Hyperspectral Signal Subspace Identification in the presence of rare vectors and signal dependent noise

Orthogonal subspace projection (OSP) is a powerful tool for dimensionality reduction (DR) in hyperspectral images (HSIs). In the OSP approach, the basis of the signal subspace must be estimated from the data themselves. Such estimation task s referred to as signal subspace identification (SSI). Most of the SSI methods in the literature are based on the analysis of the data second-order statistics (SOS) and have two main drawbacks: 1) They do not take into account the rare signal components (orrare vectors), 2) they assume that noise is spatially stationary. Rare vectors are those signal components that are present in pixels scarcely represented in the image and linearly independent on the signal components characterizing the rest of the image pixels. SOS-based SSI algorithms estimate the signal subspace addressing mostly the background and ignoring the presence of the rare pixels. This may be detrimental for the performance of detectionm algorithms when DR is adopted as a pre-processing step in small target detection applications. In this paper, a new technique for SSI in HSIs is presented. The algorithm is developed to account for both the abundant and the rare signal components. The method is derived by assuming a signal-dependent model for the noise affecting the data. This makes the SSI algorithm particularly suitable for the processing of images acquired by new generation sensors where, due to the improved sensitivity of the electronic components, noise includes a signal-dependent term. Results on simulated data are discussed, and the comparison with a recently proposed technique based on the analysis of SOS is performed. Furthermore, the results obtained by applying the SSI algorithm to a real HSI affected by signal-dependent noise are presented and discussed

Anomalous change detection in multi-temporal hyperspectral images

In latest years, the possibility to exploit the high amount of spectral information has made hyperspectral remote sensing a very promising approach to detect changes occurred in multi-temporal images. Detection of changes in images of the same area collected at different times is of crucial interest in military and civilian applications, spanning from wide area surveillance and damage assessment to geology and land cover. In military operations, the interest is in rapid location and tracking of objects of interest, people, vehicles or equipment that pose a potential threat. In civilian contexts, changes of interest may include different types of natural or manmade threats, such as the path of an impending storm or the source of a hazardous material spill. In this PhD thesis, the focus is on Anomalous Change Detection (ACD) in airborne hyperspectral images. The goal is the detection of small changes occurred in two images of the same scene, i.e. changes having size comparable with the sensor ground resolution. The objects of interest typically occupy few pixels of the image and change detection must be accomplished in a pixel-wise fashion. Moreover, since the images are in general not radiometrically comparable, because illumination, atmospheric and environmental conditions change from one acquisition to the other, pervasive and uninteresting changes must be accounted for in developing ACD strategies. ACD process can be distinguished into two main phases: a pre-processing step, which includes radiometric correction, image co-registration and noise filtering, and a detection step, where the pre-processed images are compared according to a defined criterion in order to derive a statistical ACD map highlighting the anomalous changes occurred in the scene. In the literature, ACD has been widely investigated providing valuable methods in order to cope with these problems. In this work, a general overview of ACD methods is given reviewing the most known pre-processing and detection methods proposed in the literature. The analysis has been conducted unifying different techniques in a common framework based on binary decision theory, where one has to test the two competing hypotheses H0 (change absent) and H1 (change present) on the basis of an observation vector derived from the radiance measured on each pixel of the two images. Particular emphasis has been posed on statistical approaches, where ACD is derived in the framework of Neymann Pearson theory and the decision rule is carried out on the basis of the statistical properties assumed for the two hypotheses distribution, the observation vector space and the secondary data exploited for the estimation of the unknown parameters. Typically, ACD techniques assume that the observation represents the realization of jointly Gaussian spatially stationary random process. Though such assumption is adopted because of its mathematical tractability, it may be quite simplistic to model the multimodality usually met in real data. A more appropriate model is that adopted to derive the well known RX anomaly detector which assumes the local Gaussianity of the hyperspectral data. In this framework, a new statistical ACD method has been proposed considering the local Gaussianity of the hyperspectral data. The assumption of local stationarity for the observations in the two hypotheses is taken into account by considering two different models, leading to two different detectors. In addition, when data are collected by airborne platforms, perfect co-registration between images is very difficult to achieve. As a consequence, a residual misregistration (RMR) error should be taken into account in developing ACD techniques. Different techniques have been proposed to cope with the performance degradation problem due to the RMR, embedding the a priori knowledge on the statistical properties of the RMR in the change detection scheme. In this context, a new method has been proposed for the estimation of the first and second order statistics of the RMR. The technique is based on a sequential strategy that exploits the Scale Invariant Feature Transform (SIFT) algorithm cascaded with the Minimum Covariance Determinant algorithm. The proposed method adapts the SIFT procedure to hyperspectral images and improves the robustness of the outliers filtering by means of a highly robust estimator of multivariate location. Then, the attention has been focused on noise filtering techniques aimed at enforcing the consistency of the ACD process. To this purpose, a new method has been proposed to mitigate the negative effects due to random noise. In particular, this is achieved by means of a band selection technique aimed at discarding spectral channels whose useful signal content is low compared with the noise contribution. Band selection is performed on a per-pixel basis by exploiting the estimates of the noise variance accounting also for the presence of the signal dependent noise component. Finally, the effectiveness of the proposed techniques has been extensively evaluated by employing different real hyperspectral datasets containing anomalous changes collected in different acquisition conditions and on different scenarios, highlighting advantages and drawbacks of each method. In summary, the main issues related to ACD in multi-temporal hyperspectral images have been examined in this PhD thesis. With reference to the pre-processing step, two original contributions have been offered: i) an unsupervised technique for the estimation of the RMR noise affecting hyperspectral images, and ii) an adaptive approach for ACD which mitigates the negative effects due to random noise. As to the detection step, a survey of the existing techniques has been carried out, highlighting the major drawbacks and disadvantages, and a novel contribution has been offered by presenting a new statistical ACD method which considers the local Gaussianity of the hyperspectral data