9 research outputs found
Matched shrunken subspace detectors for hyperspectral target detection
In this paper, we propose a new approach, called the matched shrunken subspace detector (MSSD), to target detection from hyperspectral images. The MSSD is developed by shrinking the abundance vectors of the target and background subspaces in the hypothesis models of the matched subspace detector (MSD), a popular subspace-based approach to target detection. The shrinkage is achieved by introducing simple l2-norm regularisation (also known as ridge regression or Tikhonov regularisation). We develop two types of MSSD, one with isotropic shrinkage and termed MSSD-i and the other with anisotropic shrinkage and termed MSSD-a. For these two new methods, we provide both the frequentist and Bayesian derivations. Experiments on a real hyperspectral imaging dataset called Hymap demonstrate that the proposed MSSD methods can outperform the original MSD for hyperspectral target detection
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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
MSDH: matched subspace detector with heterogeneous noise
The matched subspace detector (MSD) is a classical subspace-based method for hyperspectral subpixel target detection. However, the model assumes that noise has the same variance over different bands, which is usually unrealistic in practice. In this letter, we relax the equal variance assumption and propose a matched subspace detector with heterogeneous noise (MSDH). In essence, the noise variances are different for different bands and they can be estimated by using iteratively reweighted least squares methods. Experiments on two benchmark real hyperspectral datasets demonstrate the superiority of MSDH over MSD for subpixel target detection
Essays on hyperspectral image analysis: classification and target detection
Over the past a few decades, hyperspectral imaging has drawn significant attention and become an important scientific tool for various fields of real-world applications. Among the research topics of hyperspectral image (HSI) analysis, two major topics -- HSI classification and HSI target detection have been intensively studied. Statistical learning has played a pivotal role in promoting the development of algorithms and methodologies for the two topics. Among the existing methods for HSI classification, sparse representation classification (SRC) has been widely investigated, which is based on the assumption that a signal can be represented by a linear combination of a small number of redundant bases (so called dictionary atoms). By virtue of the signal coherence in HSIs, a joint sparse model (JSM) has been successfully developed for HSI classification and has achieved promising performance. However, the JSM-based dictionary learning for HSIs is barely discussed. In addition, the non-negativity properties of coefficients in the JSM are also little touched. HSI target detection can be regarded as a special case of classification, i.e. a binary classification, but faces more challenges. Traditional statistical methods regard a test HSI pixel as a linear combination of several endmembers with corresponding fractions, i.e. based on the linear mixing model (LMM). However, due to the complicated environments in real-world problems, complex mixing effects may exist in HSIs and make the detection of targets more difficult. As a consequence, the performance of traditional LMM is limited. In this thesis, we focus on the topics of HSI classification and HSI target detection and propose five new methods to tackle the aforementioned issues in the two tasks. For the HSI classification, two new methods are proposed based on the JSM. The first proposed method focuses on the dictionary learning, which incorporates the JSM in the discriminative K-SVD learning algorithm, in order to learn a quality dictionary with rich information for improving the classification performance. The second proposed method focuses on developing the convex cone-based JSM, i.e. by incorporating the non-negativity constraints in the coefficients in the JSM. For the HSI target detection, three approaches are proposed based on the linear mixing model (LMM). The first approach takes account of interaction effects to tackle the mixing problems in HSI target detection. The second approach called matched shrunken subspace detector (MSSD) and the third approach, called matched cone shrunken detector (MSCD), both offer on Bayesian derivatives of regularisation constrained LMM. Specifically, the proposed MSSD is a regularised subspace-representation of LMM, while the proposed MSCD is a regularised cone-representation of LMM
Generalized likelihood ratio test for optical subpixel objects’ detection with hypothesis-dependent background covariance matrix
Much interest has arisen in the problem of detecting weak optical subpixel objects in a sequence of images immersed in a heavy homogeneous Gaussian clutter background. In optical systems, the presence of the objects changes the background plus the channel noise covariance matri
