Models and Methods for Estimation and Filtering of Signal-Dependent Noise in Imaging

The work presented in this thesis focuses on Image Processing, that is the branch of Signal Processing that centers its interest on images, sequences of images, and videos. It has various applications: imaging for traditional cameras, medical imaging, e.g., X-ray and magnetic resonance imaging (MRI), infrared imaging (thermography), e.g., for security purposes, astronomical imaging for space exploration, three-dimensional (video+depth) signal processing, and many more.This thesis covers a small but relevant slice that is transversal to this vast pool of applications: noise estimation and denoising. To appreciate the relevance of this thesis it is essential to understand why noise is such an important part of Image Processing. Every acquisition device, and every measurement is subject to interferences that causes random fluctuations in the acquired signals. If not taken into consideration with a suitable mathematical approach, these fluctuations might invalidate any use of the acquired signal. Consider, for example, an MRI used to detect a possible condition; if not suitably processed and filtered, the image could lead to a wrong diagnosis. Therefore, before any acquired image is sent to an end-user (machine or human), it undergoes several processing steps. Noise estimation and denoising are usually parts of these fundamental steps.Some sources of noise can be removed by suitably modeling the acquisition process of the camera, and developing hardware based on that model. Other sources of noise are instead inevitable: high/low light conditions of the acquired scene, hardware imperfections, temperature of the device, etc. To remove noise from an image, the noise characteristics have to be first estimated. The branch of image processing that fulfills this role is called noise estimation. Then, it is possible to remove the noise artifacts from the acquired image. This process is referred to as denoising.For practical reasons, it is convenient to model noise as random variables. In this way, we assume that the noise fluctuations take values whose probabilities follow specific distributions characterized only by few parameters. These are the parameters that we estimate. We focus our attention on noise modeled by Gaussian distributions, Poisson distributions, or a combination of these. These distributions are adopted for modeling noise affecting images from digital cameras, microscopes, telescopes, radiography systems, thermal cameras, depth-sensing cameras, etc. The parameters that define a Gaussian distribution are its mean and its variance, while a Poisson distribution depends only on its mean, since its variance is equal to the mean (signal-dependent variance). Consequently, the parameters of a Poisson-Gaussian distribution describe the relation between the intensity of the noise-free signal and the variance of the noise affecting it. Degradation models of this kind are referred to as signal-dependent noise.Estimation of signal-dependent noise is commonly performed by processing, individually, groups of pixels with equal intensity in order to sample the aforementioned relation between signal mean and noise variance. Such sampling is often subject to outliers; we propose a robust estimation model where the noise parameters are estimated optimizing a likelihood function that models the local variance estimates from each group of pixels as mixtures of Gaussian and Cauchy distributions. The proposed model is general and applicable to a variety of signal-dependent noise models, including also possible clipping of the data. We also show that, under certain hypotheses, the relation between signal mean and noise variance can also be effectively sampled from groups of pixels of possibly different intensities.Then, we propose a spatially adaptive transform to improve the denoising performance of a specific class of filters, namely nonlocal transformdomain collaborative filters. In particular, the proposed transform exploits the spatial coordinates of nonlocal similar features from an image to better decorrelate the data, and consequently to improve the filtering. Unlike non-adaptive transforms, the proposed spatially adaptive transform is capable of representing spatially smooth coarse-scale variations in the similar features of the image. Further, based on the same paradigm, we propose a method that adaptively enhances the local image features depending on their orientation with respect to the relative coordinates of other similar features at other locations in the image.An established approach for removing Poisson noise utilizes so-called variance-stabilizing transformations (VST) to make the noise variance independent of the mean of the signal, hence enabling denoising by a standard denoiser for additive Gaussian noise. Within this framework, we propose an iterative method where at each iteration the previous estimate is summed back to the noisy image in order to improve the stabilizing performance of the transformation, and consequently to improve the denoising results. The proposed iterative procedure allows to circumvent the typical drawbacks that VSTs experience at very low intensities, and thus allows us to apply the standard denoiser effectively even at extremely low counts.The developed methods achieve state-of-the-art results in their respective field of application

Solving, Estimating and Selecting Nonlinear Dynamic Economic Models without the Curse of Dimensionality

