previous beat, a sequential Monte Carlo method is presented, with a marginalized particle filter that efficiently estimates the unknown parameters of the dynamic model. Both methods are evaluated on the annotated QT database and observed to achieve significant improvements in detection rate and delineation accuracy compared to state-of-the-art methods, thus providing promising approaches for sequential P and T wave analysis.

The concept of delay/Doppler (DD) altimetry (DDA) has been under study since the mid-1990s, aiming at reducing the measurement noise and increasing the along-track resolution in comparison with the conventional pulse-limited altimetry. This paper introduces a new model for the mean backscattered power waveform acquired by a radar altimeter operating in synthetic aperture radar mode, as well as an associated least squares (LS) estimation algorithm. As in conventional altimetry (CA), the mean power can be expressed as the convolution of three terms: the flat surface impulse response (FSIR), the probability density function of the heights of the specular scatterers, and the time/frequency point target response of the radar. An important contribution of this paper is to derive an analytical formula for the FSIR associated with DDA. This analytical formula is obtained for a circular antenna pattern, no mispointing, no vertical speed effect, and a uniform scattering. The double convolution defining the mean echo power can then be computed numerically, resulting in a 2-D semi-analytical model called the DD map (DDM). This DDM depends on three altimetric parameters: the epoch, the sea surface wave height, and the amplitude. A multi-look model is obtained by summing all the reflected echoes from the same along-track surface location of interest after applying appropriate delay compensation (range migration) to align the DDM on the same reference. The second contribution of this paper concerns the estimation of the parameters associated with the multi-look semi-analytical model. An LS approach is investigated by means of the Levenberg–Marquardt algorithm. Simulations conducted on simulated altimetric waveforms allow the performance of the proposed estimation algorithm to be appreciated. The analysis of Cryosat-2 waveforms shows an improvement in parameter estimation when compared to the CA.

Much attention has been recently devoted to the analysis of coastal altimetric waveforms. When approaching the coast, altimetric waveforms are sometimes corrupted by peaks caused by high reflective areas inside the illuminated land surfaces or by the modification of the sea state close to the shoreline. This paper introduces a new parametric model for these peaky altimetric waveforms. This model assumes that the received alti- metric waveform is the sum of a Brown echo and an asymmetric Gaussian peak. The asymmetric Gaussian peak is parameterized by a location, an amplitude, a width, and an asymmetry coefficient. A maximum-likelihood estimator is studied to estimate the Brown plus peak model parameters. The Cramér–Rao lower bounds of the model parameters are then derived providing minimum variances for any unbiased estimator, i.e., a reference in terms of estimation error. The performance of the proposed model and the resulting estimation strategy are evaluated via many simulations conducted on synthetic and real data. Results obtained in this paper show that the proposed model can be used to retrack efficiently standard oceanic Brown echoes as well as coastal echoes corrupted by symmetric or asymmetric Gaussian peaks. Thus, the Brown with Gaussian peak model is useful for analyzing altimetric measurements closer to the coast.

Detection and delineation of P- and T-waves are important issues in the analysis and interpretation of electrocardiogram (ECG) signals. This paper addresses this problem by using Bayesian inference to represent a priori relationships among ECG wave components. Based on the recently introduced partially collapsed Gibbs sampler principle, the wave delineation and estimation are conducted simultaneously by using a Bayesian algorithm combined with a Markov chain Monte Carlo method. This method exploits the strong local dependency of ECG signals. The proposed strategy is evaluated on the annotated QT database and compared to other classical algorithms. An important feature of this paper is that it allows not only for the detection of P- and T-wave peaks and boundaries, but also for the accurate estimation of waveforms for each analysis window. This can be useful for some ECG analysis that require wave morphology information.

This paper studies a new Bayesian unmixing algorithm for hyperspectral images. Each pixel of the image is modeled as a linear combination of so-called endmembers. These endmembers are supposed to be random in order to model uncertainties regarding their knowledge. More precisely, we model endmembers as Gaussian vectors whose means have been determined using an endmember extraction algorithm such as the famous N-finder (N-FINDR) or Vertex Component Analysis (VCA) algorithms. This paper proposes to estimate the mixture coefficients (referred to as abundances) using a Bayesian algorithm. Suitable priors are assigned to the abundances in order to satisfy positivity and additivity constraints whereas conjugate priors are chosen for the remaining parameters. A hybrid Gibbs sampler is then constructed to generate abundance and variance samples distributed according to the joint posterior of the abundances and noise variances. The performance of the proposed methodology is evaluated by comparison with other unmixing algorithms on synthetic and real images.

