Simultaneous Spectral-Spatial Feature Selection and Extraction for Hyperspectral Images

In hyperspectral remote sensing data mining, it is important to take into account of both spectral and spatial information, such as the spectral signature, texture feature and morphological property, to improve the performances, e.g., the image classification accuracy. In a feature representation point of view, a nature approach to handle this situation is to concatenate the spectral and spatial features into a single but high dimensional vector and then apply a certain dimension reduction technique directly on that concatenated vector before feed it into the subsequent classifier. However, multiple features from various domains definitely have different physical meanings and statistical properties, and thus such concatenation hasn't efficiently explore the complementary properties among different features, which should benefit for boost the feature discriminability. Furthermore, it is also difficult to interpret the transformed results of the concatenated vector. Consequently, finding a physically meaningful consensus low dimensional feature representation of original multiple features is still a challenging task. In order to address the these issues, we propose a novel feature learning framework, i.e., the simultaneous spectral-spatial feature selection and extraction algorithm, for hyperspectral images spectral-spatial feature representation and classification. Specifically, the proposed method learns a latent low dimensional subspace by projecting the spectral-spatial feature into a common feature space, where the complementary information has been effectively exploited, and simultaneously, only the most significant original features have been transformed. Encouraging experimental results on three public available hyperspectral remote sensing datasets confirm that our proposed method is effective and efficient

Interpretable Hyperspectral AI: When Non-Convex Modeling meets Hyperspectral Remote Sensing

Hyperspectral imaging, also known as image spectrometry, is a landmark technique in geoscience and remote sensing (RS). In the past decade, enormous efforts have been made to process and analyze these hyperspectral (HS) products mainly by means of seasoned experts. However, with the ever-growing volume of data, the bulk of costs in manpower and material resources poses new challenges on reducing the burden of manual labor and improving efficiency. For this reason, it is, therefore, urgent to develop more intelligent and automatic approaches for various HS RS applications. Machine learning (ML) tools with convex optimization have successfully undertaken the tasks of numerous artificial intelligence (AI)-related applications. However, their ability in handling complex practical problems remains limited, particularly for HS data, due to the effects of various spectral variabilities in the process of HS imaging and the complexity and redundancy of higher dimensional HS signals. Compared to the convex models, non-convex modeling, which is capable of characterizing more complex real scenes and providing the model interpretability technically and theoretically, has been proven to be a feasible solution to reduce the gap between challenging HS vision tasks and currently advanced intelligent data processing models

Deep learning model-aware regulatization with applications to Inverse Problems

There are various inverse problems – including reconstruction problems arising in medical imaging - where one is often aware of the forward operator that maps variables of interest to the observations. It is therefore natural to ask whether such knowledge of the forward operator can be exploited in deep learning approaches increasingly used to solve inverse problems. In this paper, we provide one such way via an analysis of the generalisation error of deep learning approaches to inverse problems. In particular, by building on the algorithmic robustness framework, we offer a generalisation error bound that encapsulates key ingredients associated with the learning problem such as the complexity of the data space, the size of the training set, the Jacobian of the deep neural network and the Jacobian of the composition of the forward operator with the neural network. We then propose a ‘plug-and-play’ regulariser that leverages the knowledge of the forward map to improve the generalization of the network. We likewise also use a new method allowing us to tightly upper bound the Jacobians of the relevant operators that is much more computationally efficient than existing ones. We demonstrate the efficacy of our model-aware regularised deep learning algorithms against other state-of-the-art approaches on inverse problems involving various sub-sampling operators such as those used in classical compressed sensing tasks, image super-resolution problems and accelerated Magnetic Resonance Imaging (MRI) setups

Sparse Modeling for Image and Vision Processing

In recent years, a large amount of multi-disciplinary research has been conducted on sparse models and their applications. In statistics and machine learning, the sparsity principle is used to perform model selection---that is, automatically selecting a simple model among a large collection of them. In signal processing, sparse coding consists of representing data with linear combinations of a few dictionary elements. Subsequently, the corresponding tools have been widely adopted by several scientific communities such as neuroscience, bioinformatics, or computer vision. The goal of this monograph is to offer a self-contained view of sparse modeling for visual recognition and image processing. More specifically, we focus on applications where the dictionary is learned and adapted to data, yielding a compact representation that has been successful in various contexts.Comment: 205 pages, to appear in Foundations and Trends in Computer Graphics and Visio

Unsupervised spectral sub-feature learning for hyperspectral image classification

Spectral pixel classification is one of the principal techniques used in hyperspectral image (HSI) analysis. In this article, we propose an unsupervised feature learning method for classification of hyperspectral images. The proposed method learns a dictionary of sub-feature basis representations from the spectral domain, which allows effective use of the correlated spectral data. The learned dictionary is then used in encoding convolutional samples from the hyperspectral input pixels to an expanded but sparse feature space. Expanded hyperspectral feature representations enable linear separation between object classes present in an image. To evaluate the proposed method, we performed experiments on several commonly used HSI data sets acquired at different locations and by different sensors. Our experimental results show that the proposed method outperforms other pixel-wise classification methods that make use of unsupervised feature extraction approaches. Additionally, even though our approach does not use any prior knowledge, or labelled training data to learn features, it yields either advantageous, or comparable, results in terms of classification accuracy with respect to recent semi-supervised methods

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

Nonconvex Nonsmooth Low-Rank Minimization via Iteratively Reweighted Nuclear Norm

The nuclear norm is widely used as a convex surrogate of the rank function in compressive sensing for low rank matrix recovery with its applications in image recovery and signal processing. However, solving the nuclear norm based relaxed convex problem usually leads to a suboptimal solution of the original rank minimization problem. In this paper, we propose to perform a family of nonconvex surrogates of $L_0$-norm on the singular values of a matrix to approximate the rank function. This leads to a nonconvex nonsmooth minimization problem. Then we propose to solve the problem by Iteratively Reweighted Nuclear Norm (IRNN) algorithm. IRNN iteratively solves a Weighted Singular Value Thresholding (WSVT) problem, which has a closed form solution due to the special properties of the nonconvex surrogate functions. We also extend IRNN to solve the nonconvex problem with two or more blocks of variables. In theory, we prove that IRNN decreases the objective function value monotonically, and any limit point is a stationary point. Extensive experiments on both synthesized data and real images demonstrate that IRNN enhances the low-rank matrix recovery compared with state-of-the-art convex algorithms