A welfare analysis of a risky policy is impossible within a linear or linearized model and its certainty equivalence property. The presented algorithms are designed as a toolbox for a general model class. The computational challenges are considerable and I concentrate on the numerics and statistics for a simple model of dynamic consumption and labor choice. I calculate the optimal policy and estimate the posterior density of structural parameters and the marginal likelihood within a nonlinear state space model. My approach is even in an interpreted language twenty time faster than the only alternative compiled approach. The model is estimated on simulated data in order to test the routines against known true parameters. The policy function is approximated by Smolyak Chebyshev polynomials and the rational expectation integral by Smolyak Gaussian quadrature. The Smolyak operator is used to extend univariate approximation and integration operators to many dimensions. It reduces the curse of dimensionality from exponential to polynomial growth. The likelihood integrals are evaluated by a Gaussian quadrature and Gaussian quadrature particle filter. The bootstrap or sequential importance resampling particle filter is used as an accuracy benchmark. The posterior is estimated by the Gaussian filter and a Metropolis- Hastings algorithm. I propose a genetic extension of the standard Metropolis-Hastings algorithm by parallel random walk sequences. This improves the robustness of start values and the global maximization properties. Moreover it simplifies a cluster implementation and the random walk variances decision is reduced to only two parameters so that almost no trial sequences are needed. Finally the marginal likelihood is calculated as a criterion for nonnested and quasi-true models in order to select between the nonlinear estimates and a first order perturbation solution combined with the Kalman filter.stochastic dynamic general equilibrium model, Chebyshev polynomials, Smolyak operator, nonlinear state space filter, Curse of Dimensionality, posterior of structural parameters, marginal likelihood

Evolutionary dynamics promoting and accompanying rapid adaptive trait loss

Understanding the conditions which promote adaptation is a key goal of evolutionary biology, and a pressing issue across fields of biology. Addressing this involves investigating not just the genetic and developmental mechanisms through which adaptive phenotypes arise, but also the environmental and ecological conditions which promote their spread. A major challenge in addressing these aims is that contemporary examples of rapid adaptive evolution are difficult to study, owing to the difficulty of identifying traits under selection during the early stages of adaptation. In this thesis, I use a Hawaiian field cricket system which provides a useful exception; males of the species Teleogryllus oceanicus ordinarily sing to attract females, however adaptive male-silencing (‘flatwing’) phenotypes have recently emerged and spread on at least three islands, under selection against male song exerted by a parasitoid fly, Ormia ochracea, which is attracted to singing males. Prior work indicates at least two of these flatwing phenotypes, from islands of Kauai and Oahu, have evolved independently under this shared selection pressure. This example of rapid, convergent evolution provides an opportunity to identify conditions which have promoted and resulted from rapid adaptation in wild populations evolving under extreme selection pressure. I investigate features which have contributed to the ability of these populations to rapidly, and repeatedly, adapt under strong selection against male song. The results indicate convergent sexual trait loss has been promoted by sex-biased development pathways maintained by sexually antagonistic selection; that pleiotropic, or associated, effects of adaptive mutation(s) in both sexes have played an important role in their spread; that adaptive male song-loss phenotypes have evolved repeatedly, above and beyond flatwing morphology; and that silent males nevertheless invest as much energy in practicing wing movement patterns associated with song and, despite reduced sexual dimorphism, are just as likely to be involved in aggressive intrasexual contests."This work was supported by the Natural Environment Research Council [grant numbers NE/I027800/1, NE/G014906/1, NE/L011255/1]. This work was supported by the University of St Andrews [School of Biology]." -- Funding (p. 2

Unravelling the determinants of the rate of adaptive evolution at the molecular level

