Scene-adapted plug-and-play algorithm with convergence guarantees

Recent frameworks, such as the so-called plug-and-play, allow us to leverage the developments in image denoising to tackle other, and more involved, problems in image processing. As the name suggests, state-of-the-art denoisers are plugged into an iterative algorithm that alternates between a denoising step and the inversion of the observation operator. While these tools offer flexibility, the convergence of the resulting algorithm may be difficult to analyse. In this paper, we plug a state-of-the-art denoiser, based on a Gaussian mixture model, in the iterations of an alternating direction method of multipliers and prove the algorithm is guaranteed to converge. Moreover, we build upon the concept of scene-adapted priors where we learn a model targeted to a specific scene being imaged, and apply the proposed method to address the hyperspectral sharpening problem

Bayesian fusion of multi-band images : A powerful tool for super-resolution

Hyperspectral (HS) imaging, which consists of acquiring a same scene in several hundreds of contiguous spectral bands (a three dimensional data cube), has opened a new range of relevant applications, such as target detection [MS02], classification [C.-03] and spectral unmixing [BDPD+12]. However, while HS sensors provide abundant spectral information, their spatial resolution is generally more limited. Thus, fusing the HS image with other highly resolved images of the same scene, such as multispectral (MS) or panchromatic (PAN) images is an interesting problem. The problem of fusing a high spectral and low spatial resolution image with an auxiliary image of higher spatial but lower spectral resolution, also known as multi-resolution image fusion, has been explored for many years [AMV+11]. From an application point of view, this problem is also important as motivated by recent national programs, e.g., the Japanese next-generation space-borne hyperspectral image suite (HISUI), which fuses co-registered MS and HS images acquired over the same scene under the same conditions [YI13]. Bayesian fusion allows for an intuitive interpretation of the fusion process via the posterior distribution. Since the fusion problem is usually ill-posed, the Bayesian methodology offers a convenient way to regularize the problem by defining appropriate prior distribution for the scene of interest. The aim of this thesis is to study new multi-band image fusion algorithms to enhance the resolution of hyperspectral image. In the first chapter, a hierarchical Bayesian framework is proposed for multi-band image fusion by incorporating forward model, statistical assumptions and Gaussian prior for the target image to be restored. To derive Bayesian estimators associated with the resulting posterior distribution, two algorithms based on Monte Carlo sampling and optimization strategy have been developed. In the second chapter, a sparse regularization using dictionaries learned from the observed images is introduced as an alternative of the naive Gaussian prior proposed in Chapter 1. instead of Gaussian prior is introduced to regularize the ill-posed problem. Identifying the supports jointly with the dictionaries circumvented the difficulty inherent to sparse coding. To minimize the target function, an alternate optimization algorithm has been designed, which accelerates the fusion process magnificently comparing with the simulation-based method. In the third chapter, by exploiting intrinsic properties of the blurring and downsampling matrices, a much more efficient fusion method is proposed thanks to a closed-form solution for the Sylvester matrix equation associated with maximizing the likelihood. The proposed solution can be embedded into an alternating direction method of multipliers or a block coordinate descent method to incorporate different priors or hyper-priors for the fusion problem, allowing for Bayesian estimators. In the last chapter, a joint multi-band image fusion and unmixing scheme is proposed by combining the well admitted linear spectral mixture model and the forward model. The joint fusion and unmixing problem is solved in an alternating optimization framework, mainly consisting of solving a Sylvester equation and projecting onto a simplex resulting from the non-negativity and sum-to-one constraints. The simulation results conducted on synthetic and semi-synthetic images illustrate the advantages of the developed Bayesian estimators, both qualitatively and quantitatively

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

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

Models and Methods for Automated Background Density Estimation in Hyperspectral Anomaly Detection

