A convex formulation for hyperspectral image superresolution via subspace-based regularization

Hyperspectral remote sensing images (HSIs) usually have high spectral resolution and low spatial resolution. Conversely, multispectral images (MSIs) usually have low spectral and high spatial resolutions. The problem of inferring images which combine the high spectral and high spatial resolutions of HSIs and MSIs, respectively, is a data fusion problem that has been the focus of recent active research due to the increasing availability of HSIs and MSIs retrieved from the same geographical area. We formulate this problem as the minimization of a convex objective function containing two quadratic data-fitting terms and an edge-preserving regularizer. The data-fitting terms account for blur, different resolutions, and additive noise. The regularizer, a form of vector Total Variation, promotes piecewise-smooth solutions with discontinuities aligned across the hyperspectral bands. The downsampling operator accounting for the different spatial resolutions, the non-quadratic and non-smooth nature of the regularizer, and the very large size of the HSI to be estimated lead to a hard optimization problem. We deal with these difficulties by exploiting the fact that HSIs generally "live" in a low-dimensional subspace and by tailoring the Split Augmented Lagrangian Shrinkage Algorithm (SALSA), which is an instance of the Alternating Direction Method of Multipliers (ADMM), to this optimization problem, by means of a convenient variable splitting. The spatial blur and the spectral linear operators linked, respectively, with the HSI and MSI acquisition processes are also estimated, and we obtain an effective algorithm that outperforms the state-of-the-art, as illustrated in a series of experiments with simulated and real-life data.Comment: IEEE Trans. Geosci. Remote Sens., to be publishe

Maximum-a-posteriori estimation with Bayesian confidence regions

Solutions to inverse problems that are ill-conditioned or ill-posed may have significant intrinsic uncertainty. Unfortunately, analysing and quantifying this uncertainty is very challenging, particularly in high-dimensional problems. As a result, while most modern mathematical imaging methods produce impressive point estimation results, they are generally unable to quantify the uncertainty in the solutions delivered. This paper presents a new general methodology for approximating Bayesian high-posterior-density credibility regions in inverse problems that are convex and potentially very high-dimensional. The approximations are derived by using recent concentration of measure results related to information theory for log-concave random vectors. A remarkable property of the approximations is that they can be computed very efficiently, even in large-scale problems, by using standard convex optimisation techniques. In particular, they are available as a by-product in problems solved by maximum-a-posteriori estimation. The approximations also have favourable theoretical properties, namely they outer-bound the true high-posterior-density credibility regions, and they are stable with respect to model dimension. The proposed methodology is illustrated on two high-dimensional imaging inverse problems related to tomographic reconstruction and sparse deconvolution, where the approximations are used to perform Bayesian hypothesis tests and explore the uncertainty about the solutions, and where proximal Markov chain Monte Carlo algorithms are used as benchmark to compute exact credible regions and measure the approximation error

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

Application of Deep Learning Approaches for Enhancing Mastcam Images

There are two mast cameras (Mastcam) onboard the Mars rover Curiosity. Both Mastcams are multispectral imagers with nine bands in each. The right Mastcam has three times higher resolution than the left. In this chapter, we apply some recently developed deep neural network models to enhance the left Mastcam images with help from the right Mastcam images. Actual Mastcam images were used to demonstrate the performance of the proposed algorithms

AN IMPROVED VARIATIONAL METHOD FOR HYPERSPECTRAL IMAGE PANSHARPENING WITH THE CONSTRAINT OF SPECTRAL DIFFERENCE MINIMIZATION

Variational pansharpening can enhance the spatial resolution of a hyperspectral (HS) image using a high-resolution panchromatic (PAN) image. However, this technology may lead to spectral distortion that obviously affect the accuracy of data analysis. In this article, we propose an improved variational method for HS image pansharpening with the constraint of spectral difference minimization. We extend the energy function of the classic variational pansharpening method by adding a new spectral fidelity term. This fidelity term is designed following the definition of spectral angle mapper, which means that for every pixel, the spectral difference value of any two bands in the HS image is in equal proportion to that of the two corresponding bands in the pansharpened image. Gradient descent method is adopted to find the optimal solution of the modified energy function, and the pansharpened image can be reconstructed. Experimental results demonstrate that the constraint of spectral difference minimization is able to preserve the original spectral information well in HS images, and reduce the spectral distortion effectively. Compared to original variational method, our method performs better in both visual and quantitative evaluation, and achieves a good trade-off between spatial and spectral information