Ever since Darwin presented natural selection as a driver of evolution, evolutionary biologists have thrived to understand how beneficial mutations shape species adaptation to their environment. Studying adaptation, however, requires an understanding of the complex dynamics between nucleotides, sequences, proteins, organisms, populations, and species. In other words, it requires assessing the interplay of evolutionary processes across systems. Here, I studied adaptation in such a way by exploring the frequency and nature of adaptive mutations within genes, within genomes, and between species. At the intramolecular level, this project revealed that the residue’s solvent accessibility acts as the primary determinant of rates of adaptive substitutions both in animals and in plants, where adaptive mutations are more frequent at the protein surface. These analyses further showed higher rates of adaptation for genes encoding proteins with central cellular functions, which are the ones usually targeted by pathogens during host infection. These findings, therefore, suggested that protein adaptive evolution proceeds through interactions between molecules, particularly at the interspecific level, where host-pathogen coevolution likely plays a central role. By taking a step back and looking at adaptation at different time-scales within the genome, this thesis revealed the role of young genes in adaptive evolution. As these genes are further away from their fitness optimum, these findings suggested that proteins adapt in an “adaptive walk” manner. This project further highlighted that the distribution of adaptive mutations across time follows a pattern of diminishing returns. Looking at an even broader scale by studying adaptation at the species level and considering the effect of intramolecular variation across several animal species, this thesis demonstrated a negative correlation between rates of adaptive substitutions and the effective population size (N_e). Despite the relatively weak signal, these findings contradict initial population genetics theory. Instead, they seem to agree with theoretical expectations at the phenotypic space. In turn, the results regarding negative selection confirm the N_e hypothesis, where the efficiency of selection is stronger in large-N_e species. This effect was well depicted in the differences of the distribution of fitness effects between buried and exposed residues, where the former accumulates comparatively more mild effect mutations in low-N_e species. This project further expanded our findings at the intramolecular level, by revealing the strong influence of the protein’s macromolecular structure on rates of molecular adaptation across several taxa. By assessing the interplay of adaptive mutations across distinct organizational levels, this thesis provided a more profound understanding of rates of adaptive evolution at the molecular level, thus delivering a comprehensive view of the molecular basis of adaptation

RESOURCE DIMENSIONING OF BROADBAND SATELLITE RETURN NETWORKS AFFECTED BY RAIN FADE

The use of Ka-band in satellite links has made rain attenuation a major concern in satellite network design. Fade mitigation techniques come at the expense of higher satellite resource consumption, such as bandwidth and power. An accurate estimation of this consumption is essential for the satellite service providers' business case, product strategy, and overall service pricing. However, the spatial correlation of rain fade introduces a high level of model complexity, and no method is currently available to compute its impact on resource consumption. Focusing on the return link of satellite broadband networks, this dissertation proposes a satellite resource dimensioning process that accounts for such a correlation in several scenarios, depending on the network's adaptability to rain fade. Firstly, we investigate nonadaptive network scenarios and answer the following question: how can the long-term bandwidth requirement of the network be minimized, given a set of ground terminals, modulations and codings, and discrete bandwidths? We formally define the long-term carrier allocation problem and analyze current practical solutions. We subsequently investigate two other potential solutions, found to be more bandwidth-efficient: one based on heuristics and another based on mixed integer linear programming. Finally, we look at the impact of several parameters on the performance of those three methods. Overall, we observe marginal reductions in bandwidth, however, significant (>10%) gains are reached for networks with small return links with low committed information rates. Secondly, we investigate semi-adaptive network scenarios with the introduction of adaptive coding and modulation. However, these technologies come at the cost of higher complexity when designing the network's carrier plan and user terminals. Taking into account those issues is even more important when the satellite link uses frequencies in Ka-band and above, where rain attenuation is a major concern. To consider such phenomena, we reformulate the previously presented solutions to factor in spatially correlated attenuation time series, in the form of a mixed integer linear programming optimization problem. The numerical results for a test scenario in Europe show significant bandwidth improvements. Lastly, we investigate fully-adaptive network scenarios and introduce multibeam aspects. We formulate a quantile estimation problem based on the broadband service level agreements. Then, we solve this problem for a given confidence relative interval using spatially correlated rain fade sample generators. Finally, we provide numerical results for residential and enterprise broadband satellite scenarios, allowing us to determine the underestimation and overestimation of satellite resource consumption made by optimistic (independent) and pessimistic (fully correlated) rain fade assumptions, respectively. Results show that for both assumptions, the satellite resource consumption can be significantly underestimated or overestimated, thus proving the importance of considering the spatial correlation of rain fade in the satellite resource dimensioning problem.Resource dimensioning of broadband satellite return networks affected by rain fade9. Industry, innovation and infrastructur