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 (PSD) whose slope in a log–log scale is a parameter of great interest for ocean monitoring. Estimation of this spectral slope is usually done through a cumulated periodogram using a large number of signal samples. The location and dates of the data induce the spatial and temporal resolution of the slope estimates. To improve this resolution, this article studies a new parametric method based on an autoregressive model combined with a warping of the frequency scale (denoted as ARWARP). This ARWARP model provides a PSD estimate, with a lower variance than the classical Fourier-based ones and is reliable in the case of a small sample number. To give a reference in the performance of the SLA slope estimation, the corresponding Cramér–Rao bound is derived. Then, rather than performing linear regression on the spectral estimates, a new estimator of the slope is suggested, based on a model fitting of the PSD. 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 and/or temporal resolution.

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 f-αwhere the slope α 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.

This paper proposes a new Bayesian strategy for the smooth estimation of altimetric parameters. The altimetric signal is assumed to be corrupted by a thermal and speckle noise distributed according to an independent and non-identically Gaussian distribution. We introduce a prior enforcing a smooth temporal evolution of the altimetric parameters which improves their physical interpretation. The posterior distribution of the resulting model is optimized using a gradient descent algorithm which allows us to compute the maximum a posteriori estimator of the unknown model parameters. This algorithm has a low computational cost that is suitable for real-time applications. The proposed Bayesian strategy and the corresponding estimation algorithm are evaluated using both synthetic and real data associated with conventional and delay/Doppler altimetry. The analysis of real Jason-2 and CryoSat-2 waveforms shows an improvement in parameter estimation when compared to state-of-the-art estimation algorithms.

This paper proposes a new Bayesian strategy for the estimation of smooth parameters from nonlinear models. The observed signal is assumed to be corrupted by an independent and non identically (colored) Gaussian distribution. A prior enforcing a smooth temporal evolution of the model parameters is considered. The joint posterior distribution of the unknown parameter vector is then derived. A Gibbs sampler coupled with a Hamiltonian Monte Carlo algorithm is proposed which allows samples distributed according to the posterior of interest to be generated and to estimate the unknown model parameters/hyperparameters. Simulations conducted with synthetic and real satellite altimetric data show the potential of the proposed Bayesian model and the corresponding estimation algorithm for nonlinear regression with smooth estimated parameters.

Delay/Doppler altimetry (DDA) aims at reducing the measurement noise and increasing the along-track resolution in comparison with conventional pulse-limited altimetry. In a previous paper, we have proposed a semi-analytical model for DDA, which considers some simplifications as the absence of mispointing antenna. This paper first proposes a new analytical expression for the flat surface impulse response (FSIR), considering antenna mispointing angles, a circular antenna pattern, no vertical speed effect, and uniform scattering. The 2-D delay/Doppler map is then obtained by a numerical computation of the convolution between the proposed analytical function, the probability density function of the heights of the specular scatterers, and the time/frequency point target response of the radar. The approximations used to obtain the semi-analytical model are analyzed, and the associated errors are quantified by analytical bounds for these errors. The second contribution of this paper concerns the estimation of the parameters associated with the multilook semi-analytical model. Two estimation strategies based on the least squares procedure are proposed. The proposed model and algorithms are validated on both synthetic and real waveforms. The obtained results are very promising and show the accuracy of this generalized model with respect to the previous model assuming zero antenna mispointing.

This paper introduces a new model for delay/Doppler altimetry, taking into account the effect of antenna mispointing. After defining the proposed model, the effect of the antenna mispointing on the altimetric waveform is analyzed as a function of along-track and across-track angles. Two least squares approaches are investigated for estimating the parameters associated with the proposed model. The first algorithm estimates four parameters including the across-track mispointing (which affects the echo's shape). The second algorithm uses the mispointing angles provided by the star-trackers and estimates the three remaining parameters. The proposed model and algorithms are validated via simulations conducted on both synthetic and real data.

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 altimetric 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.

The delineation of P and T waves is important for the interpretation of ECG signals. We propose a Bayesian detection-estimation algorithm for simultaneous detection, delineation, and estimation of P and T waves. A block Gibbs sampler exploits the strong local dependencies in ECG signals by imposing block constraints on the P and T wave locations. The proposed algorithm is evaluated on the annotated QT database and compared with two classical algorithms.

Coastal altimetric waveforms may be corrupted by peaks. A simple parametric model was recently introduced to model peaky altimetric waveforms. This model assumes that the received altimetric waveform is the sum of a Brown echo and a Gaussian peak. This model has provided interesting results for symmetric peaks affecting altimetric signals. However, it is not appropriate for altimetric signals corrupted by asymmetric peaks. This paper introduces a Brown with asymmetric Gaussian peak model for altimetric waveforms. The parameters of this model are estimated by a maximum likelihood estimator. The performance of the proposed model and the resulting estimation strategy is evaluated via simulations con ducted on synthetic and real data.

This paper addresses the problem of classifying altimetric signals according to their shapes. The proposed classifier is divided into three steps. A one-class support vector machine method is first used to isolate the large amount of Brown-like echoes from others signals which are considered as outliers. The second step extracts pertinent features from the the remaining echoes (which cannot be well described by the Brown model). These features are projected onto discriminant axes using linear discriminant analysis. The final step classifies the projected feature vectors using a standard Bayesian classifier. The proposed three step classification strategy is evaluated on supervised real altimetric echoes.

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.