Detecting targets with unknown spectral signatures in hyperspectral imagery has been proven to be a topic of great interest in several applications. Because no knowledge about the targets of interest is assumed, this task is performed by searching the image for anomalous pixels, i.e. those pixels deviating from a statistical model of the background. According to the hyperspectral literature, there are two main approaches to Anomaly Detection (AD) thus leading to the definition of different ways for background modeling: global and local. Global AD algorithms are designed to locate small rare objects that are anomalous with respect to the global background, identified by a large portion of the image. On the other hand, in local AD strategies, pixels with significantly different spectral features from a local neighborhood just surrounding the observed pixel are detected as anomalies. In this thesis work, a new scheme is proposed for detecting both global and local anomalies. Specifically, a simplified Likelihood Ratio Test (LRT) decision strategy is derived that involves thresholding the background log-likelihood and, thus, only needs the specification of the background Probability Density Function (PDF). Within this framework, the use of parametric, semi-parametric (in particular finite mixtures), and non-parametric models is investigated for the background PDF estimation. Although such approaches are well known and have been widely employed in multivariate data analysis, they have been seldom applied to estimate the hyperspectral background PDF, mostly due to the difficulty of reliably learning the model parameters without the need of operator intervention, which is highly desirable in practical AD tasks. In fact, this work represents the first attempt to jointly examine such methods in order to asses and discuss the most critical issues related to their employment for PDF estimation of hyperspectral background with specific reference to the detection of anomalous objects in a scene. Specifically, semi- and non-parametric estimators have been successfully employed to estimate the image background PDF with the aim of detecting global anomalies in a scene by means of the use of ad hoc learning procedures. In particular, strategies developed within a Bayesian framework have been considered for automatically estimating the parameters of mixture models and one of the most well-known non-parametric techniques, i.e. the fixed kernel density estimator (FKDE). In this latter, the performance and the modeling ability depend on scale parameters, called bandwidths. It has been shown that the use of bandwidths that are fixed across the entire feature space, as done in the FKDE, is not effective when the sample data exhibit different local peculiarities across the entire data domain, which generally occurs in practical applications. Therefore, some possibilities are investigated to improve the image background PDF estimation of FKDE by allowing the bandwidths to vary over the estimation domain, thus adapting the amount of smoothing to the local density of the data so as to more reliably and accurately follow the background data structure of hyperspectral images of a scene. The use of such variable bandwidth kernel density estimators (VKDE) is also proposed for estimating the background PDF within the considered AD scheme for detecting local anomalies. Such a choice is done with the aim to cope with the problem of non-Gaussian background for improving classical local AD algorithms involving parametric and non-parametric background models. The locally data-adaptive non-parametric model has been chosen since it encompasses the potential, typical of non-parametric PDF estimators, in modeling data regardless of specific distributional assumption together with the benefits deriving from the employment of bandwidths that vary across the data domain. The ability of the proposed AD scheme resulting from the application of different background PDF models and learning methods is experimentally evaluated by employing real hyperspectral images containing objects that are anomalous with respect to the background

A review of spatial enhancement of hyperspectral remote sensing imaging techniques

Remote sensing technology has undeniable importance in various industrial applications, such as mineral exploration, plant detection, defect detection in aerospace and shipbuilding, and optical gas imaging, to name a few. Remote sensing technology has been continuously evolving, offering a range of image modalities that can facilitate the aforementioned applications. One such modality is Hyperspectral Imaging (HSI). Unlike Multispectral Images (MSI) and natural images, HSI consist of hundreds of bands. Despite their high spectral resolution, HSI suffer from low spatial resolution in comparison to their MSI counterpart, which hinders the utilization of their full potential. Therefore, spatial enhancement, or Super Resolution (SR), of HSI is a classical problem that has been gaining rapid attention over the past two decades. The literature is rich with various SR algorithms that enhance the spatial resolution of HSI while preserving their spectral fidelity. This paper reviews and discusses the most important algorithms relevant to this area of research between 2002-2022, along with the most frequently used datasets, HSI sensors, and quality metrics. Meta-analysis are drawn based on the aforementioned information, which is used as a foundation that summarizes the state of the field in a way that bridges the past and the present, identifies the current gap in it, and recommends possible future directions

Deep Image Prior for Disentangling Mixed Pixels

A mixed pixel in remotely sensed images measures the reflectance and emission from multiple target types (e.g., tree, grass, and building) from a certain area. Mixed pixels exist commonly in spaceborne hyper-/multi-spectral images due to sensor limitations, causing the signature ambiguity problem and impeding high-resolution remote sensing mapping. Disentangling mixed pixels into the underlying constituent components is a challenging ill-posed inverse problem, which requires efficient modeling of spatial prior information and other application-dependent prior knowledge concerning the mixed pixel generation process. The recent deep image prior (DIP) approach and other application-dependent prior information are integrated into a Bayesian framework in the research, which allows comprehensive usage of different prior knowledge. The research improves mixed pixel disentangling using the Bayesian DIP in three key applications: spectral unmixing (SU), subpixel mapping (SPM), and soil moisture product downscaling (SMD). The main contributions are summarized as follows. First, to improve the decomposition of mixed pixels into pure material spectra (i.e., endmembers) and their constituting fractions (i.e., abundances) in SU, a designed deep fully convolutional neural network (DCNN) and a new spectral mixture model (SMM) with heterogeneous noise are integrated into a Bayesian framework that is efficiently solved by a new iterative optimization algorithm. Second, to improve the decomposition of mixed pixels into class labels of subpixels in SPM, a dedicated DCNN architecture and a new discrete SMM are integrated into the Bayesian framework to allow the use of both spatial prior and the forward model. Third, to improve the decomposition of mixed pixels into soil moisture concentrations of subpixels in SMD, a new DIP architecture and a forward degradation model are integrated into the Bayesian framework that is solved by the stochastic gradient descent approach. These new Bayesian approaches improve the state-of-the-art in their respective applications (i.e., SU, SPM, and SMD), which can be potentially utilized for solving other ill-posed inverse problems where simultaneously modeling of the spatial prior and other prior knowledge is needed