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

Multispectral and Hyperspectral Image Fusion by MS/HS Fusion Net

Hyperspectral imaging can help better understand the characteristics of different materials, compared with traditional image systems. However, only high-resolution multispectral (HrMS) and low-resolution hyperspectral (LrHS) images can generally be captured at video rate in practice. In this paper, we propose a model-based deep learning approach for merging an HrMS and LrHS images to generate a high-resolution hyperspectral (HrHS) image. In specific, we construct a novel MS/HS fusion model which takes the observation models of low-resolution images and the low-rankness knowledge along the spectral mode of HrHS image into consideration. Then we design an iterative algorithm to solve the model by exploiting the proximal gradient method. And then, by unfolding the designed algorithm, we construct a deep network, called MS/HS Fusion Net, with learning the proximal operators and model parameters by convolutional neural networks. Experimental results on simulated and real data substantiate the superiority of our method both visually and quantitatively as compared with state-of-the-art methods along this line of research.Comment: 10 pages, 7 figure

Deep Plug-and-Play Prior for Hyperspectral Image Restoration

Deep-learning-based hyperspectral image (HSI) restoration methods have gained great popularity for their remarkable performance but often demand expensive network retraining whenever the specifics of task changes. In this paper, we propose to restore HSIs in a unified approach with an effective plug-and-play method, which can jointly retain the flexibility of optimization-based methods and utilize the powerful representation capability of deep neural networks. Specifically, we first develop a new deep HSI denoiser leveraging gated recurrent convolution units, short- and long-term skip connections, and an augmented noise level map to better exploit the abundant spatio-spectral information within HSIs. It, therefore, leads to the state-of-the-art performance on HSI denoising under both Gaussian and complex noise settings. Then, the proposed denoiser is inserted into the plug-and-play framework as a powerful implicit HSI prior to tackle various HSI restoration tasks. Through extensive experiments on HSI super-resolution, compressed sensing, and inpainting, we demonstrate that our approach often achieves superior performance, which is competitive with or even better than the state-of-the-art on each task, via a single model without any task-specific training.Comment: code at https://github.com/Zeqiang-Lai/DPHSI

A Tensor-Based Dictionary Learning Approach to Tomographic Image Reconstruction

We consider tomographic reconstruction using priors in the form of a dictionary learned from training images. The reconstruction has two stages: first we construct a tensor dictionary prior from our training data, and then we pose the reconstruction problem in terms of recovering the expansion coefficients in that dictionary. Our approach differs from past approaches in that a) we use a third-order tensor representation for our images and b) we recast the reconstruction problem using the tensor formulation. The dictionary learning problem is presented as a non-negative tensor factorization problem with sparsity constraints. The reconstruction problem is formulated in a convex optimization framework by looking for a solution with a sparse representation in the tensor dictionary. Numerical results show that our tensor formulation leads to very sparse representations of both the training images and the reconstructions due to the ability of representing repeated features compactly in the dictionary.Comment: 29 page

A Low-rank Tensor Regularization Strategy for Hyperspectral Unmixing

Tensor-based methods have recently emerged as a more natural and effective formulation to address many problems in hyperspectral imaging. In hyperspectral unmixing (HU), low-rank constraints on the abundance maps have been shown to act as a regularization which adequately accounts for the multidimensional structure of the underlying signal. However, imposing a strict low-rank constraint for the abundance maps does not seem to be adequate, as important information that may be required to represent fine scale abundance behavior may be discarded. This paper introduces a new low-rank tensor regularization that adequately captures the low-rank structure underlying the abundance maps without hindering the flexibility of the solution. Simulation results with synthetic and real data show that the the extra flexibility introduced by the proposed regularization significantly improves the unmixing results

Non-local tensor completion for multitemporal remotely sensed images inpainting

Remotely sensed images may contain some missing areas because of poor weather conditions and sensor failure. Information of those areas may play an important role in the interpretation of multitemporal remotely sensed data. The paper aims at reconstructing the missing information by a non-local low-rank tensor completion method (NL-LRTC). First, nonlocal correlations in the spatial domain are taken into account by searching and grouping similar image patches in a large search window. Then low-rankness of the identified 4-order tensor groups is promoted to consider their correlations in spatial, spectral, and temporal domains, while reconstructing the underlying patterns. Experimental results on simulated and real data demonstrate that the proposed method is effective both qualitatively and quantitatively. In addition, the proposed method is computationally efficient compared to other patch based methods such as the recent proposed PM-MTGSR method

Mixture-Net: Low-Rank Deep Image Prior Inspired by Mixture Models for Spectral Image Recovery

This paper proposes a non-data-driven deep neural network for spectral image recovery problems such as denoising, single hyperspectral image super-resolution, and compressive spectral imaging reconstruction. Unlike previous methods, the proposed approach, dubbed Mixture-Net, implicitly learns the prior information through the network. Mixture-Net consists of a deep generative model whose layers are inspired by the linear and non-linear low-rank mixture models, where the recovered image is composed of a weighted sum between the linear and non-linear decomposition. Mixture-Net also provides a low-rank decomposition interpreted as the spectral image abundances and endmembers, helpful in achieving remote sensing tasks without running additional routines. The experiments show the MixtureNet effectiveness outperforming state-of-the-art methods in recovery quality with the advantage of architecture interpretability