Matched Shrunken Cone Detector (MSCD): Bayesian Derivations and Case Studies for Hyperspectral Target Detection

Hyperspectral images (HSIs) possess non-negative properties for both hyperspectral signatures and abundance coefficients, which can be naturally modeled using cone-based representation. However, in hyperspectral target detection, cone-based methods are barely studied. In this paper, we propose a new regularized cone-based representation approach to hyperspectral target detection, as well as its two working models by incorporating into the cone representation l2-norm and l1-norm regularizations, respectively. We call the new approach the matched shrunken cone detector (MSCD). Also important, we provide principled derivations of the proposed MSCD from the Bayesian perspective: we show that MSCD can be derived by assuming a multivariate half-Gaussian distribution or a multivariate half-Laplace distribution as the prior distribution of the coefficients of the models. In the experimental studies, we compare the proposed MSCD with the subspace methods and the sparse representation-based methods for HSI target detection. Two real hyperspectral data sets are used for evaluating the detection performances on sub-pixel targets and full-pixel targets, respectively. Results show that the proposed MSCD can outperform other methods in both cases, demonstrating the competitiveness of the regularized cone-based representation

The matched subspace detector with interaction effects

This paper aims to propose a new hyperspectral target-detection method termed the matched subspace detector with interaction effects (MSDinter). The MSDinter introduces “interaction effects” terms into the popular matched subspace detector (MSD), from regression analysis in multivariate statistics and the bilinear mixing model in hyperspectral unmixing. In this way, the interaction between the target and the surrounding background, which should have but not yet been considered by the MSD, is modelled and estimated, such that superior performance of target detection can be achieved. Besides deriving the MSDinter methodologically, we also demonstrate its superiority empirically using two hyperspectral imaging datasets

Hyperspectral Target Detection Based on Low-Rank Background Subspace Learning and Graph Laplacian Regularization

Hyperspectral target detection is good at finding dim and small objects based on spectral characteristics. However, existing representation-based methods are hindered by the problem of the unknown background dictionary and insufficient utilization of spatial information. To address these issues, this paper proposes an efficient optimizing approach based on low-rank representation (LRR) and graph Laplacian regularization (GLR). Firstly, to obtain a complete and pure background dictionary, we propose a LRR-based background subspace learning method by jointly mining the low-dimensional structure of all pixels. Secondly, to fully exploit local spatial relationships and capture the underlying geometric structure, a local region-based GLR is employed to estimate the coefficients. Finally, the desired detection map is generated by computing the ratio of representation errors from binary hypothesis testing. The experiments conducted on two benchmark datasets validate the effectiveness and superiority of the approach. For reproduction, the accompanying code is available at https://github.com/shendb2022/LRBSL-GLR.Comment: 4 pages, 3 figures, 1 tabl

Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)

The implicit objective of the biennial "international - Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST) is to foster collaboration between international scientific teams by disseminating ideas through both specific oral/poster presentations and free discussions. For its second edition, the iTWIST workshop took place in the medieval and picturesque town of Namur in Belgium, from Wednesday August 27th till Friday August 29th, 2014. The workshop was conveniently located in "The Arsenal" building within walking distance of both hotels and town center. iTWIST'14 has gathered about 70 international participants and has featured 9 invited talks, 10 oral presentations, and 14 posters on the following themes, all related to the theory, application and generalization of the "sparsity paradigm": Sparsity-driven data sensing and processing; Union of low dimensional subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph sensing/processing; Blind inverse problems and dictionary learning; Sparsity and computational neuroscience; Information theory, geometry and randomness; Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?; Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website: http://sites.google.com/site/itwist1

Using Lidar to geometrically-constrain signature spaces for physics-based target detection

