Non-convex regularization in remote sensing

In this paper, we study the effect of different regularizers and their implications in high dimensional image classification and sparse linear unmixing. Although kernelization or sparse methods are globally accepted solutions for processing data in high dimensions, we present here a study on the impact of the form of regularization used and its parametrization. We consider regularization via traditional squared (2) and sparsity-promoting (1) norms, as well as more unconventional nonconvex regularizers (p and Log Sum Penalty). We compare their properties and advantages on several classification and linear unmixing tasks and provide advices on the choice of the best regularizer for the problem at hand. Finally, we also provide a fully functional toolbox for the community.Comment: 11 pages, 11 figure

Robust Constrained Hyperspectral Unmixing Using Reconstructed-Image Regularization

Hyperspectral (HS) unmixing is the process of decomposing an HS image into material-specific spectra (endmembers) and their spatial distributions (abundance maps). Existing unmixing methods have two limitations with respect to noise robustness. First, if the input HS image is highly noisy, even if the balance between sparse and piecewise-smooth regularizations for abundance maps is carefully adjusted, noise may remain in the estimated abundance maps or undesirable artifacts may appear. Second, existing methods do not explicitly account for the effects of stripe noise, which is common in HS measurements, in their formulations, resulting in significant degradation of unmixing performance when such noise is present in the input HS image. To overcome these limitations, we propose a new robust hyperspectral unmixing method based on constrained convex optimization. Our method employs, in addition to the two regularizations for the abundance maps, regularizations for the HS image reconstructed by mixing the estimated abundance maps and endmembers. This strategy makes the unmixing process much more robust in highly-noisy scenarios, under the assumption that the abundance maps used to reconstruct the HS image with desirable spatio-spectral structure are also expected to have desirable properties. Furthermore, our method is designed to accommodate a wider variety of noise including stripe noise. To solve the formulated optimization problem, we develop an efficient algorithm based on a preconditioned primal-dual splitting method, which can automatically determine appropriate stepsizes based on the problem structure. Experiments on synthetic and real HS images demonstrate the advantages of our method over existing methods.Comment: Submitted to IEEE Transactions on Geoscience and Remote Sensin

A Constrained Convex Optimization Approach to Hyperspectral Image Restoration with Hybrid Spatio-Spectral Regularization

We propose a new constrained optimization approach to hyperspectral (HS) image restoration. Most existing methods restore a desirable HS image by solving some optimization problem, which consists of a regularization term(s) and a data-fidelity term(s). The methods have to handle a regularization term(s) and a data-fidelity term(s) simultaneously in one objective function, and so we need to carefully control the hyperparameter(s) that balances these terms. However, the setting of such hyperparameters is often a troublesome task because their suitable values depend strongly on the regularization terms adopted and the noise intensities on a given observation. Our proposed method is formulated as a convex optimization problem, where we utilize a novel hybrid regularization technique named Hybrid Spatio-Spectral Total Variation (HSSTV) and incorporate data-fidelity as hard constraints. HSSTV has a strong ability of noise and artifact removal while avoiding oversmoothing and spectral distortion, without combining other regularizations such as low-rank modeling-based ones. In addition, the constraint-type data-fidelity enables us to translate the hyperparameters that balance between regularization and data-fidelity to the upper bounds of the degree of data-fidelity that can be set in a much easier manner. We also develop an efficient algorithm based on the alternating direction method of multipliers (ADMM) to efficiently solve the optimization problem. Through comprehensive experiments, we illustrate the advantages of the proposed method over various HS image restoration methods including state-of-the-art ones.Comment: 20 pages, 4 tables, 10 figures, submitted to MDPI Remote Sensin

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

A General Destriping Framework for Remote Sensing Images Using Flatness Constraint

This paper proposes a general destriping framework using flatness constraints, where we can handle various regularization functions in a unified manner. Removing stripe noise, i.e., destriping, from remote sensing images is an essential task in terms of visual quality and subsequent processing. Most of the existing methods are designed by combining a particular image regularization with a stripe noise characterization that cooperates with the regularization, which precludes us to examine different regularizations to adapt to various target images. To resolve this, we formulate the destriping problem as a convex optimization problem involving a general form of image regularization and the flatness constraints, a newly introduced stripe noise characterization. This strong characterization enables us to consistently capture the nature of stripe noise, regardless of the choice of image regularization. For solving the optimization problem, we also develop an efficient algorithm based on a diagonally preconditioned primal-dual splitting algorithm (DP-PDS), which can automatically adjust the stepsizes. The effectiveness of our framework is demonstrated through destriping experiments, where we comprehensively compare combinations of image regularizations and stripe noise characterizations using hyperspectral images (HSI) and infrared (IR) videos.Comment: submitted to IEEE Transactions on Geoscience and Remote Sensin

Cross-Attention in Coupled Unmixing Nets for Unsupervised Hyperspectral Super-Resolution

The recent advancement of deep learning techniques has made great progress on hyperspectral image super-resolution (HSI-SR). Yet the development of unsupervised deep networks remains challenging for this task. To this end, we propose a novel coupled unmixing network with a cross-attention mechanism, CUCaNet for short, to enhance the spatial resolution of HSI by means of higher-spatial-resolution multispectral image (MSI). Inspired by coupled spectral unmixing, a two-stream convolutional autoencoder framework is taken as backbone to jointly decompose MS and HS data into a spectrally meaningful basis and corresponding coefficients. CUCaNet is capable of adaptively learning spectral and spatial response functions from HS-MS correspondences by enforcing reasonable consistency assumptions on the networks. Moreover, a cross-attention module is devised to yield more effective spatial-spectral information transfer in networks. Extensive experiments are conducted on three widely-used HS-MS datasets in comparison with state-of-the-art HSI-SR models, demonstrating the superiority of the CUCaNet in the HSI-SR application. Furthermore, the codes and datasets will be available at: https://github.com/danfenghong/ECCV2020_CUCaNet

H2TF for Hyperspectral Image Denoising: Where Hierarchical Nonlinear Transform Meets Hierarchical Matrix Factorization

Recently, tensor singular value decomposition (t-SVD) has emerged as a promising tool for hyperspectral image (HSI) processing. In the t-SVD, there are two key building blocks: (i) the low-rank enhanced transform and (ii) the accompanying low-rank characterization of transformed frontal slices. Previous t-SVD methods mainly focus on the developments of (i), while neglecting the other important aspect, i.e., the exact characterization of transformed frontal slices. In this letter, we exploit the potentiality in both building blocks by leveraging the \underline{\bf H}ierarchical nonlinear transform and the \underline{\bf H}ierarchical matrix factorization to establish a new \underline{\bf T}ensor \underline{\bf F}actorization (termed as H2TF). Compared to shallow counter partners, e.g., low-rank matrix factorization or its convex surrogates, H2TF can better capture complex structures of transformed frontal slices due to its hierarchical modeling abilities. We then suggest the H2TF-based HSI denoising model and develop an alternating direction method of multipliers-based algorithm to address the resultant model. Extensive experiments validate the superiority of our method over state-of-the-art HSI denoising methods