Regularization approaches to hyperspectral unmixing

We consider a few different approaches to hyperspectral unmixing of remotely sensed imagery which exploit and extend recent advances in sparse statistical regularization, handling of constraints and dictionary reduction. Hyperspectral unmixing methods often use a conventional least-squares based lasso which assumes that the data follows the Gaussian distribution, we use this as a starting point. In addition, we consider a robust approach to sparse spectral unmixing of remotely sensed imagery which reduces the sensitivity of the estimator to outliers. Due to water absorption and atmospheric effects that affect data collection, hyperspectral images are prone to have large outliers. The framework comprises of several well-principled penalties. A non-convex, hyper-Laplacian prior is incorporated to induce sparsity in the number of active pure spectral components, and total variation regularizer is included to exploit the spatial-contextual information of hyperspectral images. Enforcing the sum-to-one and non-negativity constraint on the models parameters is essential for obtaining realistic estimates. We consider two approaches to account for this: an iterative heuristic renormalization and projection onto the positive orthant, and a reparametrization of the coefficients which gives rise to a theoretically founded method. Since the large size of modern spectral libraries cannot only present computational challenges but also introduce collinearities between regressors, we introduce a library reduction step. This uses the multiple signal classi fication (MUSIC) array processing algorithm, which both speeds up unmixing and yields superior results in scenarios where the library size is extensive. We show that although these problems are non-convex, they can be solved by a properly de fined algorithm based on either trust region optimization or iteratively reweighted least squares. The performance of the different approaches is validated in several simulated and real hyperspectral data experiments

Image Processing and Machine Learning for Hyperspectral Unmixing: An Overview and the HySUPP Python Package

Spectral pixels are often a mixture of the pure spectra of the materials, called endmembers, due to the low spatial resolution of hyperspectral sensors, double scattering, and intimate mixtures of materials in the scenes. Unmixing estimates the fractional abundances of the endmembers within the pixel. Depending on the prior knowledge of endmembers, linear unmixing can be divided into three main groups: supervised, semi-supervised, and unsupervised (blind) linear unmixing. Advances in Image processing and machine learning substantially affected unmixing. This paper provides an overview of advanced and conventional unmixing approaches. Additionally, we draw a critical comparison between advanced and conventional techniques from the three categories. We compare the performance of the unmixing techniques on three simulated and two real datasets. The experimental results reveal the advantages of different unmixing categories for different unmixing scenarios. Moreover, we provide an open-source Python-based package available at https://github.com/BehnoodRasti/HySUPP to reproduce the results

スペクトルの線形性を考慮したハイパースペクトラル画像のノイズ除去とアンミキシングに関する研究

This study aims to generalize color line to M-dimensional spectral line feature (M>3) and introduce methods for denoising and unmixing of hyperspectral images based on the spectral linearity.For denoising, we propose a local spectral component decomposition method based on the spectral line. We first calculate the spectral line of an M-channel image, then using the line, we decompose the image into three components: a single M-channel image and two gray-scale images. By virtue of the decomposition, the noise is concentrated on the two images, thus the algorithm needs to denoise only two grayscale images, regardless of the number of channels. For unmixing, we propose an algorithm that exploits the low-rank local abundance by applying the unclear norm to the abundance matrix for local regions of spatial and abundance domains. In optimization problem, the local abundance regularizer is collaborated with the L2, 1 norm and the total variation.北九州市立大

Exploiting Cross Domain Relationships for Target Recognition

Cross domain recognition extracts knowledge from one domain to recognize samples from another domain of interest. The key to solving problems under this umbrella is to find out the latent connections between different domains. In this dissertation, three different cross domain recognition problems are studied by exploiting the relationships between different domains explicitly according to the specific real problems. First, the problem of cross view action recognition is studied. The same action might seem quite different when observed from different viewpoints. Thus, how to use the training samples from a given camera view and perform recognition in another new view is the key point. In this work, reconstructable paths between different views are built to mirror labeled actions from one source view into one another target view for learning an adaptable classifier. The path learning takes advantage of the joint dictionary learning techniques with exploiting hidden information in the seemingly useless samples, making the recognition performance robust and effective. Second, the problem of person re-identification is studied, which tries to match pedestrian images in non-overlapping camera views based on appearance features. In this work, we propose to learn a random kernel forest to discriminatively assign a specific distance metric to each pair of local patches from the two images in matching. The forest is composed by multiple decision trees, which are designed to partition the overall space of local patch-pairs into substantial subspaces, where a simple but effective local metric kernel can be defined to minimize the distance of true matches. Third, the problem of multi-event detection and recognition in smart grid is studied. The signal of multi-event might not be a straightforward combination of some single-event signals because of the correlation among devices. In this work, a concept of ``root-pattern\u27\u27 is proposed that can be extracted from a collection of single-event signals, but also transferable to analyse the constituent components of multi-cascading-event signals based on an over-complete dictionary, which is designed according to the ``root-patterns\u27\u27 with temporal information subtly embedded. The correctness and effectiveness of the proposed approaches have been evaluated by extensive experiments

Hierarchical Bayesian sparse image reconstruction with application to MRFM

This paper presents a hierarchical Bayesian model to reconstruct sparse images when the observations are obtained from linear transformations and corrupted by an additive white Gaussian noise. Our hierarchical Bayes model is well suited to such naturally sparse image applications as it seamlessly accounts for properties such as sparsity and positivity of the image via appropriate Bayes priors. We propose a prior that is based on a weighted mixture of a positive exponential distribution and a mass at zero. The prior has hyperparameters that are tuned automatically by marginalization over the hierarchical Bayesian model. To overcome the complexity of the posterior distribution, a Gibbs sampling strategy is proposed. The Gibbs samples can be used to estimate the image to be recovered, e.g. by maximizing the estimated posterior distribution. In our fully Bayesian approach the posteriors of all the parameters are available. Thus our algorithm provides more information than other previously proposed sparse reconstruction methods that only give a point estimate. The performance of our hierarchical Bayesian sparse reconstruction method is illustrated on synthetic and real data collected from a tobacco virus sample using a prototype MRFM instrument.Comment: v2: final version; IEEE Trans. Image Processing, 200

