Two constrained formulations for deblurring poisson noisy images

International audienceDeblurring noisy Poisson images has recently been subject of an increasingly amount of works in many areas such as astronomy or biological imaging. Several methods have promoted explicit prior on the solution to regularize the ill-posed inverse problem and to improve the quality of the image. In each of these methods, a regularizing parameter is introduced to control the weight of the prior. Unfortunately, this regularizing parameter has to be manually set such that it gives the best qualitative results. To tackle this issue, we present in this paper two constrained formulations for the Poisson deconvolution problem, derived from recent advances in regularizing parameter estimation for Poisson noise. We first show how to improve the accuracy of these estimators and how to link these estimators to constrained formulations. We then propose an algorithm to solve the resulting optimization problems and detail how to perform the projections on the constraints. Results on real and synthetic data are presented

Two constrained formulations for deblurring poisson noisy images

International audienceDeblurring noisy Poisson images has recently been subject of an increasingly amount of works in many areas such as astronomy or biological imaging. Several methods have promoted explicit prior on the solution to regularize the ill-posed inverse problem and to improve the quality of the image. In each of these methods, a regularizing parameter is introduced to control the weight of the prior. Unfortunately, this regularizing parameter has to be manually set such that it gives the best qualitative results. To tackle this issue, we present in this paper two constrained formulations for the Poisson deconvolution problem, derived from recent advances in regularizing parameter estimation for Poisson noise. We first show how to improve the accuracy of these estimators and how to link these estimators to constrained formulations. We then propose an algorithm to solve the resulting optimization problems and detail how to perform the projections on the constraints. Results on real and synthetic data are presented

A new steplength selection for scaled gradient methods with application to image deblurring

Gradient methods are frequently used in large scale image deblurring problems since they avoid the onerous computation of the Hessian matrix of the objective function. Second order information is typically sought by a clever choice of the steplength parameter defining the descent direction, as in the case of the well-known Barzilai and Borwein rules. In a recent paper, a strategy for the steplength selection approximating the inverse of some eigenvalues of the Hessian matrix has been proposed for gradient methods applied to unconstrained minimization problems. In the quadratic case, this approach is based on a Lanczos process applied every m iterations to the matrix of the most recent m back gradients but the idea can be extended to a general objective function. In this paper we extend this rule to the case of scaled gradient projection methods applied to non-negatively constrained minimization problems, and we test the effectiveness of the proposed strategy in image deblurring problems in both the presence and the absence of an explicit edge-preserving regularization term

Inexact Bregman iteration with an application to Poisson data reconstruction

This work deals with the solution of image restoration problems by an iterative regularization method based on the Bregman iteration. Any iteration of this scheme requires to exactly compute the minimizer of a function. However, in some image reconstruction applications, it is either impossible or extremely expensive to obtain exact solutions of these subproblems. In this paper, we propose an inexact version of the iterative procedure, where the inexactness in the inner subproblem solution is controlled by a criterion that preserves the convergence of the Bregman iteration and its features in image restoration problems. In particular, the method allows to obtain accurate reconstructions also when only an overestimation of the regularization parameter is known. The introduction of the inexactness in the iterative scheme allows to address image reconstruction problems from data corrupted by Poisson noise, exploiting the recent advances about specialized algorithms for the numerical minimization of the generalized Kullback–Leibler divergence combined with a regularization term. The results of several numerical experiments enable to evaluat

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

Distributed Deblurring of Large Images of Wide Field-Of-View

Image deblurring is an economic way to reduce certain degradations (blur and noise) in acquired images. Thus, it has become essential tool in high resolution imaging in many applications, e.g., astronomy, microscopy or computational photography. In applications such as astronomy and satellite imaging, the size of acquired images can be extremely large (up to gigapixels) covering wide field-of-view suffering from shift-variant blur. Most of the existing image deblurring techniques are designed and implemented to work efficiently on centralized computing system having multiple processors and a shared memory. Thus, the largest image that can be handle is limited by the size of the physical memory available on the system. In this paper, we propose a distributed nonblind image deblurring algorithm in which several connected processing nodes (with reasonable computational resources) process simultaneously different portions of a large image while maintaining certain coherency among them to finally obtain a single crisp image. Unlike the existing centralized techniques, image deblurring in distributed fashion raises several issues. To tackle these issues, we consider certain approximations that trade-offs between the quality of deblurred image and the computational resources required to achieve it. The experimental results show that our algorithm produces the similar quality of images as the existing centralized techniques while allowing distribution, and thus being cost effective for extremely large images.Comment: 16 pages, 10 figures, submitted to IEEE Trans. on Image Processin

Convolutional Deblurring for Natural Imaging

In this paper, we propose a novel design of image deblurring in the form of one-shot convolution filtering that can directly convolve with naturally blurred images for restoration. The problem of optical blurring is a common disadvantage to many imaging applications that suffer from optical imperfections. Despite numerous deconvolution methods that blindly estimate blurring in either inclusive or exclusive forms, they are practically challenging due to high computational cost and low image reconstruction quality. Both conditions of high accuracy and high speed are prerequisites for high-throughput imaging platforms in digital archiving. In such platforms, deblurring is required after image acquisition before being stored, previewed, or processed for high-level interpretation. Therefore, on-the-fly correction of such images is important to avoid possible time delays, mitigate computational expenses, and increase image perception quality. We bridge this gap by synthesizing a deconvolution kernel as a linear combination of Finite Impulse Response (FIR) even-derivative filters that can be directly convolved with blurry input images to boost the frequency fall-off of the Point Spread Function (PSF) associated with the optical blur. We employ a Gaussian low-pass filter to decouple the image denoising problem for image edge deblurring. Furthermore, we propose a blind approach to estimate the PSF statistics for two Gaussian and Laplacian models that are common in many imaging pipelines. Thorough experiments are designed to test and validate the efficiency of the proposed method using 2054 naturally blurred images across six imaging applications and seven state-of-the-art deconvolution methods.Comment: 15 pages, for publication in IEEE Transaction Image Processin

Block-based Collaborative 3-D Transform Domain Modeling in Inverse Imaging

The recent developments in image and video denoising have brought a new generation of filtering algorithms achieving unprecedented restoration quality. This quality mainly follows from exploiting various features of natural images. The nonlocal self-similarity and sparsity of representations are key elements of the novel filtering algorithms, with the best performance achieved by adaptively aggregating multiple redundant and sparse estimates. In a very broad sense, the filters are now able, given a perturbed image, to identify its plausible representative in the space or manifold of possible solutions. Thus, they are powerful tools not only for noise removal, but also for providing accurate adaptive regularization to many ill-conditioned inverse imaging problems. In this thesis we show how the image modeling of the well-known Block-matching 3-D transform domain (BM3D) filter can be exploited for designing efficient algorithms for image reconstruction. First, we formalize the BM3D-modeling in terms of the overcomplete sparse frame representation. We construct analysis and synthesis BM3D-frames and study their properties, making BM3D-modeling available for use in variational formulations of image reconstruction problems. Second, we demonstrate that standard variational formulations based on single objective optimization, such as Basis Pursuit Denoising and its various extensions, cannot be used with the imaging models generating non-tight frames, such as BM3D. We propose an alternative sparsity promoting problem formulation based on the generalized Nash equilibrium (GNE). Finally, using BM3D-frames we develop practical algorithms for image deblurring and super-resolution problems. To the best of our knowledge, these algorithms provide results which are the state of the art in the field