An introduction to continuous optimization for imaging

International audienceA large number of imaging problems reduce to the optimization of a cost function , with typical structural properties. The aim of this paper is to describe the state of the art in continuous optimization methods for such problems, and present the most successful approaches and their interconnections. We place particular emphasis on optimal first-order schemes that can deal with typical non-smooth and large-scale objective functions used in imaging problems. We illustrate and compare the different algorithms using classical non-smooth problems in imaging, such as denoising and deblurring. Moreover, we present applications of the algorithms to more advanced problems, such as magnetic resonance imaging, multilabel image segmentation, optical flow estimation, stereo matching, and classification

First order algorithms in variational image processing

Variational methods in imaging are nowadays developing towards a quite universal and flexible tool, allowing for highly successful approaches on tasks like denoising, deblurring, inpainting, segmentation, super-resolution, disparity, and optical flow estimation. The overall structure of such approaches is of the form ${\cal D}(Ku) + \alpha {\cal R} (u) \rightarrow \min_u$ ; where the functional ${\cal D}$ is a data fidelity term also depending on some input data $f$ and measuring the deviation of $Ku$ from such and ${\cal R}$ is a regularization functional. Moreover $K$ is a (often linear) forward operator modeling the dependence of data on an underlying image, and $\alpha$ is a positive regularization parameter. While ${\cal D}$ is often smooth and (strictly) convex, the current practice almost exclusively uses nonsmooth regularization functionals. The majority of successful techniques is using nonsmooth and convex functionals like the total variation and generalizations thereof or $\ell_1$-norms of coefficients arising from scalar products with some frame system. The efficient solution of such variational problems in imaging demands for appropriate algorithms. Taking into account the specific structure as a sum of two very different terms to be minimized, splitting algorithms are a quite canonical choice. Consequently this field has revived the interest in techniques like operator splittings or augmented Lagrangians. Here we shall provide an overview of methods currently developed and recent results as well as some computational studies providing a comparison of different methods and also illustrating their success in applications.Comment: 60 pages, 33 figure

4D imaging in tomography and optical nanoscopy

Diese Dissertation gehört zu den Gebieten mathematische Bildverarbeitung und inverse Probleme. Ein inverses Problem ist die Aufgabe, Modellparameter anhand von gemessenen Daten zu berechnen. Solche Probleme treten in zahlreichen Anwendungen in Wissenschaft und Technik auf, z.B. in medizinischer Bildgebung, Biophysik oder Astronomie. Wir betrachten Rekonstruktionsprobleme mit Poisson Rauschen in der Tomographie und optischen Nanoskopie. Bei letzterer gilt es Bilder ausgehend von verzerrten und verrauschten Messungen zu rekonstruieren, wohingegen in der Positronen-Emissions-Tomographie die Aufgabe in der Visualisierung physiologischer Prozesse eines Patienten besteht. Standardmethoden zur 3D Bildrekonstruktion berücksichtigen keine zeitabhängigen Informationen oder Dynamik, z.B. Herzschlag oder Atmung in der Tomographie oder Zellmigration in der Mikroskopie. Diese Dissertation behandelt Modelle, Analyse und effiziente Algorithmen für 3D und 4D zeitabhängige inverse Probleme. This thesis contributes to the field of mathematical image processing and inverse problems. An inverse problem is a task, where the values of some model parameters must be computed from observed data. Such problems arise in a wide variety of applications in sciences and engineering, such as medical imaging, biophysics or astronomy. We mainly consider reconstruction problems with Poisson noise in tomography and optical nanoscopy. In the latter case, the task is to reconstruct images from blurred and noisy measurements, whereas in positron emission tomography the task is to visualize physiological processes of a patient. In 3D static image reconstruction standard methods do not incorporate time-dependent information or dynamics, e.g. heart beat or breathing in tomography or cell motion in microscopy. This thesis is a treatise on models, analysis and efficient algorithms to solve 3D and 4D time-dependent inverse problems

Blind image deconvolution: nonstationary Bayesian approaches to restoring blurred photos

