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 EURASIP Journal on Advances in Signal Processing , 2011, Abstract: For the instrument limitation and imperfect imaging optics, it is difficult to acquire high spatial resolution hyperspectral imagery. Low spatial resolution will result in a lot of mixed pixels and greatly degrade the detection and recognition performance, affect the related application in civil and military fields. As a powerful statistical image modeling technique, sparse representation can be utilized to analyze the hyperspectral image efficiently. Hyperspectral imagery is intrinsically sparse in spatial and spectral domains, and image super-resolution quality largely depends on whether the prior knowledge is utilized properly. In this article, we propose a novel hyperspectral imagery super-resolution method by utilizing the sparse representation and spectral mixing model. Based on the sparse representation model and hyperspectral image acquisition process model, small patches of hyperspectral observations from different wavelengths can be represented as weighted linear combinations of a small number of atoms in pre-trained dictionary. Then super-resolution is treated as a least squares problem with sparse constraints. To maintain the spectral consistency, we further introduce an adaptive regularization terms into the sparse representation framework by combining the linear spectrum mixing model. Extensive experiments validate that the proposed method achieves much better results.
 Computer Science , 2014, Abstract: This paper introduces a graph Laplacian regularization in the hyperspectral unmixing formulation. The proposed regularization relies upon the construction of a graph representation of the hyperspectral image. Each node in the graph represents a pixel's spectrum, and edges connect spectrally and spatially similar pixels. The proposed graph framework promotes smoothness in the estimated abundance maps and collaborative estimation between homogeneous areas of the image. The resulting convex optimization problem is solved using the Alternating Direction Method of Multipliers (ADMM). A special attention is given to the computational complexity of the algorithm, and Graph-cut methods are proposed in order to reduce the computational burden. Finally, simulations conducted on synthetic data illustrate the effectiveness of the graph Laplacian regularization with respect to other classical regularizations for hyperspectral unmixing.
 Statistics , 2009, Abstract: We use convex relaxation techniques to provide a sequence of solutions to the matrix completion problem. Using the nuclear norm as a regularizer, we provide simple and very efficient algorithms for minimizing the reconstruction error subject to a bound on the nuclear norm. Our algorithm iteratively replaces the missing elements with those obtained from a thresholded SVD. With warm starts this allows us to efficiently compute an entire regularization path of solutions.
 Computer Science , 2015, Abstract: This paper considers the problem of knowledge inference on large-scale imperfect repositories with incomplete coverage by means of embedding entities and relations at the first attempt. We propose IIKE (Imperfect and Incomplete Knowledge Embedding), a probabilistic model which measures the probability of each belief, i.e. $\langle h,r,t\rangle$, in large-scale knowledge bases such as NELL and Freebase, and our objective is to learn a better low-dimensional vector representation for each entity ($h$ and $t$) and relation ($r$) in the process of minimizing the loss of fitting the corresponding confidence given by machine learning (NELL) or crowdsouring (Freebase), so that we can use $||{\bf h} + {\bf r} - {\bf t}||$ to assess the plausibility of a belief when conducting inference. We use subsets of those inexact knowledge bases to train our model and test the performances of link prediction and triplet classification on ground truth beliefs, respectively. The results of extensive experiments show that IIKE achieves significant improvement compared with the baseline and state-of-the-art approaches.
 Computer Science , 2015, Abstract: We present a supervised hyperspectral image segmentation algorithm based on a convex formulation of a marginal maximum a posteriori segmentation with hidden fields and structure tensor regularization: Segmentation via the Constraint Split Augmented Lagrangian Shrinkage by Structure Tensor Regularization (SegSALSA-STR). This formulation avoids the generally discrete nature of segmentation problems and the inherent NP-hardness of the integer optimization associated. We extend the Segmentation via the Constraint Split Augmented Lagrangian Shrinkage (SegSALSA) algorithm by generalizing the vectorial total variation prior using a structure tensor prior constructed from a patch-based Jacobian. The resulting algorithm is convex, time-efficient and highly parallelizable. This shows the potential of combining hidden fields with convex optimization through the inclusion of different regularizers. The SegSALSA-STR algorithm is validated in the segmentation of real hyperspectral images.