Hyperspectral images present some specific characteristics that should be used by an efficient compression system. In compression, wavelets have shown a good adaptability to a wide range of data, while being of reasonable complexity. Some wavelet-based compression algorithms have been successfully used for some hyperspectral space missions. This paper focuses on the optimization of a full wavelet compression system for hyperspectral images. Each step of the compression algorithm is studied and optimized. First, an algorithm to find the optimal 3-D wavelet decomposition in a rate-distortion sense is defined. Then, it is shown that a specific fixed decomposition has almost the same performance, while being more useful in terms of complexity issues. It is shown that this decomposition significantly improves the classical isotropic decomposition. One of the most useful properties of this fixed decomposition is that it allows the use of zero tree algorithms. Various tree structures, creating a relationship between coefficients, are compared. Two efficient compression methods based on zerotree coding (EZW and SPIHT) are adapted on this near-optimal decomposition with the best tree structure found. Performances are compared with the adaptation of JPEG 2000 for hyperspectral images on six different areas presenting different statistical properties.

It has already been shown that spectral estimation can be improved when applied to subband outputs of an adapted filterbank rather than to the original fullband signal. In the present paper, this procedure is applied jointly to a novel predictive autoregressive (AR) model. The model exploits time-shifting and is therefore referred to as time-shift AR (TSAR) model. Estimators are proposed for the unknown TS-AR parameters and the spectrum of the observed signal. The TS-AR model yields improved spectrum estimation by taking advantage of the correlation between subseries that arises after decimation. Simulation results on signals with continuous and line spectra that demonstrate the performance of the proposed method are provided.

Zerotrees of wavelet coefficients have shown a good adaptability for the compression of three-dimensional images. EZW, the original algorithm using zerotree, shows good performance and was successfully adapted to 3D image compression. This paper focuses on the adaptation of EZW for the compression of hyperspectral images. The subordinate pass is suppressed to remove the necessity to keep the significant pixels in memory. To compensate the loss due to this removal, signed binary digit representations are used to increase the efficiency of zerotrees. Contextual arithmetic coding with very limited contexts is also used. Finally, we show that this simplified version of 3D-EZW performs almost as well as the original one.

Hyperspectral data appear to be of a growing interest over the past few years. However, applications for hyperspectral data are still in their infancy as handling the significant size of the data presents a challenge for the user community. Efficient compression techniques are required, and lossy compression, specifically, will have a role to play, provided its impact on remote sensing applications remains insignificant. To assess the data quality, suitable distortion measures relevant to end-user applications are required. Quality criteria are also of a major interest for the conception and development of new sensors to define their requirements and specifications. This paper proposes a method to evaluate quality criteria in the context of hyperspectral images. The purpose is to provide quality criteria relevant to the impact of degradations on several classification applications. Different quality criteria are considered. Some are traditionnally used in image and video coding and are adapted here to hyperspectral images. Others are specific to hyperspectral data.We also propose the adaptation of two advanced criteria in the presence of different simulated degradations on AVIRIS hyperspectral images. Finally, five criteria are selected to give an accurate representation of the nature and the level of the degradation affecting hyperspectral data.

Satellite altimeters provide sea level measurements along satellite track. A mean profile based on the measurements averaged over a time period is then subtracted to estimate the sea level anomaly (SLA). In the spectral domain, SLA is characterized by a power spectral density of the form one over a power of the frequency where the power (the slope) is a parameter of great interest for ocean monitoring. However, this information lies in a narrow frequency band, located at very low frequencies, which calls for some specific spectral analysis methods. This paper studies a new parametric method based on an autoregressive model combined with a warping of the frequency scale (denoted as ARWARP). A statistical validation is proposed on simulated SLA signals, showing the performance of slope estimation using this ARWARP spectral estimator, compared to classical Fourier-based methods. Application to Sentinel-3 real data highlights the main advantage of the ARWARP model, making possible SLA slope estimation on a short signal segment, i.e., with a high spatial resolution.