Adaptive Optimized Discriminative Learning based Image Deblurring using Deep CNN

Image degradation plays a major problem in many image processing applications. Due to blurring, the quality of an image is degraded and there will be a reduction in bandwidth. Blur in an image is due to variations in atmospheric turbulence, focal length, camera settings, etc. Various types of blurs include Gaussian blur, Motion blur, Out-of-focus blur. The effect of noise along with blur further corrupts the captured image. Many techniques have evolved to deblur the degraded image. The leading approach to solve various degraded images are either based on discriminative learning models or on optimization models. Each method has its own advantages and disadvantages.  Learning by discriminative methods is faster but restricted to a specific task whereas optimization models handle flexibly but consume more time. Integrating optimization models suitably by learning with discriminative manner results in effective image restoration. In this paper, a set of effective and fast Convolutional Neural Networks (CNNs) are employed to deblur the Gaussian, motion and out-of-focus blurred images that integrate with optimization models to further avoid noise effects. The proposed methods work more efficiently for applications with low-level vision

An extension of min/max flow framework

In this paper, the min/max flow scheme for image restoration is revised. The novelty consists of the fol- 24 lowing three parts. The first is to analyze the reason of the speckle generation and then to modify the 25 original scheme. The second is to point out that the continued application of this scheme cannot result 26 in an adaptive stopping of the curvature flow. This is followed by modifications of the original scheme 27 through the introduction of the Gradient Vector Flow (GVF) field and the zero-crossing detector, so as 28 to control the smoothing effect. Our experimental results with image restoration show that the proposed 29 schemes can reach a steady state solution while preserving the essential structures of objects. The third is 30 to extend the min/max flow scheme to deal with the boundary leaking problem, which is indeed an 31 intrinsic shortcoming of the familiar geodesic active contour model. The min/max flow framework pro- 32 vides us with an effective way to approximate the optimal solution. From an implementation point of 33 view, this extended scheme makes the speed function simpler and more flexible. The experimental 34 results of segmentation and region tracking show that the boundary leaking problem can be effectively 35 suppressed

A hamiltonian Monte Carlo method for non-smooth energy sampling

International audienceEfficient sampling from high-dimensional distribu- tions is a challenging issue that is encountered in many large data recovery problems. In this context, sampling using Hamil- tonian dynamics is one of the recent techniques that have been proposed to exploit the target distribution geometry. Such schemes have clearly been shown to be efficient for multidimensional sam- pling but, rather, are adapted to distributions from the exponential family with smooth energy functions. In this paper, we address the problem of using Hamiltonian dynamics to sample from probabil- ity distributions having non-differentiable energy functions such as those based on the l1 norm. Such distributions are being used intensively in sparse signal and image recovery applications. The technique studied in this paper uses a modified leapfrog transform involving a proximal step. The resulting nonsmooth Hamiltonian Monte Carlo method is tested and validated on a number of exper- iments. Results show its ability to accurately sample according to various multivariate target distributions. The proposed technique is illustrated on synthetic examples and is applied to an image denoising problem

Removing multiplicative noise by Douglas-Rachford splitting methods

Multiplicative noise appears in various image processing applications, e.g., in synthetic aperture radar (SAR), ultrasound imaging or in connection with blur in electronic microscopy, single particle emission computed tomography (SPECT) and positron emission tomography (PET). In this paper, we consider a variational restoration model consisting of the I-divergence as data fitting term and the total variation semi-norm or nonlocal means as regularizer. Although the I-divergence is the typical data fitting term when dealing with Poisson noise we substantiate why it is also appropriate for cleaning Gamma noise. We propose to compute the minimizer of our restoration functional by applying Douglas-Rachford splitting techniques, resp. alternating split Bregman methods, combined with an efficient algorithm to solve the involved nonlinear systems of equations. We prove the Q-linear convergence of the latter algorithm. Finally, we demonstrate the performance of our whole scheme by numerical examples. It appears that the nonlocal means approach leads to very good qualitative results