This paper studies a Bayesian algorithm for estimating the parameters associated to Brown's model. The joint posterior distribution of the unknown parameter vector (amplitude, epoch and significant wave height) associated with this model is derived. This posterior is too complex to obtain closed form expressions of the minimum mean square error and the maximumaposterioriestimators. We propose to sample according to this distribution using an hybrid Metropolis within Gibbs algorithm. The simulated samples are then used to estimate the unknown parameters of Brown's model. The proposed strategy provides better estimations than the standard maximum likelihood estimator at the price of an increased computational cost.

This paper addresses the problem of classifying altimetric waveforms backscattered from different kinds of surfaces including oceans, ices, deserts and forests. Appropriate features associated with altimetric radar waveforms are first introduced for this classification. These features are completed by radiometer temperatures and pre-processed using a linear discriminant analysis for dimensionality reduction. The classification of altimetric waveforms is finally achieved using the resulting pre-processed vector with reduced dimension. Different classification strategies are finally considered. These strategies are based on the nearest mean rule, the nearest neighbor method or on the multilayer perceptron. Various simulation results illustrate the performance of the proposed classifier.

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.

Zerotree based coders have shown a good ability to be successfully adapted to 3D image coding. This paper focuses on the adaptation of EZW for the compression of hyperspectral images with reduced complexity. The subordinate pass is removed so that the location of significant coefficients does not need to be kept in memory. To compensate the quality loss due to this removal, a signed binary digit representation is 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 sensors have been of a growing interest over the past few decades for Earth observation as well as deep space exploration. However, the amount of data provided by such sensors requires an efficient compression system which is yet to be defined. It is hoped that the particular statistical properties of such images can be used to obtain very efficient compression algorithms. This paper proposes a method to find the most suitable wavelet decomposition for hyperspectral images and introduces the possibility of non isotropic decomposition. The decomposition is made by choosing the decomposition that provides an optimal rate-distortion trade-off. The obtained decomposition exhibits better performances in terms of rate-distortion curves compared to isotropic decomposition for high bitrates as well as for low bitrates

Subband decomposition has been shown to be a useful tool for spectral estimation, in particular when parametric methods have to be considered. Indeed, the loss of observed samples due to decimation can be compensated by the use of a suitable model, if available. This paper studies a subband multichannel autoregressive spectral estimation (SMASE) method. The proposed method decomposes the observed signal through an appropriate filter bank and processes the decimated signals by means of a multichannel autoregressive (AR) model. This model takes advantage of known correlations between different subband signals. This a priori knowledge allows to improve spectral estimation performance. Simulation results illustrate the interest of the proposed methodology for signals with continuous spectra and for sinusoids.

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 traditionally 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.

In the case of uniform sampling, when the Nyquist condition is fulfilled, exact reconstruction of the time-continuous process can be achieved based on the observation of the samples. When the Nyquist condition is not fulfilled, the linear minimum mean square estimator (LMMSE) of the time-continuous process can be derived. It is shown that in some cases, surprisingly, unobserved timing jitter can improve the quality of the LMMSE.

Subband decomposition has already been shown to increase the performance of spectral estimators, but induced frequency overlapping may be troublesome, bringing edge effects at subband borders. A recent paper (Bonacci, D. et al., EUSIPCO, 2002) proposed a method (SDFW - subband decomposition and frequency warping) allowing subband decomposition to be performed without aliasing. We modify this subband decomposition in order to improve frequency resolution for any correlation based spectral estimator when applied to the subband outputs. Three main improvements are proposed: the subband decomposition is based on comb filters; the SDFW method warping operation is performed using a complex frequency modulation; the autocorrelation is estimated using all sub-series from each subband. Simulation results demonstrate the anticipated performance of the proposed method.

This paper addresses the problem of frequency overlapping which occurs when spectral estimation is applied after subband decomposition. Subband decomposition has already been shown to increase the performances of spectral estimation but induced frequency overlapping may be troublesome. This paper proposes a new spectral estimation procedure based on sub band decomposition and frequency warping which reduces the overlapping frequency problem. Simulations confirm the interest of this new algorithm.

Periodic sampling of random processes can be altered by several phenomena. Jitter is a one of them, which was studied for a long time. This paper investigates the problem of a random integration width in the periodic sampling process. Taking into account the statistics of the random integration width, the expression of the best linear reconstruction (in the mean square sense) of the continuous process is given, based on the observation of the samples. Particular examples are given with a comparison with the Shannon interpolator.

This paper studies the effects of jitter in a multipath environment. The power spectral density of a process subjected to jitter and multipath is first derived. The problem of reconstruction of a time-continuous process from observations subjected to jitter and multipath is then considered. Simulation and theoretical results are finally shown to be in good agreement.

This paper studies an alternative to the Watterson (1970) model for multi-path channels. The new model is based on the introduction of random delays. This model is shown to well-represent different kinds of spectra. An application is presented in the case of backscattering from sea surface at small grazing angles of incidence. This clock change-based model allows one to well-describe the physical phenomenon.

The Prony method is a technique for modeling a data set of N samples using a linear combination of p exponentials (N>p) in a least square estimation procedure. In this paper, a study of the amplitude and phase estimator is presented. In particular, theoretical results are given for bias and variance, which are confirmed by simulations. An optimal number of equations in the corresponding least square estimation procedure is derived, minimizing estimation errors.

An alternative Prony model representation requiring a low computational cost is presented. It is shown that a Prony model of order p is equivalent to an autoregressive recurrence of order p and p least squared (LS) initial values. Computational examples show that choosing the p first signal points as recurrence initialization may fairly approximate the LS values for medium signal-to-noise ratios.>