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

Robust hyperspectral image classification with rejection fields

In this paper we present a novel method for robust hyperspectral image classification using context and rejection. Hyperspectral image classification is generally an ill-posed image problem where pixels may belong to unknown classes, and obtaining representative and complete training sets is costly. Furthermore, the need for high classification accuracies is frequently greater than the need to classify the entire image. We approach this problem with a robust classification method that combines classification with context with classification with rejection. A rejection field that will guide the rejection is derived from the classification with contextual information obtained by using the SegSALSA algorithm. We validate our method in real hyperspectral data and show that the performance gains obtained from the rejection fields are equivalent to an increase the dimension of the training sets.Comment: This paper was submitted to IEEE WHISPERS 2015: 7th Workshop on Hyperspectral Image and Signal Processing: Evolution on Remote Sensing. 5 pages, 1 figure, 2 table

Application of Least Square Denoising to Improve ADMM Based Hyperspectral Image Classification

AbstractHyperspectral images contain a huge amount of spatial and spectral information so that, almost any type of Earth feature can be discriminated from any other feature. But, for this classification to be possible, it is to be ensured that there is as less noise as possible in the captured data. Unfortunately, noise is unavoidable in nature and most hyperspectral images need denoising before they can be processed for classification work. In this paper, we are presenting a new approach for denoising hyperspectral images based on Least Square Regularization. Then, the hyperspectral data is classified using Basis Pursuit classifier, a constrained L1 minimization problem. To improve the time requirement for classification, Alternating Direction Method of Multipliers (ADMM) solver is used instead of CVX (convex optimization) solver. The method proposed is compared with other existing denoising methods such as Legendre-Fenchel (LF), Wavelet thresholding and Total Variation (TV). It is observed that the proposed Least Square (LS) denoising method improves classification accuracy much better than other existing denoising techniques. Even with fewer training sets, the proposed denoising technique yields better classification accuracy, thus proving least square denoising to be a powerful denoising technique

A 3-stage Spectral-spatial Method for Hyperspectral Image Classification

Hyperspectral images often have hundreds of spectral bands of different wavelengths captured by aircraft or satellites that record land coverage. Identifying detailed classes of pixels becomes feasible due to the enhancement in spectral and spatial resolution of hyperspectral images. In this work, we propose a novel framework that utilizes both spatial and spectral information for classifying pixels in hyperspectral images. The method consists of three stages. In the first stage, the pre-processing stage, Nested Sliding Window algorithm is used to reconstruct the original data by {enhancing the consistency of neighboring pixels} and then Principal Component Analysis is used to reduce the dimension of data. In the second stage, Support Vector Machines are trained to estimate the pixel-wise probability map of each class using the spectral information from the images. Finally, a smoothed total variation model is applied to smooth the class probability vectors by {ensuring spatial connectivity} in the images. We demonstrate the superiority of our method against three state-of-the-art algorithms on six benchmark hyperspectral data sets with 10 to 50 training labels for each class. The results show that our method gives the overall best performance in accuracy. Especially, our gain in accuracy increases when the number of labeled pixels decreases and therefore our method is more advantageous to be applied to problems with small training set. Hence it is of great practical significance since expert annotations are often expensive and difficult to collect.Comment: 18 pages, 9 figure

From representation learning to thematic classification - Application to hierarchical analysis of hyperspectral images

Numerous frameworks have been developed in order to analyze the increasing amount of available image data. Among those methods, supervised classification has received considerable attention leading to the development of state-of-the-art classification methods. These methods aim at inferring the class of each observation given a specific class nomenclature by exploiting a set of labeled observations. Thanks to extensive research efforts of the community, classification methods have become very efficient. Nevertheless, the results of a classification remains a highlevel interpretation of the scene since it only gives a single class to summarize all information in a given pixel. Contrary to classification methods, representation learning methods are model-based approaches designed especially to handle high-dimensional data and extract meaningful latent variables. By using physic-based models, these methods allow the user to extract very meaningful variables and get a very detailed interpretation of the considered image. The main objective of this thesis is to develop a unified framework for classification and representation learning. These two methods provide complementary approaches allowing to address the problem using a hierarchical modeling approach. The representation learning approach is used to build a low-level model of the data whereas classification is used to incorporate supervised information and may be seen as a high-level interpretation of the data. Two different paradigms, namely Bayesian models and optimization approaches, are explored to set up this hierarchical model. The proposed models are then tested in the specific context of hyperspectral imaging where the representation learning task is specified as a spectral unmixing proble