High quality digital images have become pervasive in modern scientific and everyday life — in areas from photography to astronomy, CCTV, microscopy, and medical imaging. However there are always limits to the quality of these images due to uncertainty and imprecision in the measurement systems. Modern signal processing methods offer the promise of overcoming some of these problems by postprocessing these blurred and noisy images. In this thesis, novel methods using nonstationary statistical models are developed for the removal of blurs from out of focus and other types of degraded photographic images. The work tackles the fundamental problem blind image deconvolution (BID); its goal is to restore a sharp image from a blurred observation when the blur itself is completely unknown. This is a “doubly illposed” problem — extreme lack of information must be countered by strong prior constraints about sensible types of solution. In this work, the hierarchical Bayesian methodology is used as a robust and versatile framework to impart the required prior knowledge. The thesis is arranged in two parts. In the first part, the BID problem is reviewed, along with techniques and models for its solution. Observation models are developed, with an emphasis on photographic restoration, concluding with a discussion of how these are reduced to the common linear spatially-invariant (LSI) convolutional model. Classical methods for the solution of illposed problems are summarised to provide a foundation for the main theoretical ideas that will be used under the Bayesian framework. This is followed by an indepth review and discussion of the various prior image and blur models appearing in the literature, and then their applications to solving the problem with both Bayesian and nonBayesian techniques. The second part covers novel restoration methods, making use of the theory presented in Part I. Firstly, two new nonstationary image models are presented. The first models local variance in the image, and the second extends this with locally adaptive noncausal autoregressive (AR) texture estimation and local mean components. These models allow for recovery of image details including edges and texture, whilst preserving smooth regions. Most existing methods do not model the boundary conditions correctly for deblurring of natural photographs, and a Chapter is devoted to exploring Bayesian solutions to this topic. Due to the complexity of the models used and the problem itself, there are many challenges which must be overcome for tractable inference. Using the new models, three different inference strategies are investigated: firstly using the Bayesian maximum marginalised a posteriori (MMAP) method with deterministic optimisation; proceeding with the stochastic methods of variational Bayesian (VB) distribution approximation, and simulation of the posterior distribution using the Gibbs sampler. Of these, we find the Gibbs sampler to be the most effective way to deal with a variety of different types of unknown blurs. Along the way, details are given of the numerical strategies developed to give accurate results and to accelerate performance. Finally, the thesis demonstrates state of the art results in blind restoration of synthetic and real degraded images, such as recovering details in out of focus photographs

Investigating epileptiform activity associated with slow wave sleep

PhD ThesisThe characteristic EEG trait of patients with nocturnal idiopathic epilepsies during childhood is the spike and wave discharge. Cognitive dysfunction is prevalent among these patients and is thought to be linked to disturbances in memory consolidation processes that normally occur during slow wave sleep. Several genetic mutations of nicotinic receptor subunits have been linked to these disorders. However, there is little known about the underlying mechanisms or the spatiotemporal characteristics of this epileptiform activity within the neocortex. This thesis presents a rat in vitro model of the epileptiform activity synonymous with nocturnal childhood epilepsies, that allows for pharmacological manipulation of receptor subunits linked to these disorders. The application of DTC [10 M], a non-selective, competitive nicotinic acetylcholine receptor antagonist, to an in vitro model of the cortical delta rhythm induced two individual forms of paroxysm events - wave discharges and the conventional spike and wave discharges. Pharmacological manipulation of this model suggest that the epileptiform activity is mediated by excitatory currents which is consistent with the use of glutamate antagonists as anticonvulsants. A blanket blockade of inhibition by a GABAA antagonist resulted in severe discharges, hence hugely increasing excitatory response. Only partial disinhibition is suggested to be required to generate epileptiform activity as nicotinic acetylcholine receptors and 5-HT3 receptors are located on dendrite targeting interneurons. Mapping of unit activity revealed the di erence between the two paroxysm events was recruitment of super cial layers with simultaneous paroxysm events in delta frequency-generating Layer V pyramidal cells. It is proposed that the hyperexcitability responsible for the generation of the spike component of a spike and wave discharge is mediated by the lack of excitatory tone in 5-HT3 and nicotinic acetylecholine receptor expressing inhibitory interneuron subtypes. The disinhibition, spike generation and disruption of interplay between deep and super cial layers of the neocortex is thought to be associated with synaptic plastic changes

Software for Exascale Computing - SPPEXA 2016-2019

This open access book summarizes the research done and results obtained in the second funding phase of the Priority Program 1648 "Software for Exascale Computing" (SPPEXA) of the German Research Foundation (DFG) presented at the SPPEXA Symposium in Dresden during October 21-23, 2019. In that respect, it both represents a continuation of Vol. 113 in Springer’s series Lecture Notes in Computational Science and Engineering, the corresponding report of SPPEXA’s first funding phase, and provides an overview of SPPEXA’s contributions towards exascale computing in today's sumpercomputer technology. The individual chapters address one or more of the research directions (1) computational algorithms, (2) system software, (3) application software, (4) data management and exploration, (5) programming, and (6) software tools. The book has an interdisciplinary appeal: scholars from computational sub-fields in computer science, mathematics, physics, or engineering will find it of particular interest