영상 복원 문제의 변분법적 접근

학위논문 (박사)-- 서울대학교 대학원 : 수리과학부, 2013. 2. 강명주.Image restoration has been an active research area in image processing and computer vision during the past several decades. We explore variational partial differential equations (PDE) models in image restoration problem. We start our discussion by reviewing classical models, by which the works of this dissertation are highly motivated. The content of the dissertation is divided into two main subjects. First topic is on image denoising, where we propose non-convex hybrid total variation model, and then we apply iterative reweighted algorithm to solve the proposed model. Second topic is on image decomposition, in which we separate an image into structural component and oscillatory component using local gradient constraint.Abstract i 1 Introduction 1 1.1 Image restoration 2 1.2 Brief overview of the dissertation 3 2 Previous works 4 2.1 Image denoising 4 2.1.1 Fundamental model 4 2.1.2 Higher order model 7 2.1.3 Hybrid model 9 2.1.4 Non-convex model 12 2.2 Image decomposition 22 2.2.1 Meyers model 23 2.2.2 Nonlinear filter 24 3 Non-convex hybrid TV for image denoising 28 3.1 Variational model with non-convex hybrid TV 29 3.1.1 Non-convex TV model and non-convex HOTV model 29 3.1.2 The Proposed model: Non-convex hybrid TV model 31 3.2 Iterative reweighted hybrid Total Variation algorithm 33 3.3 Numerical experiments 35 3.3.1 Parameter values 37 3.3.2 Comparison between the non-convex TV model and the non-convex HOTV model 38 3.3.3 Comparison with other non-convex higher order regularizers 40 3.3.4 Comparison between two non-convex hybrid TV models 42 3.3.5 Comparison with Krishnan et al. [39] 43 3.3.6 Comparison with state-of-the-art 44 4 Image decomposition 59 4.1 Local gradient constraint 61 4.1.1 Texture estimator 62 4.2 The proposed model 65 4.2.1 Algorithm : Anisotropic TV-L2 67 4.2.2 Algorithm : Isotropic TV-L2 69 4.2.3 Algorithm : Isotropic TV-L1 71 4.3 Numerical experiments and discussion 72 5 Conclusion and future works 80 Abstract (in Korean) 92Docto

Novel integro-differential schemes for multiscale image representation

Multiscale representation of a given image is the problem of constructing a family of images, where each image in this family represents a scaled version of the given image. This finds its motivation from biological vision studies. Using the hierarchical multiscale image representation proposed by Tadmor et. al. [32], an image is decomposed into sums of simpler `slices', which extract more refined information from the previous scales. This approach motivates us to propose a novel integro-differential equation (IDE), for a multiscale image representation. We examine various properties of this IDE. The advantage of formulating the IDE this way is that, although this IDE is motivated by variational approach, we no longer need to be associated with any minimization problem and can modify the IDE, suitable to our image processing needs. For example, we may need to find different scales in the image, while retaining or enhancing prominent edges, which may define boundaries of objects. We propose some edge preserving modifications to our IDE. One of the important problems in image processing is deblurring a blurred image. Images get blurred due to various reasons, such as unfocused camera lens, relative motion between the camera and the object pictured, etc. The blurring can be modeled with a continuous, linear operator. Recovering a clean image from a blurry image, is an ill-posed problem, which is solved using Tikhonov-like regularization. We propose a different IDE to solve the deblurring problem. We propose hierarchical multiscale scheme based on (BV; L1) decomposition, proposed by Chan, Esedoglu, Nikolova and Alliney [12, 25, 3]. We finally propose another hierarchical multiscale representation based on a novel weighted (BV;L1) decomposition

Image Restoration

This book represents a sample of recent contributions of researchers all around the world in the field of image restoration. The book consists of 15 chapters organized in three main sections (Theory, Applications, Interdisciplinarity). Topics cover some different aspects of the theory of image restoration, but this book is also an occasion to highlight some new topics of research related to the emergence of some original imaging devices. From this arise some real challenging problems related to image reconstruction/restoration that open the way to some new fundamental scientific questions closely related with the world we interact with

Diffusion-based spatial priors for imaging.

We describe a Bayesian scheme to analyze images, which uses spatial priors encoded by a diffusion kernel, based on a weighted graph Laplacian. This provides a general framework to formulate a spatial model, whose parameters can be optimised. The standard practice using the software statistical parametric mapping (SPM) is to smooth imaging data using a fixed Gaussian kernel as a pre-processing step before applying a mass-univariate statistical model (e.g., a general linear model) to provide images of parameter estimates (Friston et al., 2006). This entails the strong assumption that data are generated smoothly throughout the brain. An alternative is to include smoothness in a multivariate statistical model (Penny et al., 2005). The advantage of the latter is that each parameter field is smoothed automatically, according to a measure of uncertainty, given the data. Explicit spatial priors enable formal model comparison of different prior assumptions, e.g. that data are generated from a stationary (i.e. fixed throughout the brain) or non-stationary spatial process. We describe the motivation, background material and theory used to formulate diffusion-based spatial priors for fMRI data and apply it to three different datasets, which include standard and high-resolution data. We compare mass-univariate ordinary least squares estimates of smoothed data and three Bayesian models spatially independent, stationary and non-stationary spatial models of non-smoothed data. The latter of which can be used to preserve boundaries between functionally selective regional responses of the brain, thereby increasing the spatial detail of inferences about cortical responses to experimental input