PynPoint: a modular pipeline architecture for processing and analysis of high-contrast imaging data

The direct detection and characterization of planetary and substellar companions at small angular separations is a rapidly advancing field. Dedicated high-contrast imaging instruments deliver unprecedented sensitivity, enabling detailed insights into the atmospheres of young low-mass companions. In addition, improvements in data reduction and PSF subtraction algorithms are equally relevant for maximizing the scientific yield, both from new and archival data sets. We aim at developing a generic and modular data reduction pipeline for processing and analysis of high-contrast imaging data obtained with pupil-stabilized observations. The package should be scalable and robust for future implementations and in particular well suitable for the 3-5 micron wavelength range where typically (ten) thousands of frames have to be processed and an accurate subtraction of the thermal background emission is critical. PynPoint is written in Python 2.7 and applies various image processing techniques, as well as statistical tools for analyzing the data, building on open-source Python packages. The current version of PynPoint has evolved from an earlier version that was developed as a PSF subtraction tool based on PCA. The architecture of PynPoint has been redesigned with the core functionalities decoupled from the pipeline modules. Modules have been implemented for dedicated processing and analysis steps, including background subtraction, frame registration, PSF subtraction, photometric and astrometric measurements, and estimation of detection limits. The pipeline package enables end-to-end data reduction of pupil-stabilized data and supports classical dithering and coronagraphic data sets. As an example, we processed archival VLT/NACO L' and M' data of beta Pic b and reassessed the planet's brightness and position with an MCMC analysis, and we provide a derivation of the photometric error budget.Comment: 16 pages, 9 figures, accepted for publication in A&A, PynPoint is available at https://github.com/PynPoint/PynPoin

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

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

Computational optical imaging: Applications in synthetic aperture imaging, phase retrieval, and digital holography

Computational imaging has become an important field, as a merger of both algorithms and physical experiments. In the realm of microscopy and optical imaging, an important application is the problem of improving resolution, which is bounded by wavelength and numerical aperture according to the classic diffraction limit. We will investigate the resolution enhancement of phase objects such as transparent biological cells. One key challenge is how to measure phase experimentally. Standard interferometric techniques have the drawback of being sensitive to environmental vibrations and temperature fluctuations, and they use a reference arm which requires more space and cost. Non-holographic methods provide a way to overcome these disadvantages. Another challenge is how to reconstruct phase and amplitude from a digital hologram. The typical method of applying a filter in the frequency domain is limited by finite filter size. Optimization approaches offer a solution to this problem. The work presented here spans three main aspects of phase imaging microscopy including synthetic aperture imaging, phase retrieval, and digital holography. We develop a non-holographic microscope that uses off-axis illumination for resolution enhancement and demonstrate the first experimental measurements of referenceless phase retrieval at multiple angles. We implement a synthetic aperture microscope using an electrically tunable lens to defocus images, which avoids the need to mechanically move a camera on a translation stage. Finally, we improve the reconstruction of images from a digital hologram based on an iterative algorithm that alternatively updates amplitude and phase

Advanced Statistical Modeling for Model-Based Iterative Reconstruction for Single-Energy and Dual-Energy X-Ray CT

Model-based iterative reconstruction (MBIR) has been increasingly broadly applied as an improvement over traditional, analytical image reconstruction methods in X-ray CT, primarily due to its significant advantage in drastic dose reduction without diagnostic loss. Early success of the method in conventional CT has encouraged the extension to a wide range of applications that includes more advanced imaging modalities, such as dual-energy X-ray CT, and more challenging imaging conditions, such as low-dose and sparse-sampling scans, each requiring refined statistical models including the data model and the prior model. In this dissertation, we developed an MBIR algorithm for dual-energy CT that included a joint data-likelihood model to account for correlated data noise. Moreover, we developed a Gaussian-Mixture Markov random filed (GM-MRF) image model that can be used as a very expressive prior model in MBIR for X-ray CT reconstruction. The GM-MRF model is formed by merging individual patch-based Gaussian-mixture models and therefore leads to an expressive MRF model with easily estimated parameters. Experimental results with phantom and clinical datasets have demonstrated the improvement in image quality due to the advanced statistical modeling

Acquisition of 3D shapes of moving objects using fringe projection profilometry

Three-dimensional (3D) shape measurement for object surface reconstruction has potential applications in many areas, such as security, manufacturing and entertainment. As an effective non-contact technique for 3D shape measurements, fringe projection profilometry (FPP) has attracted significant research interests because of its high measurement speed, high measurement accuracy and ease to implement. Conventional FPP analysis approaches are applicable to the calculation of phase differences for static objects. However, 3D shape measurement for dynamic objects remains a challenging task, although they are highly demanded in many applications. The study of this thesis work aims to enhance the measurement accuracy of the FPP techniques for the 3D shape of objects subject to movement in the 3D space. The 3D movement of objects changes not only the position of the object but also the height information with respect to the measurement system, resulting in motion-induced errors with the use of existing FPP technology. The thesis presents the work conducted for solutions of this challenging problem

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

Segmentation of 3D Carotid Ultrasound Images Using Weak Geometric Priors

Vascular diseases are among the leading causes of death in Canada and around the globe. A major underlying cause of most such medical conditions is atherosclerosis, a gradual accumulation of plaque on the walls of blood vessels. Particularly vulnerable to atherosclerosis is the carotid artery, which carries blood to the brain. Dangerous narrowing of the carotid artery can lead to embolism, a dislodgement of plaque fragments which travel to the brain and are the cause of most strokes. If this pathology can be detected early, such a deadly scenario can be potentially prevented through treatment or surgery. This not only improves the patient's prognosis, but also dramatically lowers the overall cost of their treatment. Medical imaging is an indispensable tool for early detection of atherosclerosis, in particular since the exact location and shape of the plaque need to be known for accurate diagnosis. This can be achieved by locating the plaque inside the artery and measuring its volume or texture, a process which is greatly aided by image segmentation. In particular, the use of ultrasound imaging is desirable because it is a cost-effective and safe modality. However, ultrasonic images depict sound-reflecting properties of tissue, and thus suffer from a number of unique artifacts not present in other medical images, such as acoustic shadowing, speckle noise and discontinuous tissue boundaries. A robust ultrasound image segmentation technique must take these properties into account. Prior to segmentation, an important pre-processing step is the extraction of a series of features from the image via application of various transforms and non-linear filters. A number of such features are explored and evaluated, many of them resulting in piecewise smooth images. It is also proposed to decompose the ultrasound image into several statistically distinct components. These components can be then used as features directly, or other features can be obtained from them instead of the original image. The decomposition scheme is derived using Maximum-a-Posteriori estimation framework and is efficiently computable. Furthermore, this work presents and evaluates an algorithm for segmenting the carotid artery in 3D ultrasound images from other tissues. The algorithm incorporates information from different sources using an energy minimization framework. Using the ultrasound image itself, statistical differences between the region of interest and its background are exploited, and maximal overlap with strong image edges encouraged. In order to aid the convergence to anatomically accurate shapes, as well as to deal with the above-mentioned artifacts, prior knowledge is incorporated into the algorithm by using weak geometric priors. The performance of the algorithm is tested on a number of available 3D images, and encouraging results are obtained and discussed