A fundamental task when performing target detection on spectral imagery is ensuring that a target signature is in the same metric domain as the measured spectral data set. Remotely sensed data are typically collected in digital counts and calibrated to radiance. That is, calibrated data have units of spectral radiance, while target signatures in the visible regime are commonly characterized in units of re°ectance. A necessary precursor to running a target detection algorithm is converting the measured scene data and target signature to the same domain. Atmospheric inversion or compensation is a well-known method for transforming mea- sured scene radiance values into the re°ectance domain. While this method may be math- ematically trivial, it is computationally attractive and is most e®ective when illumination conditions are constant across a scene. However, when illumination conditions are not con- stant for a given scene, signi¯cant error may be introduced when applying the same linear inversion globally. In contrast to the inversion methodology, physics-based forward modeling approaches aim to predict the possible ways that a target might appear in a scene using atmospheric and radiometric models. To fully encompass possible target variability due to changing illumination levels, a target vector space is created. In addition to accounting for varying illumination, physics-based model approaches have a distinct advantage in that they can also incorporate target variability due to a variety of other sources, to include adjacency target orientation, and mixed pixels. Increasing the variability of the target vector space may be beneficial in a global sense in that it may allow for the detection of difficult targets, such as shadowed or partially concealed targets. However, it should also be noted that expansion of the target space may introduce unnecessary confusion for a given pixel. Furthermore, traditional physics-based approaches make certain assumptions which may be prudent only when passive, spectral data for a scene are available. Common examples include the assumption of a °at ground plane and pure target pixels. Many of these assumptions may be attributed to the lack of three-dimensional (3D) spatial information for the scene. In the event that 3D spatial information were available, certain assumptions could be levied, allowing accurate geometric information to be fed to the physics-based model on a pixel- by-pixel basis. Doing so may e®ectively constrain the physics-based model, resulting in a pixel-specific target space with optimized variability and minimized confusion. This body of work explores using spatial information from a topographic Light Detection and Ranging (Lidar) system as a means to enhance the delity of physics-based models for spectral target detection. The incorporation of subpixel spatial information, relative to a hyperspectral image (HSI) pixel, provides valuable insight about plausible geometric con¯gurations of a target, background, and illumination sources within a scene. Methods for estimating local geometry on a per-pixel basis are introduced; this spatial information is then fed into a physics-based model to the forward prediction of a target in radiance space. The target detection performance based on this spatially-enhanced, spectral target space is assessed relative to current state-of-the-art spectral algorithms

Spectral Target Detecting Using Schroedinger Eigenmaps

Applications of optical remote sensing processes include environmental monitoring, military monitoring, meteorology, mapping, surveillance, etc. Many of these tasks include the detection of specific objects or materials, usually few or small, which are surrounded by other materials that clutter the scene and hide the relevant information. This target detection process has been boosted lately by the use of hyperspectral imagery (HSI) since its high spectral dimension provides more detailed spectral information that is desirable in data exploitation. Typical spectral target detectors rely on statistical or geometric models to characterize the spectral variability of the data. However, in many cases these parametric models do not fit well HSI data that impacts the detection performance. On the other hand, non-linear transformation methods, mainly based on manifold learning algorithms, have shown a potential use in HSI transformation, dimensionality reduction and classification. In target detection, non-linear transformation algorithms are used as preprocessing techniques that transform the data to a more suitable lower dimensional space, where the statistical or geometric detectors are applied. One of these non-linear manifold methods is the Schroedinger Eigenmaps (SE) algorithm that has been introduced as a technique for semi-supervised classification. The core tool of the SE algorithm is the Schroedinger operator that includes a potential term that encodes prior information about the materials present in a scene, and enables the embedding to be steered in some convenient directions in order to cluster similar pixels together. A completely novel target detection methodology based on SE algorithm is proposed for the first time in this thesis. The proposed methodology does not just include the transformation of the data to a lower dimensional space but also includes the definition of a detector that capitalizes on the theory behind SE. The fact that target pixels and those similar pixels are clustered in a predictable region of the low-dimensional representation is used to define a decision rule that allows one to identify target pixels over the rest of pixels in a given image. In addition, a knowledge propagation scheme is used to combine spectral and spatial information as a means to propagate the \potential constraints to nearby points. The propagation scheme is introduced to reinforce weak connections and improve the separability between most of the target pixels and the background. Experiments using different HSI data sets are carried out in order to test the proposed methodology. The assessment is performed from a quantitative and qualitative point of view, and by comparing the SE-based methodology against two other detection methodologies that use linear/non-linear algorithms as transformations and the well-known Adaptive Coherence/Cosine Estimator (ACE) detector. Overall results show that the SE-based detector outperforms the other two detection methodologies, which indicates the usefulness of the SE transformation in spectral target detection problems