Recent Progress in Image Deblurring

This paper comprehensively reviews the recent development of image deblurring, including non-blind/blind, spatially invariant/variant deblurring techniques. Indeed, these techniques share the same objective of inferring a latent sharp image from one or several corresponding blurry images, while the blind deblurring techniques are also required to derive an accurate blur kernel. Considering the critical role of image restoration in modern imaging systems to provide high-quality images under complex environments such as motion, undesirable lighting conditions, and imperfect system components, image deblurring has attracted growing attention in recent years. From the viewpoint of how to handle the ill-posedness which is a crucial issue in deblurring tasks, existing methods can be grouped into five categories: Bayesian inference framework, variational methods, sparse representation-based methods, homography-based modeling, and region-based methods. In spite of achieving a certain level of development, image deblurring, especially the blind case, is limited in its success by complex application conditions which make the blur kernel hard to obtain and be spatially variant. We provide a holistic understanding and deep insight into image deblurring in this review. An analysis of the empirical evidence for representative methods, practical issues, as well as a discussion of promising future directions are also presented.Comment: 53 pages, 17 figure

D3^3PO - Denoising, Deconvolving, and Decomposing Photon Observations

The analysis of astronomical images is a non-trivial task. The D3PO algorithm addresses the inference problem of denoising, deconvolving, and decomposing photon observations. Its primary goal is the simultaneous but individual reconstruction of the diffuse and point-like photon flux given a single photon count image, where the fluxes are superimposed. In order to discriminate between these morphologically different signal components, a probabilistic algorithm is derived in the language of information field theory based on a hierarchical Bayesian parameter model. The signal inference exploits prior information on the spatial correlation structure of the diffuse component and the brightness distribution of the spatially uncorrelated point-like sources. A maximum a posteriori solution and a solution minimizing the Gibbs free energy of the inference problem using variational Bayesian methods are discussed. Since the derivation of the solution is not dependent on the underlying position space, the implementation of the D3PO algorithm uses the NIFTY package to ensure applicability to various spatial grids and at any resolution. The fidelity of the algorithm is validated by the analysis of simulated data, including a realistic high energy photon count image showing a 32 x 32 arcmin^2 observation with a spatial resolution of 0.1 arcmin. In all tests the D3PO algorithm successfully denoised, deconvolved, and decomposed the data into a diffuse and a point-like signal estimate for the respective photon flux components.Comment: 22 pages, 8 figures, 2 tables, accepted by Astronomy & Astrophysics; refereed version, 1 figure added, results unchanged, software available at http://www.mpa-garching.mpg.de/ift/d3po

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

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