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

Image Restoration for Remote Sensing: Overview and Toolbox

Remote sensing provides valuable information about objects or areas from a distance in either active (e.g., RADAR and LiDAR) or passive (e.g., multispectral and hyperspectral) modes. The quality of data acquired by remotely sensed imaging sensors (both active and passive) is often degraded by a variety of noise types and artifacts. Image restoration, which is a vibrant field of research in the remote sensing community, is the task of recovering the true unknown image from the degraded observed image. Each imaging sensor induces unique noise types and artifacts into the observed image. This fact has led to the expansion of restoration techniques in different paths according to each sensor type. This review paper brings together the advances of image restoration techniques with particular focuses on synthetic aperture radar and hyperspectral images as the most active sub-fields of image restoration in the remote sensing community. We, therefore, provide a comprehensive, discipline-specific starting point for researchers at different levels (i.e., students, researchers, and senior researchers) willing to investigate the vibrant topic of data restoration by supplying sufficient detail and references. Additionally, this review paper accompanies a toolbox to provide a platform to encourage interested students and researchers in the field to further explore the restoration techniques and fast-forward the community. The toolboxes are provided in https://github.com/ImageRestorationToolbox.Comment: This paper is under review in GRS

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

Image Fusion in Remote Sensing and Quality Evaluation of Fused Images

In remote sensing, acquired optical images of high spectral resolution have usually a lower spatial resolution than images of lower spectral resolution. This is due to physical, cost and complexity constraints. To make the most of the available imagery, many image fusion techniques have been developed to address this problem. Image fusion is an ill-posed inverse problem where an image of low spatial resolution and high spectral resolution is enhanced in spatial-resolution by using an auxiliary image of high spatial resolution and low spectral resolution. It is assumed that both images display the same scene and are properly co-registered. Thus, the problem is essentially to transfer details from the higher spatial resolution auxiliary image to the upscaled lower resolution image in a manner that minimizes the spatial and spectral distortion of the fused image. The most common image fusion problem is pansharpening, where a multispectral (MS) image is enhanced using wide-band panchromatic (PAN) image. A similar problem is the enhancement of a hyperspectral (HS) image by either a PAN image or an MS image. As there is no reference image available, the reliable quantitative evaluation of the quality of the fused image is a difficult problem. This thesis addresses the image fusion problem in three different ways and also addresses the problem of quantitative quality evaluation.Í fjarkönnun hafa myndir með háa rófsupplausn lægri rúmupplausn en myndir með lægri rófsupplausn vegna eðlisfræðilegra og kostnaðarlegra takmarkana. Til að auka upplýsingamagn slíkra mynda hafa verið þróaðar fjölmargar sambræðsluaðferðir á síðustu tveimur áratugum. Myndsambræðsla er illa framsett andhverft vandmál (e. inverse problem) þar sem rúmupplausn myndar af hárri rófsupplausn er aukin með því að nota upplýsingar frá mynd af hárri rúmupplausn og lægri rófsupplausn. Það er gert ráð fyrir að báðar myndir sýni nákvæmlega sama landsvæði. Þannig er vandamálið í eðli sínu að flytja fíngerða eiginleika myndar af hærri rúmupplausn yfir á mynd af lægri rúmupplausn sem hefur verið brúuð upp í stærð hinnar myndarinnar, án þess að skerða gæði rófsupplýsinga upphaflegu myndarinnar. Algengasta myndbræðsluvandamálið í fjarkönnun er svokölluð panskerpun (e. pansharpening) þar sem fjölrásamynd (e. multispectral image) er endurbætt í rúmi með svokallaðri víðbandsmynd (e. panchromatic image) sem hefur aðeins eina rás af hárri upplausn. Annað svipað vandamál er sambræðsla háfjölrásamyndar (e. hyperspectral image) og annaðhvort fjölrásamyndar eða víðbandsmyndar. Þar sem myndsambræðsla er andhverft vandmál er engin háupplausnar samanburðarmynd tiltæk, sem gerir mat á gæðum sambræddu myndarinnar að erfiðu vandamáli. Í þessari ritgerð eru kynntar þrjár aðferðir sem taka á myndsambræðlsu og einnig er fjallað um mat á gæðum sambræddra mynda, þá sérstaklega panskerptra mynda

Variational semi-blind sparse deconvolution with orthogonal kernel bases and its application to MRFM

We present a variational Bayesian method of joint image reconstruction and point spread function (PSF) estimation when the PSF of the imaging device is only partially known. To solve this semi-blind deconvolution problem, prior distributions are specified for the PSF and the 3D image. Joint image reconstruction and PSF estimation is then performed within a Bayesian framework, using a variational algorithm to estimate the posterior distribution. The image prior distribution imposes an explicit atomic measure that corresponds to image sparsity. Importantly, the proposed Bayesian deconvolution algorithm does not require hand tuning. Simulation results clearly demonstrate that the semi-blind deconvolution algorithm compares favorably with previous Markov chain Monte Carlo (MCMC) version of myopic sparse reconstruction. It significantly outperforms mismatched non-blind algorithms that rely on the assumption of the perfect knowledge of the PSF. The algorithm is illustrated on real data from magnetic resonance force microscopy (MRFM)

Variational semi-blind sparse deconvolution with orthogonal kernel bases and its application to MRFM

We present a variational Bayesian method of joint image reconstruction and point spread function (PSF) estimation when the PSF of the imaging device is only partially known. To solve this semi-blind deconvolution problem, prior distributions are specified for the PSF and the 3D image. Joint image reconstruction and PSF estimation is then performed within a Bayesian framework, using a variational algorithm to estimate the posterior distribution. The image prior distribution imposes an explicit atomic measure that corresponds to image sparsity. Importantly, the proposed Bayesian deconvolution algorithm does not require hand tuning. Simulation results clearly demonstrate that the semi-blind deconvolution algorithm compares favorably with previous Markov chain Monte Carlo (MCMC) version of myopic sparse reconstruction. It significantly outperforms mismatched non-blind algorithms that rely on the assumption of the perfect knowledge of the PSF. The algorithm is illustrated on real data from magnetic resonance force microscopy (MRFM)

Dimensionality reduction for hyperspectral data

This thesis is about dimensionality reduction for hyperspectral data. Special emphasis is given to dimensionality reduction techniques known as kernel eigenmap methods and manifold learning algorithms. Kernel eigenmap methods require a nearest neighbor or a radius parameter be set. A new algorithm that does not require these neighborhood parameters is given. Most kernel eigenmap methods use the eigenvectors of the kernel as coordinates for the data. An algorithm that uses the frame potential along with subspace frames to create nonorthogonal coordinates is given. The algorithms are demonstrated on hyperspectral data. The last two chapters include analysis of representation systems for LIDAR data and motion blur estimation, respectively