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

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