In hyperspectral imaging the replacement model where a target, if present, partly replaces the disturbance is often advocated. In this paper, we consider a somehow more realistic model where only the ...low-rank background is substituted for the target while a residual noise, which belongs to the orthogonal complement, is unaffected by the presence/absence of the target. A two-step generalized likelkihood ratio test is formulated for such a model. Furthermore we show that the log likelihood can be well approximated by a weighted combination of the log likelihoods of the FTMF and the AMF, and that the dimension of the background subspace is the tuning parameter which enables to balance between these two well-known detectors. A comparison with standard techniques on real hyperspectral data reveals a good performance of the new detectors.
The replacement model, which assumes that the abundances sum up to one, is often advocated for subpixel target detection in hyperspectral imaging, and various detection schemes based on this model ...have been developed in the literature. However, in practical situations, this unitary constraint may be too strong due to possible attenuation of the target bidirectional reflectance distribution function, signature mismatches or impediments in the radiometric corrections. The aim of this paper is to improve the replacement-model detection algorithms by relaxing this unitary constraint. To this end, we propose to consider a modified replacement model. One step and two steps generalized likelihood ratio tests are developed for this new model and compared to standard solutions through numerical simulations. An application to real data shows the improvement offered by the proposed approach.
•Derivation of a robust Likelihood Ratio (LR) in case of detection with a small noise mismatch between the hypotheses.•Derivation of a robust Adaptive Matched Filter (AMF).•Pointing out differences ...with standard detection schemes using Matched Filter Residual (MFR) plots.•Performance improvement based on a hyperspectral imaging detection benchmark.
One of the main issue in detecting a target from an hyperspectral image relies on properly identifying the background. Many assumptions about its distribution can be advocated, even if the Gaussian hypothesis prevails. Nevertheless, the huge majority of the resulting detection schemes assume that the background distribution remains the same whether the target is present or not. In practice, because of the spectral variability of the target and the non-linear mixing with the background radiance, this hypothesis is not strictly true. In this paper, we consider that an unknown background mismatch exists between the two hypotheses. Under the assumption that this mismatch is small, we derive an approximation of the Likelihood Ratio for the problem at hand. This general formulation is then applied to the case of Gaussian distributed background, leading to a robust Adaptive Matched Filter. The behaviour of this new detector is analysed and compared to popular detectors. Numerical simulations, based on real data, show the possible improvement in case of target signature mismatch.
Detection of a target with known spectral signature when this target may occupy only a fraction of the pixel is an important issue in hyperspectral imaging. We recently derived the generalized ...likelihood ratio test (GLRT) for such sub-pixel targets, either for the so-called replacement model where the presence of a target induces a decrease of the background power, due to the sum of abundances equal to one, or for a mixed model which alleviates some of the limitations of the replacement model. In both cases, the background was assumed to be Gaussian distributed. The aim of this short communication is to extend these detectors to the broader class of elliptically contoured distributions, more precisely matrix-variate t-distributions with unknown mean and covariance matrix. We show that the generalized likelihood ratio tests in the t-distributed case coincide with their Gaussian counterparts, which confers the latter an increased generality for application. The performance as well as the robustness of these detectors are evaluated through numerical simulations.
