This thesis introduces the rank-order model and investigates its use in several image restoration problems. More commonly used as filters, the rank-order operators are here employed as predictors. A Laplacian excitation sequence is chosen to complete the model. Images are generated with the model and compared with those formed with an AR model. A multidimensional rankorder model is formed from vector medians for use with multidimensional image data. The first application using the rank-order model is an impulsive noise detector. This exploits the notion of ‘multimodality’ in the histogram of a difference image of the degraded image and a rank-order filtered version. It uses the EM algorithm and a mixture model to automatically determine thresholds for detecting the impulsive noise. This method compares well with other detection methods, which require manual setting of thresholds, and to stack filtering, which requires ...

This dissertation is concerned with the development of Markov chain Monte Carlo (MCMC) methods for the Bayesian restoration of degraded audio signals. First, the Bayesian approach to time series modelling is reviewed, then established MCMC methods are introduced. The first problem to be addressed is that of model order uncertainty. A reversible-jump sampler is proposed which can move between models of different order. It is shown that faster convergence can be achieved by exploiting the analytic structure of the time series model. This approach to model order uncertainty is applied to the problem of noise reduction using the simulation smoother. The effects of incorrect autoregressive (AR) model orders are demonstrated, and a mixed model order MCMC noise reduction scheme is developed. Nonlinear time series models are surveyed, and the advantages of linear-in- the-parameters models explained. A nonlinear AR (NAR) model, ...

In this thesis, a general solution to the component separation problem in images is introduced. Unlike most existing works, the spatial dependencies of images are modelled in the separation process with the use of Markov random fields (MRFs). In the MRFs model, Cauchy density is used for the gradient images. We provide a general Bayesian framework for the estimation of the parameters of this model. Due to the intractability of the problem we resort to numerical solutions for the joint maximization of the a posteriori distribution of the sources, the mixing matrix and the noise variances. For numerical solution, four different methods are proposed. In first method, the difficulty of working analytically with general Gibbs distributions of MRF is overcome by using an approximate density. In this approach, the Gibbs distribution is modelled by the product of directional Gaussians. The ...

Digital video technology has been characterized by a steady growth in the last decade. New applications like video e-mail, third generation mobile phone video communications, videoconferencing, video streaming on the web continuously push for further evolution of research in digital video coding. In order to be sent over the internet or even wireless networks, video information clearly needs compression to meet bandwidth requirements. Compression is mainly realized by exploiting the redundancy present in the data. A sequence of images contains an intrinsic, intuitive and simple idea of redundancy: two successive images are very similar. This simple concept is called temporal redundancy. The research of a proper scheme to exploit the temporal redundancy completely changes the scenario between compression of still pictures and sequence of images. It also represents the key for very high performances in image sequence coding when compared ...

It is increasingly more common that an occasion is recorded by multiple individuals with the proliferation of recording devices such as smart phones. When properly aligned, these recordings may provide several audio and visual perspectives to a scene which leads to several applications in restoring, remastering and remixing frameworks in various fields. In this study, we interpret the problem of aligning multiple unsynchronized audio sequences in a probabilistic framework. In this manner, we propose a novel, model based approach where we define a template generative model. We define 6 different generative models using this template covering basically all kinds of features (real valued, positive, binary and categorical). Proper scoring functions that evaluates the quality of an alignment are derived from each model where we are able to penalize non-overlapping alignments and alignment of a single sequence against a pre-aligned sequences. ...

The large number of practical applications involving digital images has motivated a significant interest towards restoration solutions that improve the visual quality of the data under the presence of various acquisition and compression artifacts. Digital images are the results of an acquisition process based on the measurement of a physical quantity of interest incident upon an imaging sensor over a specified period of time. The quantity of interest depends on the targeted imaging application. Common imaging sensors measure the number of photons impinging over a dense grid of photodetectors in order to produce an image similar to what is perceived by the human visual system. Different applications focus on the part of the electromagnetic spectrum not visible by the human visual system, and thus require different sensing technologies to form the image. In all cases, even with the advance of ...

Resistivity distribution estimation, widely known as Electrical Impedance Tomography (EIT), is a non linear ill-posed inverse problem. However, the partial derivative equation ruling this experiment yields no analytical solution for arbitrary conductivity distribution. Thus, solving the forward problem requires an approximation. The Finite Element Method (FEM) provides us with a computationally cheap forward model which preserves the non linear image-data relation and also reveals sufficiently accurate for the inversion. Within the Bayesian approach, Markovian priors on the log-conductivity distribution are introduced for regularization. The neighborhood system is directly derived from the FEM triangular mesh structure. We first propose a maximum a posteriori (MAP) estimation with a Huber-Markov prior which favours smooth distributions while preserving locally discontinuous features. The resulting criterion is minimized with the pseudo-conjugate gradient method. Simulation results reveal significant improvements in terms of robustness to noise, computation rapidity ...

Sequential Monte Carlo (SMC) and Markov chain Monte Carlo (MCMC) methods provide computational tools for systematic inference and learning in complex dynamical systems, such as nonlinear and non-Gaussian state-space models. This thesis builds upon several methodological advances within these classes of Monte Carlo methods. Particular emphasis is placed on the combination of SMC and MCMC in so called particle MCMC algorithms. These algorithms rely on SMC for generating samples from the often highly autocorrelated state-trajectory. A specific particle MCMC algorithm, referred to as particle Gibbs with ancestor sampling (PGAS), is suggested. By making use of backward sampling ideas, albeit implemented in a forward-only fashion, PGAS enjoys good mixing even when using seemingly few particles in the underlying SMC sampler. This results in a computationally competitive particle MCMC algorithm. As illustrated in this thesis, PGAS is a useful tool for both ...