 Mathematics , 2005, Abstract: Suppose we wish to recover an n-dimensional real-valued vector x_0 (e.g. a digital signal or image) from incomplete and contaminated observations y = A x_0 + e; A is a n by m matrix with far fewer rows than columns (n << m) and e is an error term. Is it possible to recover x_0 accurately based on the data y? To recover x_0, we consider the solution x* to the l1-regularization problem min \|x\|_1 subject to \|Ax-y\|_2 <= epsilon, where epsilon is the size of the error term e. We show that if A obeys a uniform uncertainty principle (with unit-normed columns) and if the vector x_0 is sufficiently sparse, then the solution is within the noise level \|x* - x_0\|_2 \le C epsilon. As a first example, suppose that A is a Gaussian random matrix, then stable recovery occurs for almost all such A's provided that the number of nonzeros of x_0 is of about the same order as the number of observations. Second, suppose one observes few Fourier samples of x_0, then stable recovery occurs for almost any set of p coefficients provided that the number of nonzeros is of the order of n/[\log m]^6. In the case where the error term vanishes, the recovery is of course exact, and this work actually provides novel insights on the exact recovery phenomenon discussed in earlier papers. The methodology also explains why one can also very nearly recover approximately sparse signals.
 Statistics , 2013, Abstract: Incorporating spatial information into hyperspectral unmixing procedures has been shown to have positive effects, due to the inherent spatial-spectral duality in hyperspectral scenes. Current research works that consider spatial information are mainly focused on the linear mixing model. In this paper, we investigate a variational approach to incorporating spatial correlation into a nonlinear unmixing procedure. A nonlinear algorithm operating in reproducing kernel Hilbert spaces, associated with an $\ell_1$ local variation norm as the spatial regularizer, is derived. Experimental results, with both synthetic and real data, illustrate the effectiveness of the proposed scheme.
 Sensors , 2015, DOI: 10.3390/s150102041 Abstract: Due to the instrumental and imaging optics limitations, it is difficult to acquire high spatial resolution hyperspectral imagery (HSI). Super-resolution (SR) imagery aims at inferring high quality images of a given scene from degraded versions of the same scene. This paper proposes a novel hyperspectral imagery super-resolution (HSI-SR) method via dictionary learning and spatial-spectral regularization. The main contributions of this paper are twofold. First, inspired by the compressive sensing (CS) framework, for learning the high resolution dictionary, we encourage stronger sparsity on image patches and promote smaller coherence between the learned dictionary and sensing matrix. Thus, a sparsity and incoherence restricted dictionary learning method is proposed to achieve higher efficiency sparse representation. Second, a variational regularization model combing a spatial sparsity regularization term and a new local spectral similarity preserving term is proposed to integrate the spectral and spatial-contextual information of the HSI. Experimental results show that the proposed method can effectively recover spatial information and better preserve spectral information. The high spatial resolution HSI reconstructed by the proposed method outperforms reconstructed results by other well-known methods in terms of both objective measurements and visual evaluation.
 Computer Science , 2015, Abstract: This paper tackles algorithmic and theoretical aspects of dictionary learning from incomplete and random block-wise image measurements and the performance of the adaptive dictionary for sparse image recovery. This problem is related to blind compressed sensing in which the sparsifying dictionary or basis is viewed as an unknown variable and subject to estimation during sparse recovery. However, unlike existing guarantees for a successful blind compressed sensing, our results do not rely on additional structural constraints on the learned dictionary or the measured signal. In particular, we rely on the spatial diversity of compressive measurements to guarantee that the solution is unique with a high probability. Moreover, our distinguishing goal is to measure and reduce the estimation error with respect to the ideal dictionary that is based on the complete image. Using recent results from random matrix theory, we show that applying a slightly modified dictionary learning algorithm over compressive measurements results in accurate estimation of the ideal dictionary for large-scale images. Empirically, we experiment with both space-invariant and space-varying sensing matrices and demonstrate the critical role of spatial diversity in measurements. Simulation results confirm that the presented algorithm outperforms the typical non-adaptive sparse recovery based on offline-learned universal dictionaries.
 Mathematics , 2014, Abstract: Sparse regression methods have been proven effective in a wide range of signal processing problems such as image compression, speech coding, channel equalization, linear regression and classification. In this paper we develop a new method of hyperspectral image classification based on the sparse unmixing algorithm SUnSAL for which a pixel adaptive L1-norm regularization term is introduced. To further enhance class separability, the algorithm is kernelized using a RBF kernel and the final results are improved by a combination of spatial pre and post-processing operations. We show that our method is competitive with state of the art algorithms such as SVM-CK, KLR-CK, KSOMP and KSSP.
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