A Non-Local Structure Tensor Based Approach for Multicomponent Image Recovery Problems

Non-Local Total Variation (NLTV) has emerged as a useful tool in variational methods for image recovery problems. In this paper, we extend the NLTV-based regularization to multicomponent images by taking advantage of the Structure Tensor (ST) resulting from the gradient of a multicomponent image. The proposed approach allows us to penalize the non-local variations, jointly for the different components, through various $\ell_{1,p}$ matrix norms with $p \ge 1$. To facilitate the choice of the hyper-parameters, we adopt a constrained convex optimization approach in which we minimize the data fidelity term subject to a constraint involving the ST-NLTV regularization. The resulting convex optimization problem is solved with a novel epigraphical projection method. This formulation can be efficiently implemented thanks to the flexibility offered by recent primal-dual proximal algorithms. Experiments are carried out for multispectral and hyperspectral images. The results demonstrate the interest of introducing a non-local structure tensor regularization and show that the proposed approach leads to significant improvements in terms of convergence speed over current state-of-the-art 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

Denoising of Hyperspectral Images Using Group Low-Rank Representation

Hyperspectral images (HSIs) have been used in a wide range of fields, such as agriculture, food safety, mineralogy and environment monitoring, but being corrupted by various kinds of noise limits its efficacy. Low-rank representation (LRR) has proved its effectiveness in the denoising of HSIs. However, it just employs local information for denoising, which results in ineffectiveness when local noise is heavy. In this paper, we propose an approach of group low-rank representation (GLRR) for the HSI denoising. In our GLRR, a corrupted HSI is divided into overlapping patches, the similar patches are combined into a group, and the group is reconstructed as a whole using LRR. The proposed method enables the exploitation of both the local similarity within a patch and the nonlocal similarity across the patches in a group simultaneously. The additional nonlocallysimilar patches can bring in extra structural information to the corrupted patches, facilitating the detection of noise as outliers. LRR is applied to the group of patches, as the uncorrupted patches enjoy intrinsic low-rank structure. The effectiveness of the proposed GLRR method is demonstrated qualitatively and quantitatively by using both simulated and real-world data in experiments

Adaptive Regularized Low-Rank Tensor Decomposition for Hyperspectral Image Denoising and Destriping

Hyperspectral images (HSIs) are inevitably degraded by a mixture of various types of noise, such as Gaussian noise, impulse noise, stripe noise, and dead pixels, which greatly limits the subsequent applications. Although various denoising methods have already been developed, accurately recovering the spatial-spectral structure of HSIs remains a challenging problem to be addressed. Furthermore, serious stripe noise, which is common in real HSIs, is still not fully separated by the previous models. In this paper, we propose an adaptive hyperLaplacian regularized low-rank tensor decomposition (LRTDAHL) method for HSI denoising and destriping. On the one hand, the stripe noise is separately modeled by the tensor decomposition, which can effectively encode the spatial-spectral correlation of the stripe noise. On the other hand, adaptive hyper-Laplacian spatial-spectral regularization is introduced to represent the distribution structure of different HSI gradient data by adaptively estimating the optimal hyper-Laplacian parameter, which can reduce the spatial information loss and over-smoothing caused by the previous total variation regularization. The proposed model is solved using the alternating direction method of multipliers (ADMM) algorithm. Extensive simulation and real-data experiments all demonstrate the effectiveness and superiority of the proposed method

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