Motion estimation and compensation is of great importance for the compression of video sequences. In this dissertation a motion estimation/compensation approach based on a non-overlapping connected mesh of triangles is proposed. To manipulate the triangles within the connected mesh or ‘rubber sheet’ structure affin transforms are used which allow many different types of motion to be accurately modelled. Another advantage of this structure is that the non-overlapping triangles do not generate the typical artefacts associated with the current block based standards when operating at very low bitrates. The initial motion estimation/ compensation algorithms investigated implement a full search method which updates one vertex at a time matching sets of triangles between adjacent frames. Although the prediction performance is good the resulting computational load is high. This issue is addressed by deriving gradient-based algorithms which are found to be between one ...

The development of a fully unsupervised algorithm to achieve image segmentation is the central theme of this dissertation. Existing literature falls short of such a goal providing many algorithms capable of solving a subset of this highly challenging problem. Unsupervised segmentation is the process of identifying and locating the constituent regions of an observed image, while having no prior knowledge of the number of regions. The problem can be formulated in a Bayesian framework and through the use of an assumed model unsupervised segmentation can be posed as a problem of optimisation. This is the approach pursued throughout this dissertation. Throughout the literature, the commonly adopted model is an hierarchical image model whose underlying components are various forms of Markov Random Fields Gaussian. Markov Random Field models are used to model the textural content of the observed images regions, while ...

Dynamic textures are common in natural scenes. Examples of dynamic textures in video include fire, smoke, clouds, volatile organic compound (VOC) plumes in infra-red (IR) videos, trees in the wind, sea and ocean waves, etc. Researchers extensively studied 2-D textures and related problems in the fields of image processing and computer vision. On the other hand, there is very little research on dynamic texture detection in video. In this dissertation, signal and image processing methods developed for detection of a specific set of dynamic textures are presented. Signal and image processing methods are developed for the detection of flames and smoke in open and large spaces with a range of up to $30$m to the camera in visible-range (IR) video. Smoke is semi-transparent at the early stages of fire. Edges present in image frames with smoke start loosing their sharpness ...

Hyperspectral (HS) imaging, which consists of acquiring a same scene in several hundreds of contiguous spectral bands (a three dimensional data cube), has opened a new range of relevant applications, such as target detection [MS02], classification [C.-03] and spectral unmixing [BDPD+12]. However, while HS sensors provide abundant spectral information, their spatial resolution is generally more limited. Thus, fusing the HS image with other highly resolved images of the same scene, such as multispectral (MS) or panchromatic (PAN) images is an interesting problem. The problem of fusing a high spectral and low spatial resolution image with an auxiliary image of higher spatial but lower spectral resolution, also known as multi-resolution image fusion, has been explored for many years [AMV+11]. From an application point of view, this problem is also important as motivated by recent national programs, e.g., the Japanese next-generation space-borne ...

The main objective of this thesis is to suggest a general Bayesian framework for model selection based on the reversible jump Markov chain Monte Carlo (RJMCMC) algorithm. In particular, we aim to reveal the undiscovered potentials of RJMCMC in model selection applications by exploiting the original formulation to explore spaces of di erent classes or structures and thus, to show that RJMCMC o ers a wider interpretation than just being a trans-dimensional model selection algorithm. The general practice is to use RJMCMC in a trans-dimensional framework e.g. in model estimation studies of linear time series, such as AR and ARMA and mixture processes, etc. In this thesis, we propose a new interpretation on RJMCMC which reveals the undiscovered potentials of the algorithm. This new interpretation, firstly, extends the classical trans-dimensional approach to a much wider meaning by exploring the spaces ...

This thesis contributes to motion characterization through inertial and physiological signals captured by wearable devices and analyzed using signal processing and deep learning techniques. This research leverages the possibilities of motion analysis for three main applications: to know what physical activity a person is performing (Human Activity Recognition), to identify who is performing that motion (user identification) or know how the movement is being performed (motor anomaly detection). Most previous research has addressed human motion modeling using invasive sensors in contact with the user or intrusive sensors that modify the user’s behavior while performing an action (cameras or microphones). In this sense, wearable devices such as smartphones and smartwatches can collect motion signals from users during their daily lives in a less invasive or intrusive way. Recently, there has been an exponential increase in research focused on inertial-signal processing to ...

The field of Life Science Engineering (LSE) is rapidly expanding and predicted to grow strongly in the next decades. It covers areas of food and medical research, plant and pests’ research, and environmental research. In each research area, engineers try to find equations that model a certain life science problem. Once found, they research different numerical techniques to solve for the unknown variables of these equations. Afterwards, solution improvement is examined by adopting more accurate conventional techniques, or developing novel algorithms. In particular, signal and image processing techniques are widely used to solve those LSE problems require pattern recognition. However, due to the continuous evolution of the life science problems and their natures, these solution techniques can not cover all aspects, and therefore demanding further enhancement and improvement. The thesis presents numerical algorithms of digital signal and image processing to ...