Mireille Guillaume

A Bilinear–Bilinear Nonnegative Matrix Factorization Method for Hyperspectral Unmixing

Spectral unmixing of hyperspectral images consists of estimating pure material spectra with their corresponding proportions (or abundances). Nonlinear mixing models for spectral unmixing are of very recent interest within the signal and image processing community. This letter proposes a new nonlinear unmixing approach using the Fan bilinear-bilinear model and nonnegative matrix factorization method that takes into account physical constraints on spectra (positivity) and abundances (positivity and sum-to-one). The proposed method is tested using a projected-gradient algorithm on synthetic and real data. The performances of this method are compared to the linear approach and to the recent nonlinear approach.

Estimationofwater column parameters with a maximum likelihood approach

In this article, we use a well-known reflectance model of a water column for estimating the model parameters (depth and concentrations of different water constituents) with a maximum likelihood approach. Tested on simulated data, the method performs well, especially for depths between a few meters and about 10m, and a SNR greater than 10dB. Moreover, we calculate the Cramér-Rao lower bounds in order to assess the performances of this estimation process. We show that the variances of the estimators come closer to these CRBs when the number of training pixels grows. Moreover, it turns out that the ML estimates of Cϕ, Ccdom and CNap are efficient even for low sample sizes.

Underwater target detection with hyperspectral remote-sensing imagery

This paper presents a new way of detecting underwater targets with hyperspectral remote-sensing data. The idea is to use a bathymetric model of subsurface reflectance to correct the spectral distortions due to water crossing. Then we derive the Matched filter (MF) from the Likelihood Ratio Test (LRT) built to decide whether the target is present or absent. Tested on both simulated and real images, this new detector appears to overcome classical filters in case of underwater targets. If the depth is unknown, it can be estimated using the maximum likelihood approach, and we show on simulations that detection performances are not very sensitive to the depth estimation accuracy.

Hyperspectral change detection by direction pursuit

Change detection is an important area of interest within the hyperspectral community. Generally, a first step in the detection consists in predicting some general changes as shadows or atmosphere evolution which should not be detected, and in a second step the local changes are detected. Here we choose the covariance equalization to predict those changes. We present in this paper a change detection method based on an anomaly component pursuit algorithm, namely ACP, recently proposed for anomaly detection, which combines anomaly classification and detection. We experimentally show the efficiency of this method, and we compare the results obtained with those of the classical RX detector. We also compare this pursuitbased change detector to two information-based change detection methods, using respectively the Kullback-Liebler divergence information, and the Kendalls tau dependence measure. We show that in our simulation conditions, the ACP algorithm gives very interesting results for change detection analysis.

A CFAR algorithm for anomaly detection and discrimination in hyperspectral images

paper proposes an anomaly detection algorithm for hy- perspectral images. It is unsupervised (the researched spectra are not required a priori), discriminates the anomalies according to their spectra and has a constant false alarm rate (CFAR). The main specificity of this algorithm is to combine these three assets rather than make a tradeoff which is generally necessary with existing methods. It is based on a physically convenient probabilistic model of the fastICA gener ated independent components. We compare it with the adaptive cosine/coherence estimator (a reference supervised target detection algorithm) on a real HYDICE dataset.

Predicting minimum uncertainties in the inversion of ocean color geophysical parameters based on Cramer-Rao bounds

We present an analytical approach based on Cramer-Rao Bounds (CRBs) to investigate the uncertainties in estimated ocean color parameters resulting from the propagation of uncertainties in the bio-optical reflectance modeling through the inversion process. Based on given bio-optical and noise probabilistic models, CRBs can be computed efficiently for any set of ocean color parameters and any sensor configuration, directly providing the minimum estimation variance that can be possibly attained by any unbiased estimator of any targeted parameter. Here, CRBs are explicitly developed using (1) two water reflectance models corresponding to deep and shallow waters, resp., and (2) four probabilistic models describing the environmental noises observed within four Sentinel-2 MSI, HICO, Sentinel-3 OLCI and MODIS images, resp. For both deep and shallow waters, CRBs are shown to be consistent with the experimental estimation variances obtained using two published remote-sensing methods, while not requiring one to perform any inversion. CRBs are also used to investigate to what extent perfect a priori knowledge on one or several geophysical parameters can improve the estimation of remaining unknown parameters. For example, using pre-existing knowledge of bathymetry (e.g., derived from LiDAR) within the inversion is shown to greatly improve the retrieval of bottom cover for shallow waters. Finally, CRBs are shown to provide valuable information on the best estimation performances that may be achieved with the MSI, HICO, OLCI and MODIS configurations for a variety of oceanic, coastal and inland waters. CRBs are thus demonstrated to be an informative and efficient tool to characterize minimum uncertainties in inverted ocean color geophysical parameters.

Joint estimation of water column parameters and seabed reflectance combining maximum likelihood and unmixing algorithm

Bathymetry and Water column constituent estimation is a challenging task for the study of coastal zones. Although most extensively used methods are based on the pixel wise inversion of semi empirical models, we have recently proposed a Maximum Likelihood (ML) method to retrieve such parameters. One limitation of the method is that the seabed reflectance is supposed to be known and homogeneous in a sample zone. We propose here to go beyond this limitation by jointly estimating the bathymetry, the concentrations of the constituents, and the reflectance spectra in an inhomogeneous seabed zone. To do so we introduce a non stationary Likelihood for the sample zone, and we also exploit a triple non-negative matrix factorization. We propose an Estimation-Unmixing (E-U) recursive algorithm to solve the problem. The water column parameters are estimated within the ML step, while the unmixing step allows to recover the bottom reflectance in each pixel. When tested on real hyper-spectral data acquired in the Quiberon peninsula on French West coast, the method leads to consistent estimated maps of bathymetry and seabed reflectance.

Rare endmembers estimation by NMF methods using multitemporal hyperspectral data and change informations

Rare endmembers estimation is a very interesting and difficult issue in the unmixing field. We focus on the case of a rare endmember which appear as a change between two images of a same scene. We use both the information of the image where the new endmember is missing and change detection results to estimate the appearing endmember. We base the proposed approach on spectral unmixing with non negative matrix factorization (NMF), adding appropriate constraints on changed or non-changed pixels. We choose to test and discuss the alternate projected gradient optimization scheme. We compare the results to those of the estimation of appearing endmember through classical NMF unmixing on simulated data.

A non-negative matrix factorization method for bilinear-bilinear unmixing of hyperspectral images

Spectral unmixing of hyperspectral images consists of estimating pure material spectra with their corresponding proportions (or abundances). Recently, non-linear unmixing has received growing interest in the geoscience and remote sensing community. This article proposes a new non-linear unmixing approach using non-negative matrix factorization method that takes into account physical constraints on spectra (positivity) and abundances (positivity and sum-to-one). The proposed method is tested using a projected Gradient algorithm on synthetic and real data. The performances of this method are compared to the linear approach ones and to recent non-linear approaches results.

Seabed estimation using triple NMF method

Spectral unmixing of hyperspectral remote sensing reflectance data is a challenging task, being the subject of many recent researches, and aims to retrieve both endmembers spectra and abundances. It turns out to be hardly feasible when the data are attenuated by additional mediums such as water column in the case of seabed estimation. In this case, a possible solution is to first correct the attenuation due to the water column and then proceed to the unmixing process. This paper presents a new approach, jointly estimating the attenuation, the endmembers spectra and the abundances with a triple non-negative matrix factorization (tri-NMF) method. The method has been tested on synthetic and real data and allow one to obtain accurate abundance maps of the seabed.