The black caiman is one of the largest neotropical top predators, which means that it could play a structuring role within swamp ecosystems. However, because of the difficulties inherent to studying ...black caimans, data are sorely lacking on many aspects of their general biology, natural history, and ecology, especially in French Guiana. We conducted a detailed study of the Agami Pond black caiman population using a multidisciplinary approach. The aim was to better understand the species' dietary ecology and movements in the pond, and thus its functional role in pond system. We gathered natural history data, tracked caiman movements using satellite transmitters, and characterized feeding ecology via stable isotope analysis. Our study was carried out over three sampling periods and spanned both wet and dry seasons, which differ in their hydrological and ecological conditions. Our results show that black caiman abundance and age demographics differed between seasons in Agami Pond. In the dry season, Agami Pond is one of the only areas within the marsh to hold water. It thus contains large quantities of different fish species, which form the basis of the black caiman's diet. Caiman body size, a proxy for age class, was around 1.5 meters. During the wet season, which corresponds to the breeding period for migratory birds (e.g., Agami herons), adult black caimans are present in Agami Pond. Adults were most abundant in the inundated forest. There, most individuals measured up to 2 meters. They also exhibited a particular "predatory" behavior near bird nests, preying on fallen chicks and adults. Juveniles and subadults were present during both seasons in the pond's open waters. These behavioral observations were backed up by stable isotope analysis, which revealed ontogenetic variation in the caiman's isotopic values. This isotopic variation reflected variation in diet that likely reduced intraspecific competition between adults and young. The telemetry and microchip data show that different age classes had different movement patterns and that seasonal variation in the pond may influence caiman prey availability and reproductive behavior. The new information gathered should help predict this species' responses to potential ecosystem disturbance (e.g., water pollution, habitat destruction) and inform the development of an effective conservation plan that involves locals and wildlife officials.
Improved post detection integration Gigleux, Benjamin; Vincent, François; Besson, Olivier ...
Signal processing,
12/2023, Letnik:
213
Journal Article
Recenzirano
Odprti dostop
In many signal processing applications, conducting a coherent integration over the whole observation duration is not possible due to uncontrolled phase evolutions. In such a case one may refer to ...Post Detection Integration that consists in wisely combine shorter time integration outputs. In this paper, we propose a new detector that improves the state of art ones. Compared with the GLRT from which it is derived, it consists in a closed-form expression. Moreover, it is based on a simple linear phase assumption and can be used, by the way, in a wide area of applications.
We develop Adaptive Cosine Estimator (ACE) type detector for non-zero mean Gaussian interference specifically for the replacement and additive target models of the hyperspectral imaging problem. We ...consider the case where the data under test and the training samples differ from one scaling factor on the mean and one scaling factor on the covariance matrix. We derive two-step generalized likelihood ratio tests for both the additive model and the replacement model and show that the new detectors differ in the way the mean value is removed. A real data experiment shows that they outperform the standard version.
Maximum Likelihood (ML) frequency estimation of a single tone in noise is known to be a computationally intensive task that does not cope with many real-time and embedded hardware architectures. ...Thereby, many sub-optimal techniques, based on approximations, have been proposed in the literature. In this paper, we show that the ML criterion can be solved directly, using an appropriate two-step procedure. The closed-form solution is shown to be asymptotically equivalent to the ML. Moreover, its formulation is very close to the popular Fitz's expression, with a slight correction. Numerical simulations show that the proposed scheme is very close to the ML.
•We consider the use of partial Cholesky factorization to retrieve low-rank interference.•We provide some results about the angles with the interference subspace.•We conduct a statistical analysis of ...the reduced-rank beamformer obtained.•We show that partial Cholesky performs as well as SVD and better in some situations.
Reduced-rank adaptive beamforming is a well established and efficient methodology, notably for disturbance covariance matrices which are the sum of a strong low-rank component (interference) and a scaled identity matrix (thermal noise). Eigenvalue or singular decomposition is often used to achieve rank reduction. In this paper, we study and analyze an alternative, namely a partial Cholesky factorization, as a means to retrieve interference subspace and to compute reduced-rank beamformers. First, we study the angles between the true subspace and that obtained from partial Cholesky factorization of the covariance matrix. Then, a statistical analysis is carried out in finite samples. Using properties of partitioned Wishart matrices, we provide a stochastic representation of the beamformer based on partial Cholesky factorization and of the corresponding signal to interference and noise ratio loss. We show that the latter follows approximately a beta distribution, similarly to the beamformer based on eigenvalue decomposition. Finally, numerical simulations are presented which indicate that a reduced-rank adaptive beamformer based on partial Cholesky factorization incurs almost no loss, and can even perform better in some scenarios than its eigenvalue or singular value-based counterpart.
PDF