Error characterization of spectral products using a factorial designed experiment
The main objective of any imaging system is to collect information. Information is conveyed in remotely sensed imagery by the spatial and spectral distribution of the energy reflected/emitted from the earth. This energy is subsequently captured by an overhead imaging system. Post-processing algorithms, which rely on this spectral and spatial energy distribution, allow us to extract useful information from the collected data. Typically, spectral processing algorithms include such procedures as target detection, thematic mapping and spectral pixel unmixing. The final spectral products from these algorithms include detection maps, classification maps and endmember fraction maps. The spatial resolution, spectral sampling and signal-to-noise characteristics of a spectral imaging system share a strong relationship with one another based on the law of conservation of energy. If any one of these initial image collection parameters were changed then we would expect the accuracy of the information derived from the spectral processing algorithms to also change. The goal of this thesis study was to investigate the accuracy and effectiveness of spectral processing algorithms under different image levels of spectral resolution, spatial resolution and noise. In order to fulfill this goal a tool was developed that degrades hyperspectral images spatially, spectrally and by adding spectrally correlated noise. These degraded images were then subjected to several spectral processing algorithms. The information utility and error characterization of these degraded spectral products is assessed using algorithm-specific metrics. By adopting a factorial designed experimental approach, the joint effects of spatial resolution, spectral sampling and signal-to-noise with respect to algorithm performance was also studied. Finally, a quantitative performance comparison of the tested spectral processing algorithms was made
Shrinkage corrections of sample linear estimators in the small sample size regime
We are living in a data deluge era where the dimensionality of the data gathered by inexpensive sensors is growing at a fast pace, whereas the availability of independent samples of the observed data is limited. Thus, classical statistical inference methods relying on the assumption that the sample size is large, compared to the observation dimension, are suffering a severe performance degradation.
Within this context, this thesis focus on a popular problem in signal processing, the estimation of a parameter, observed through a linear model. This inference is commonly based on a linear filtering of the data. For instance, beamforming in array signal processing, where a spatial filter steers the beampattern of the antenna array towards a direction to obtain the signal of interest (SOI). In signal processing the design of the optimal filters relies on the optimization of performance measures such as the Mean Square Error (MSE) and the Signal to Interference plus Noise Ratio (SINR). When the first two moments of the SOI are known, the optimization of the MSE leads to the Linear Minimum Mean Square Error (LMMSE). When such statistical information is not available one may force a no distortion constraint towards the SOI in the optimization of the MSE, which is equivalent to maximize the SINR. This leads to the Minimum Variance Distortionless Response (MVDR) method.
The LMMSE and MVDR are optimal, though unrealizable in general, since they depend on the inverse of the data correlation, which is not known. The common approach to circumvent this problem is to substitute it for the inverse of the sample correlation matrix (SCM), leading to the sample LMMSE and sample MVDR. This approach is optimal when the number of available statistical samples tends to infinity for a fixed observation dimension. This large sample size scenario hardly holds in practice and the sample methods undergo large performance degradations in the small sample size regime, which may be due to short stationarity constraints or to a system with a high observation dimension.
The aim of this thesis is to propose corrections of sample estimators, such as the sample LMMSE and MVDR, to circumvent their performance degradation in the small sample size regime. To this end, two powerful tools are used, shrinkage estimation and random matrix theory (RMT). Shrinkage estimation introduces a structure on the filters that forces some corrections in small sample size situations. They improve sample based estimators by optimizing a bias variance tradeoff. As direct optimization of these shrinkage methods leads to unrealizable estimators, then a consistent estimate of these optimal shrinkage estimators is obtained, within the general asymptotics where both the observation dimension and the sample size tend to infinity, but at a fixed rate. That is, RMT is used to obtain consistent estimates within an asymptotic regime that deals naturally with the small sample size. This RMT approach does not require any assumptions about the distribution of the observations.
