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

A CURE for noisy magnetic resonance images: Chi-square unbiased risk estimation

In this article we derive an unbiased expression for the expected mean-squared error associated with continuously differentiable estimators of the noncentrality parameter of a chi-square random variable. We then consider the task of denoising squared-magnitude magnetic resonance image data, which are well modeled as independent noncentral chi-square random variables on two degrees of freedom. We consider two broad classes of linearly parameterized shrinkage estimators that can be optimized using our risk estimate, one in the general context of undecimated filterbank transforms, and another in the specific case of the unnormalized Haar wavelet transform. The resultant algorithms are computationally tractable and improve upon state-of-the-art methods for both simulated and actual magnetic resonance image data.Comment: 30 double-spaced pages, 11 figures; submitted for publicatio

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

Models and Methods for Estimation and Filtering of Signal-Dependent Noise in Imaging

The work presented in this thesis focuses on Image Processing, that is the branch of Signal Processing that centers its interest on images, sequences of images, and videos. It has various applications: imaging for traditional cameras, medical imaging, e.g., X-ray and magnetic resonance imaging (MRI), infrared imaging (thermography), e.g., for security purposes, astronomical imaging for space exploration, three-dimensional (video+depth) signal processing, and many more.This thesis covers a small but relevant slice that is transversal to this vast pool of applications: noise estimation and denoising. To appreciate the relevance of this thesis it is essential to understand why noise is such an important part of Image Processing. Every acquisition device, and every measurement is subject to interferences that causes random fluctuations in the acquired signals. If not taken into consideration with a suitable mathematical approach, these fluctuations might invalidate any use of the acquired signal. Consider, for example, an MRI used to detect a possible condition; if not suitably processed and filtered, the image could lead to a wrong diagnosis. Therefore, before any acquired image is sent to an end-user (machine or human), it undergoes several processing steps. Noise estimation and denoising are usually parts of these fundamental steps.Some sources of noise can be removed by suitably modeling the acquisition process of the camera, and developing hardware based on that model. Other sources of noise are instead inevitable: high/low light conditions of the acquired scene, hardware imperfections, temperature of the device, etc. To remove noise from an image, the noise characteristics have to be first estimated. The branch of image processing that fulfills this role is called noise estimation. Then, it is possible to remove the noise artifacts from the acquired image. This process is referred to as denoising.For practical reasons, it is convenient to model noise as random variables. In this way, we assume that the noise fluctuations take values whose probabilities follow specific distributions characterized only by few parameters. These are the parameters that we estimate. We focus our attention on noise modeled by Gaussian distributions, Poisson distributions, or a combination of these. These distributions are adopted for modeling noise affecting images from digital cameras, microscopes, telescopes, radiography systems, thermal cameras, depth-sensing cameras, etc. The parameters that define a Gaussian distribution are its mean and its variance, while a Poisson distribution depends only on its mean, since its variance is equal to the mean (signal-dependent variance). Consequently, the parameters of a Poisson-Gaussian distribution describe the relation between the intensity of the noise-free signal and the variance of the noise affecting it. Degradation models of this kind are referred to as signal-dependent noise.Estimation of signal-dependent noise is commonly performed by processing, individually, groups of pixels with equal intensity in order to sample the aforementioned relation between signal mean and noise variance. Such sampling is often subject to outliers; we propose a robust estimation model where the noise parameters are estimated optimizing a likelihood function that models the local variance estimates from each group of pixels as mixtures of Gaussian and Cauchy distributions. The proposed model is general and applicable to a variety of signal-dependent noise models, including also possible clipping of the data. We also show that, under certain hypotheses, the relation between signal mean and noise variance can also be effectively sampled from groups of pixels of possibly different intensities.Then, we propose a spatially adaptive transform to improve the denoising performance of a specific class of filters, namely nonlocal transformdomain collaborative filters. In particular, the proposed transform exploits the spatial coordinates of nonlocal similar features from an image to better decorrelate the data, and consequently to improve the filtering. Unlike non-adaptive transforms, the proposed spatially adaptive transform is capable of representing spatially smooth coarse-scale variations in the similar features of the image. Further, based on the same paradigm, we propose a method that adaptively enhances the local image features depending on their orientation with respect to the relative coordinates of other similar features at other locations in the image.An established approach for removing Poisson noise utilizes so-called variance-stabilizing transformations (VST) to make the noise variance independent of the mean of the signal, hence enabling denoising by a standard denoiser for additive Gaussian noise. Within this framework, we propose an iterative method where at each iteration the previous estimate is summed back to the noisy image in order to improve the stabilizing performance of the transformation, and consequently to improve the denoising results. The proposed iterative procedure allows to circumvent the typical drawbacks that VSTs experience at very low intensities, and thus allows us to apply the standard denoiser effectively even at extremely low counts.The developed methods achieve state-of-the-art results in their respective field of application

Optical Coherence Tomography Noise Reduction Using Anisotropic Local Bivariate Gaussian Mixture Prior in 3D Complex Wavelet Domain

In this paper, MMSE estimator is employed for noise-free 3D OCT data recovery in 3D complex wavelet domain. Since the proposed distribution for noise-free data plays a key role in the performance of MMSE estimator, a priori distribution for the pdf of noise-free 3D complex wavelet coefficients is proposed which is able to model the main statistical properties of wavelets. We model the coefficients with a mixture of two bivariate Gaussian pdfs with local parameters which are able to capture the heavy-tailed property and inter- and intrascale dependencies of coefficients. In addition, based on the special structure of OCT images, we use an anisotropic windowing procedure for local parameters estimation that results in visual quality improvement. On this base, several OCT despeckling algorithms are obtained based on using Gaussian/two-sided Rayleigh noise distribution and homomorphic/nonhomomorphic model. In order to evaluate the performance of the proposed algorithm, we use 156 selected ROIs from 650 × 512 × 128 OCT dataset in the presence of wet AMD pathology. Our simulations show that the best MMSE estimator using local bivariate mixture prior is for the nonhomomorphic model in the presence of Gaussian noise which results in an improvement of 7.8 ± 1.7 in CNR