Characterization of the acute phase response in critically ill children

Humans come into contact and interact with potential infective agents. The innate immune system is the first line of response to ward off infection. Innate immunity is, in part, under genetic control. This genetic control may help us understand the differences between individuals in preventing infection or limiting infectious and inflammatory illness. Systemic inflammation is a complex disorder that is difficult to define. Current definitions are derived from consensus meetings. A need has been expressed for a more useful definition of systemic inflammation. The work presented here identifies some of the underlying hereditability in limiting or being more vulnerable to severe infectious and injurious insults. Individual differences in complement activation potential and endotoxin recognition underlie part of the observed differences in a systemic inflammatory response to severe infection and injury. An exploratory study using heart rate variability as a non-invasive method to distinguish infectious systemic inflammation from sterile systemic inflammation was inconclusive. Chapter 1 gives the background to this study and an introduction to the approaches taken in this thesis. Chapter 2 describes in detail the methods used in the genetic association study and physiological systems analysis. Chapter 3 goes into some detail about the potential pitfalls in genotyping association studies and how these were addressed in the current study. The areas of genotypi ng quality, linkage disequilibrium, ethnicity, sample size and validation of previously done work are discussed using MBL-2 and ACE as examples. Chapter 4 is a description of the work done on genetic variability in the endotoxin receptor complex and how in may result in the host response to severe infection and physical insults. TLR4 polymorphisms were associated with lower platelet counts in severe inflammation. The reasons for this are unclear but may point to a direct effect of the TLR4 pathways on platelets or indicate that platelet counts are a more sensitive marker of systemic inflammation than SIRS criteria. These data support the view that variation in TLR4 function influences the early inflammatory response. This phenomenon may be one aspect of reduced fitness in the capacity to respond appropriately to an insult. Chapter 5 reports the central role of complement in the acute phase response. Polymorphisms in two out of the three complement activation pathways were shown to have potential modifying effects in paediatric systemic inflammation. This chapter reports that polymorphisms in the CFH gene may modulate the acute inflammatory response and corroborates the previously reported finding that MBL-2 variant genotypes are a risk factor for the early occurrence of SIRS/sepsis in a large cohort of paediatric critical care patients, independent of other potentially important functional polymorphisms in the complement and innate immunity system. A better understanding of how these polymorphisms operate at the pathophysi ol ogi cal level is needed before these findings can be translated to clinically useful therapeutic modalities. This study demonstrates that genetic polymorphisms associated with reduced complement activation may be associated with early SIRS/sepsis. This is consistent with a view that appropriate complement activation occurring early following an infectious or inflammatory insult protects children from early SIRS/sepsis. Chapter 6 assesses the usefulness of full MBL-2 genotyping and compares the MBL-2 genotype and M BL serum levels between a cohort of healthy children and a cohort of critically ill paediatric patients. MBL2 genotyping did not render more information with regards to M BL serum level when all promoter and structural polymorphisms were identified over and above structural polymorphisms and the XY promoter polymorphism. The children admitted with infection did not have a surplus of M BL deficient genotypes as compared with healthy children. This suggests that M BL deficient genotypes do not predispose to severe infection. M BL serum levels in SIRS or sepsis were lower compared with critically ill children without systemic inflammation. M BL levels were most reduced in the acute phase response in those genotypes with intermediate serum levels, which may reflect a consumption of M BL in critical illness and an inability to maintain pre-insult M BL serum levels. Chapter 7 explores a novel way to discriminate SIRS from sepsis by means of heart rate variability analysis. In this small paired sample study no differences were seen in LF metrics to differentiate sterile SIRS from sepsis. Neither was there a difference in LF metrics between those children who went on to develop a nosocomial infection and those who did not. Normalised HF was significantly higher in sterile SIRS vs. sepsis. These preliminary finding require further validation and a longitudinal approach in a larger cohort. Finally, Chapter 8 discusses the findings of this thesis in the context of interpretation and of the findings and potential future approaches. This thesis supports the view that better metrics are required to discriminate systemic inflammation as well as the concept that in children control of an inflammatory threat is aided by a vigorous capacity to respond