The proposed filters deal directly with the estimation of the SOI, which leads to performance gains compared to related work methods based on optimizing a metric related to the data covariance estimate or proposing rather ad-hoc regularizations of the SCM. Compared to related work methods which also treat directly the estimation of the SOI and which are based on a shrinkage of the SCM, the proposed filter structure is more general. It contemplates corrections of the inverse of the SCM and considers the related work methods as particular cases. This leads to performance gains which are notable when there is a mismatch in the signature vector of the SOI. This mismatch and the small sample size are the main sources of degradation of the sample LMMSE and MVDR. Thus, in the last part of this thesis, unlike the previous proposed filters and the related work, we propose a filter which treats directly both sources of degradation.Estamos viviendo en una era en la que la dimensión de los datos, recogidos por sensores de bajo precio, está creciendo a un ritmo elevado, pero la disponibilidad de muestras estadísticamente independientes de los datos es limitada. Así, los métodos clásicos de inferencia estadística sufren una degradación importante, ya que asumen un tamaño muestral grande comparado con la dimensión de los datos. En este contexto, esta tesis se centra en un problema popular en procesado de señal, la estimación lineal de un parámetro observado mediante un modelo lineal. Por ejemplo, la conformación de haz en procesado de agrupaciones de antenas, donde un filtro enfoca el haz hacia una dirección para obtener la señal asociada a una fuente de interés (SOI). El diseño de los filtros óptimos se basa en optimizar una medida de prestación como el error cuadrático medio (MSE) o la relación señal a ruido más interferente (SINR). Cuando hay información sobre los momentos de segundo orden de la SOI, la optimización del MSE lleva a obtener el estimador lineal de mínimo error cuadrático medio (LMMSE). Cuando esa información no está disponible, se puede forzar la restricción de no distorsión de la SOI en la optimización del MSE, que es equivalente a maximizar la SINR. Esto conduce al estimador de Capon (MVDR). El LMMSE y MVDR son óptimos, pero no son realizables, ya que dependen de la inversa de la matriz de correlación de los datos, que no es conocida. El procedimiento habitual para solventar este problema es sustituirla por la inversa de la correlación muestral (SCM), esto lleva al LMMSE y MVDR muestral. Este procedimiento es óptimo cuando el tamaño muestral tiende a infinito y la dimensión de los datos es fija. En la práctica este tamaño muestral elevado no suele producirse y los métodos LMMSE y MVDR muestrales sufren una degradación importante en este régimen de tamaño muestral pequeño. Éste se puede deber a periodos cortos de estacionariedad estadística o a sistemas cuya dimensión sea elevada. El objetivo de esta tesis es proponer correcciones de los estimadores LMMSE y MVDR muestrales que permitan combatir su degradación en el régimen de tamaño muestral pequeño. Para ello se usan dos herramientas potentes, la estimación shrinkage y la teoría de matrices aleatorias (RMT). La estimación shrinkage introduce una estructura de los estimadores que mejora los estimadores muestrales mediante la optimización del compromiso entre media y varianza del estimador. La optimización directa de los métodos shrinkage lleva a métodos no realizables. Por eso luego se propone obtener una estimación consistente de ellos en el régimen asintótico en el que tanto la dimensión de los datos como el tamaño muestral tienden a infinito, pero manteniendo un ratio constante. Es decir RMT se usa para obtener estimaciones consistentes en un régimen asintótico que trata naturalmente las situaciones de tamaño muestral pequeño. Esta metodología basada en RMT no requiere suposiciones sobre el tipo de distribución de los datos. Los filtros propuestos tratan directamente la estimación de la SOI, esto lleva a ganancias de prestaciones en comparación a otros métodos basados en optimizar una métrica relacionada con la estimación de la covarianza de los datos o regularizaciones ad hoc de la SCM. La estructura de filtro propuesta es más general que otros métodos que también tratan directamente la estimación de la SOI y que se basan en un shrinkage de la SCM. Contemplamos correcciones de la inversa de la SCM y los métodos del estado del arte son casos particulares. Esto lleva a ganancias de prestaciones que son notables cuando hay una incertidumbre en el vector de firma asociado a la SOI. Esa incertidumbre y el tamaño muestral pequeño son las fuentes de degradación de los LMMSE y MVDR muestrales. Así, en la última parte de la tesis, a diferencia de métodos propuestos previamente en la tesis y en la literatura, se propone un filtro que trata de forma directa ambas fuentes de degradación
Biological image analysis
In biological research images are extensively used to monitor growth, dynamics and changes in biological specimen, such as cells or plants. Many of these images are used solely for observation or are manually annotated by an expert. In this dissertation we discuss several methods to automate the annotating and analysis of bio-images. Two large clusters of methods have been investigated and developed. A first set of methods focuses on the automatic delineation of relevant objects in bio-images, such as individual cells in microscopic images. Since these methods should be useful for many different applications, e.g. to detect and delineate different objects (cells, plants, leafs, ...) in different types of images (different types of microscopes, regular colour photographs, ...), the methods should be easy to adjust. Therefore we developed a methodology relying on probability theory, where all required parameters can easily be estimated by a biologist, without requiring any knowledge on the techniques used in the actual software.
A second cluster of investigated techniques focuses on the analysis of shapes. By defining new features that describe shapes, we are able to automatically classify shapes, retrieve similar shapes from a database and even analyse how an object deforms through time