Ανάπτυξη και αξιολόγηση αλγορίθμων συμπερασμού κατά Bayes κατάλληλων για φασματικό διαχωρισμό

Η παρούσα εργασία, επικεντρώνεται στο πρόβλημα του ημί-επιβλεπόμενου υπέρ- φασματικού διαχωρισμού, όπου, γνωρίζοντας τις φασματικές υπογραφές κάποιων υλικών, στόχος κατά την ανάλυση ενός συγκεκριμένου εικονοστοιχείου είναι ο προσδιορισμός των υλικών που το συνθέτουν, αλλά και του διανύσματος που περιέχει τα ποσοστά αυτών των υλικών στη σύνθεση. Υιοθετώντας το γραμμικό μοντέλο μίξης για την υπό εξέταση υπερφασματική εικόνα, αναπτύσσεται μία ιεραρχική προσέγγιση κατά Bayes κατάλληλη για ημί-επιβλεπόμενο υπέρ-φασματικό διαχωρισμό, όπου έχουν ανατεθεί κατάλληλες εκ των προτέρων κατανομές πιθανότητας στις εμπλεκόμενες υπό εκτίμηση παραμέτρους, οι οποίες μοντελοποιούν τις ιδιότητες της αραιότητας και μη αρνητικότητας του διανύσματος των ποσοστών. Στη συνέχεια, εξάγεται νέος επαναληπτικός αλγόριθμος συμπερασμού κατά Bayes, ονόματι BI-ICE-single, που παράγει αραιές μη αρνητικές εκτιμήσεις του διανύσματος ποσοστών. Τέλος, περιγράφεται μια νέα απλή τεχνική, η οποία λαμβάνει υπ' όψιν της την πιθανή χωρική συσχέτιση γειτονικών εικονοστοιχείων της υπερφασματικής εικόνας. Πειραματικά φαίνεται ότι ο BI-ICE-single δεν παρουσιάζει την ακρίβεια στην εκτίμηση της μεθόδου BI-ICE, στην περίπτωση όπου οι φασματικές υπογραφές των υλικών παρουσιάζουν υψηλή συσχέτιση. Αντίθετα, όταν η συσχέτιση είναι χαμηλή, οι δύο αλγόριθμοι παρουσιάζουν παρόμοια συμπεριφορά. Επιπλέον, η προαναφερόμενη προτεινόμενη τεχνική οδηγεί σε σημαντική εξοικονόμηση υπολογιστικής ισχύος, χωρίς να υστερεί στην ποιότητα σε σχέση με την περίπτωση που η πιθανή χωρική συσχέτιση αγνοείται.In this thesis, the problem of semisupervised hyperspectral unmixing is considered, where the spectral signatures of some materials are known and the aim during the analysis of a specific pixel is to determine both the materials that contribute to the composition of the pixel and the vector containing the abundance fractions of them in the composition. Adopting the linear mixture model for the examined hyperspectral image, a hierarchical Bayesian approach suitable for semisupervised hyperspectral unmixing is proposed, where suitable priors are selected for the model parameters, such that they favor sparse solutions for the abundance vector and they ensure the non-negativity of the abundances. Then, a new Bayesian inference iterative scheme, named BI-ICE-single, is developed, which produces sparse estimations for the abundance vector. Finally, a new simple technique is described, which takes into account the possible spatial correlation between adjacent pixels of the hyperspectral image. Experimental results illustrate that the BI-ICE-single algorithm does not present the estimation accuracy of BI-ICE method, in the case where the spectral signatures of the endmembers are highly correlated. On the contrary, the two algorithms exhibit similar performance, when the correlation is low. In addition, the proposed technique offers significant computational savings, without leading to inferior quality results compared to the case where the possible spatial correlation is ignored

Sparse representation based hyperspectral image compression and classification

Abstract This thesis presents a research work on applying sparse representation to lossy hyperspectral image compression and hyperspectral image classification. The proposed lossy hyperspectral image compression framework introduces two types of dictionaries distinguished by the terms sparse representation spectral dictionary (SRSD) and multi-scale spectral dictionary (MSSD), respectively. The former is learnt in the spectral domain to exploit the spectral correlations, and the latter in wavelet multi-scale spectral domain to exploit both spatial and spectral correlations in hyperspectral images. To alleviate the computational demand of dictionary learning, either a base dictionary trained offline or an update of the base dictionary is employed in the compression framework. The proposed compression method is evaluated in terms of different objective metrics, and compared to selected state-of-the-art hyperspectral image compression schemes, including JPEG 2000. The numerical results demonstrate the effectiveness and competitiveness of both SRSD and MSSD approaches. For the proposed hyperspectral image classification method, we utilize the sparse coefficients for training support vector machine (SVM) and k-nearest neighbour (kNN) classifiers. In particular, the discriminative character of the sparse coefficients is enhanced by incorporating contextual information using local mean filters. The classification performance is evaluated and compared to a number of similar or representative methods. The results show that our approach could outperform other approaches based on SVM or sparse representation. This thesis makes the following contributions. It provides a relatively thorough investigation of applying sparse representation to lossy hyperspectral image compression. Specifically, it reveals the effectiveness of sparse representation for the exploitation of spectral correlations in hyperspectral images. In addition, we have shown that the discriminative character of sparse coefficients can lead to superior performance in hyperspectral image classification.EM201