비가우시안 잡음 영상 복원을 위한 그룹 희소 표현

학위논문(박사)--서울대학교 대학원 :자연과학대학 수리과학부,2020. 2. 강명주.For the image restoration problem, recent variational approaches exploiting nonlocal information of an image have demonstrated significant improvements compared with traditional methods utilizing local features. Hence, we propose two variational models based on the sparse representation of image groups, to recover images with non-Gaussian noise. The proposed models are designed to restore image with Cauchy noise and speckle noise, respectively. To achieve efficient and stable performance, an alternating optimization scheme with a novel initialization technique is used. Experimental results suggest that the proposed methods outperform other methods in terms of both visual perception and numerical indexes.영상 복원 문제에서, 영상의 비국지적인 정보를 활용하는 최근의 다양한 접근 방식은 국지적인 특성을 활용하는 기존 방법과 비교하여 크게 개선되었다. 따라서, 우리는 비가우시안 잡음 영상을 복원하기 위해 영상 그룹 희소 표현에 기반한 두 가지 변분법적 모델을 제안한다. 제안된 모델은 각각 코시 잡음과 스펙클 잡음 영상을 복원하도록 설계되었다. 효율적이고 안정적인 성능을 달성하기 위해, 교대 방향 승수법과 새로운 초기화 기술이 사용된다. 실험 결과는 제안된 방법이 시각적인 인식과 수치적인 지표 모두에서 다른 방법보다 우수함을 나타낸다.1 Introduction 1 2 Preliminaries 5 2.1 Cauchy Noise 5 2.1.1 Introduction 6 2.1.2 Literature Review 7 2.2 Speckle Noise 9 2.2.1 Introduction 10 2.2.2 Literature Review 13 2.3 GSR 15 2.3.1 Group Construction 15 2.3.2 GSR Modeling 16 2.4 ADMM 17 3 Proposed Models 19 3.1 Proposed Model 1: GSRC 19 3.1.1 GSRC Modeling via MAP Estimator 20 3.1.2 Patch Distance for Cauchy Noise 22 3.1.3 The ADMM Algorithm for Solving (3.7) 22 3.1.4 Numerical Experiments 28 3.1.5 Discussion 45 3.2 Proposed Model 2: GSRS 48 3.2.1 GSRS Modeling via MAP Estimator 50 3.2.2 Patch Distance for Speckle Noise 52 3.2.3 The ADMM Algorithm for Solving (3.42) 53 3.2.4 Numerical Experiments 56 3.2.5 Discussion 69 4 Conclusion 74 Abstract (in Korean) 84Docto

Multiscale hierarchical decomposition methods for images corrupted by multiplicative noise

Recovering images corrupted by multiplicative noise is a well known challenging task. Motivated by the success of multiscale hierarchical decomposition methods (MHDM) in image processing, we adapt a variety of both classical and new multiplicative noise removing models to the MHDM form. On the basis of previous work, we further present a tight and a refined version of the corresponding multiplicative MHDM. We discuss existence and uniqueness of solutions for the proposed models, and additionally, provide convergence properties. Moreover, we present a discrepancy principle stopping criterion which prevents recovering excess noise in the multiscale reconstruction. Through comprehensive numerical experiments and comparisons, we qualitatively and quantitatively evaluate the validity of all proposed models for denoising and deblurring images degraded by multiplicative noise. By construction, these multiplicative multiscale hierarchical decomposition methods have the added benefit of recovering many scales of an image, which can provide features of interest beyond image denoising

An algorithm for hybrid regularizers based image restoration with Poisson noise

summary:In this paper, a hybrid regularizers model for Poissonian image restoration is introduced. We study existence and uniqueness of minimizer for this model. To solve the resulting minimization problem, we employ the alternating minimization method with rigorous convergence guarantee. Numerical results demonstrate the efficiency and stability of the proposed method for suppressing Poisson noise

On Solving SAR Imaging Inverse Problems Using Non-Convex Regularization with a Cauchy-based Penalty

Synthetic aperture radar (SAR) imagery can provide useful information in a multitude of applications, including climate change, environmental monitoring, meteorology, high dimensional mapping, ship monitoring, or planetary exploration. In this paper, we investigate solutions to a number of inverse problems encountered in SAR imaging. We propose a convex proximal splitting method for the optimization of a cost function that includes a non-convex Cauchy-based penalty. The convergence of the overall cost function optimization is ensured through careful selection of model parameters within a forward-backward (FB) algorithm. The performance of the proposed penalty function is evaluated by solving three standard SAR imaging inverse problems, including super-resolution, image formation, and despeckling, as well as ship wake detection for maritime applications. The proposed method is compared to several methods employing classical penalty functions such as total variation ($TV$) and $L_1$ norms, and to the generalized minimax-concave (GMC) penalty. We show that the proposed Cauchy-based penalty function leads to better image reconstruction results when compared to the reference penalty functions for all SAR imaging inverse problems in this paper.Comment: 18 pages, 7 figure

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