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

Hierarchical Bayesian sparse image reconstruction with application to MRFM

This paper presents a hierarchical Bayesian model to reconstruct sparse images when the observations are obtained from linear transformations and corrupted by an additive white Gaussian noise. Our hierarchical Bayes model is well suited to such naturally sparse image applications as it seamlessly accounts for properties such as sparsity and positivity of the image via appropriate Bayes priors. We propose a prior that is based on a weighted mixture of a positive exponential distribution and a mass at zero. The prior has hyperparameters that are tuned automatically by marginalization over the hierarchical Bayesian model. To overcome the complexity of the posterior distribution, a Gibbs sampling strategy is proposed. The Gibbs samples can be used to estimate the image to be recovered, e.g. by maximizing the estimated posterior distribution. In our fully Bayesian approach the posteriors of all the parameters are available. Thus our algorithm provides more information than other previously proposed sparse reconstruction methods that only give a point estimate. The performance of our hierarchical Bayesian sparse reconstruction method is illustrated on synthetic and real data collected from a tobacco virus sample using a prototype MRFM instrument.Comment: v2: final version; IEEE Trans. Image Processing, 200

Fusing Multiple Multiband Images

We consider the problem of fusing an arbitrary number of multiband, i.e., panchromatic, multispectral, or hyperspectral, images belonging to the same scene. We use the well-known forward observation and linear mixture models with Gaussian perturbations to formulate the maximum-likelihood estimator of the endmember abundance matrix of the fused image. We calculate the Fisher information matrix for this estimator and examine the conditions for the uniqueness of the estimator. We use a vector total-variation penalty term together with nonnegativity and sum-to-one constraints on the endmember abundances to regularize the derived maximum-likelihood estimation problem. The regularization facilitates exploiting the prior knowledge that natural images are mostly composed of piecewise smooth regions with limited abrupt changes, i.e., edges, as well as coping with potential ill-posedness of the fusion problem. We solve the resultant convex optimization problem using the alternating direction method of multipliers. We utilize the circular convolution theorem in conjunction with the fast Fourier transform to alleviate the computational complexity of the proposed algorithm. Experiments with multiband images constructed from real hyperspectral datasets reveal the superior performance of the proposed algorithm in comparison with the state-of-the-art algorithms, which need to be used in tandem to fuse more than two multiband images

Recent Advances in Image Restoration with Applications to Real World Problems

In the past few decades, imaging hardware has improved tremendously in terms of resolution, making widespread usage of images in many diverse applications on Earth and planetary missions. However, practical issues associated with image acquisition are still affecting image quality. Some of these issues such as blurring, measurement noise, mosaicing artifacts, low spatial or spectral resolution, etc. can seriously affect the accuracy of the aforementioned applications. This book intends to provide the reader with a glimpse of the latest developments and recent advances in image restoration, which includes image super-resolution, image fusion to enhance spatial, spectral resolution, and temporal resolutions, and the generation of synthetic images using deep learning techniques. Some practical applications are also included

Accelerating Bayesian computation in imaging

The dimensionality and ill-posedness often encountered in imaging inverse problems are a challenge for Bayesian computational methods, particularly for state-of-the-art sampling alternatives based on the Euler-Maruyama discretisation of the Langevin diffusion process. In this thesis, we address this difficulty and propose alternatives to accelerate Bayesian computation in imaging inverse problems, focusing on its computational aspects. We introduce, as our first contribution, a highly efficient proximal Markov chain Monte Carlo (MCMC) methodology, based on a state-of-the-art approximation known as the proximal stochastic orthogonal Runge-Kutta-Chebyshev (SK-ROCK) method. It has the advantage of cleverly combining multiple gradient evaluations to significantly speed up convergence, similar to accelerated gradient optimisation techniques. We rigorously demonstrate the acceleration of the Markov chains in the 2-Wasserstein distance for Gaussian models as a function of the condition number κ. In our second contribution, we propose a more sophisticated MCMC sampler, based on the careful integration of two advanced proximal Langevin MCMC methods, SK-ROCK and split Gibbs sampling (SGS), each of which uses a unique approach to accelerate convergence. More precisely, we show how to integrate the proximal SK-ROCK sampler with the model augmentation and relaxation method used by SGS at the level of the Langevin diffusion process, to speed up Bayesian computation at the expense of asymptotic bias. This leads to a new, faster proximal SK-ROCK sampler that combines the accelerated quality of the original sampler with the computational advantages of augmentation and relaxation. Additionally, we propose the augmented and relaxed model to be considered a generalisation of the target model rather than an approximation that situates relaxation in a bias-variance trade-off. As a result, we can carefully calibrate the amount of relaxation to boost both model accuracy (as determined by model evidence) and sampler convergence speed. To achieve this, we derive an empirical Bayesian method that automatically estimates the appropriate level of relaxation via maximum marginal likelihood estimation. The proposed methodologies are demonstrated in several numerical experiments related to image deblurring, hyperspectral unmixing, tomographic reconstruction and inpainting. Comparisons with Euler-type proximal Monte Carlo approaches confirm that the Markov chains generated with our methods exhibit significantly faster convergence speeds, achieve larger effective sample sizes, and produce lower mean square estimation errors with the same computational budget

Tuning-free Plug-and-Play Hyperspectral Image Deconvolution with Deep Priors

Deconvolution is a widely used strategy to mitigate the blurring and noisy degradation of hyperspectral images~(HSI) generated by the acquisition devices. This issue is usually addressed by solving an ill-posed inverse problem. While investigating proper image priors can enhance the deconvolution performance, it is not trivial to handcraft a powerful regularizer and to set the regularization parameters. To address these issues, in this paper we introduce a tuning-free Plug-and-Play (PnP) algorithm for HSI deconvolution. Specifically, we use the alternating direction method of multipliers (ADMM) to decompose the optimization problem into two iterative sub-problems. A flexible blind 3D denoising network (B3DDN) is designed to learn deep priors and to solve the denoising sub-problem with different noise levels. A measure of 3D residual whiteness is then investigated to adjust the penalty parameters when solving the quadratic sub-problems, as well as a stopping criterion. Experimental results on both simulated and real-world data with ground-truth demonstrate the superiority of the proposed method.Comment: IEEE Trans. Geosci. Remote sens. Manuscript submitted June 30, 202