Robust particle outline extraction and its application to digital on-line holography

Peer reviewedPostprin

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

Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)

The implicit objective of the biennial "international - Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST) is to foster collaboration between international scientific teams by disseminating ideas through both specific oral/poster presentations and free discussions. For its second edition, the iTWIST workshop took place in the medieval and picturesque town of Namur in Belgium, from Wednesday August 27th till Friday August 29th, 2014. The workshop was conveniently located in "The Arsenal" building within walking distance of both hotels and town center. iTWIST'14 has gathered about 70 international participants and has featured 9 invited talks, 10 oral presentations, and 14 posters on the following themes, all related to the theory, application and generalization of the "sparsity paradigm": Sparsity-driven data sensing and processing; Union of low dimensional subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph sensing/processing; Blind inverse problems and dictionary learning; Sparsity and computational neuroscience; Information theory, geometry and randomness; Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?; Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website: http://sites.google.com/site/itwist1

Image Restoration for Remote Sensing: Overview and Toolbox

Remote sensing provides valuable information about objects or areas from a distance in either active (e.g., RADAR and LiDAR) or passive (e.g., multispectral and hyperspectral) modes. The quality of data acquired by remotely sensed imaging sensors (both active and passive) is often degraded by a variety of noise types and artifacts. Image restoration, which is a vibrant field of research in the remote sensing community, is the task of recovering the true unknown image from the degraded observed image. Each imaging sensor induces unique noise types and artifacts into the observed image. This fact has led to the expansion of restoration techniques in different paths according to each sensor type. This review paper brings together the advances of image restoration techniques with particular focuses on synthetic aperture radar and hyperspectral images as the most active sub-fields of image restoration in the remote sensing community. We, therefore, provide a comprehensive, discipline-specific starting point for researchers at different levels (i.e., students, researchers, and senior researchers) willing to investigate the vibrant topic of data restoration by supplying sufficient detail and references. Additionally, this review paper accompanies a toolbox to provide a platform to encourage interested students and researchers in the field to further explore the restoration techniques and fast-forward the community. The toolboxes are provided in https://github.com/ImageRestorationToolbox.Comment: This paper is under review in GRS

Improving reconstructions of digital holograms

Digital holography is a two step process of recording a hologram on an electronic sensor and reconstructing it numerically. This thesis makes a number of contri- butions to the second step of this process. These can be split into two distinct parts: A) speckle reduction in reconstructions of digital holograms (DHs), and B) modeling and overcoming partial occlusion e®ects in reconstructions of DHs, and using occlusions to reduce the effects of the twin image in reconstructions of DHs. Part A represents the major part of this thesis. Speckle reduction forms an important step in many digital holographic applications and we have developed a number of techniques that can be used to reduce its corruptive effect in recon- structions of DHs. These techniques range from 3D filtering of DH reconstructions to a technique that filters in the Fourier domain of the reconstructed DH. We have also investigated the most commonly used industrial speckle reduction technique - wavelet filters. In Part B, we investigate the nature of opaque and non-opaque partial occlusions. We motivate this work by trying to ¯nd a subset of pixels that overcome the effects of a partial occlusion, thus revealing otherwise hidden features on an object captured using digital holography. Finally, we have used an occlusion at the twin image plane to completely remove the corrupting effect of the out-of-focus twin image on reconstructions of DHs

Mixed Noise Removal by Processing of Patches

Sonar images are degraded by mixed noise which has an adverse impact on detection and classification of underwater objects. Existing denoising methods of sonar images remove either additive noise or multiplicative noise. In this study, the mixed noise in sonar images, the additive Gaussian noise and the multiplicative speckle effect are handled by the data adaptive methods. A patch based denoising is applied in two phases to remove the additive Gaussian and multiplicative speckle noises. In the first phase, the adaptive processing of local patches is used to remove the additive Gaussian noise by exploiting the sonar image local sparsity. The PCA and SVD methods are used for denoising the noisy image patches and blocks of patches. In the second phase, the weighted maximum likelihood denoising of the nonlocal patches reduces the speckle effect by exploiting the non-local similarity in a probability distribution. Experiments on side scan sonar images are conducted and the results show the importance of removing both the additive and multiplicative components from the sonar images

Recent Techniques for Regularization in Partial Differential Equations and Imaging

abstract: Inverse problems model real world phenomena from data, where the data are often noisy and models contain errors. This leads to instabilities, multiple solution vectors and thus ill-posedness. To solve ill-posed inverse problems, regularization is typically used as a penalty function to induce stability and allow for the incorporation of a priori information about the desired solution. In this thesis, high order regularization techniques are developed for image and function reconstruction from noisy or misleading data. Specifically the incorporation of the Polynomial Annihilation operator allows for the accurate exploitation of the sparse representation of each function in the edge domain. This dissertation tackles three main problems through the development of novel reconstruction techniques: (i) reconstructing one and two dimensional functions from multiple measurement vectors using variance based joint sparsity when a subset of the measurements contain false and/or misleading information, (ii) approximating discontinuous solutions to hyperbolic partial differential equations by enhancing typical solvers with l1 regularization, and (iii) reducing model assumptions in synthetic aperture radar image formation, specifically for the purpose of speckle reduction and phase error correction. While the common thread tying these problems together is the use of high order regularization, the defining characteristics of each of these problems create unique challenges. Fast and robust numerical algorithms are also developed so that these problems can be solved efficiently without requiring fine tuning of parameters. Indeed, the numerical experiments presented in this dissertation strongly suggest that the new methodology provides more accurate and robust solutions to a variety of ill-posed inverse problems.Dissertation/ThesisDoctoral Dissertation Mathematics 201