## Epigraphical splitting of convex constraints. Application to image recovery, supervised classification, and image forgery detection. (2015)

Signal and Image Processing Algorithms Using Interval Convex Programming and Sparsity

In this thesis, signal and image processing algorithms based on sparsity and interval convex programming are developed for inverse problems. Inverse signal processing problems are solved by minimizing the ℓ1 norm or the Total Variation (TV) based cost functions in the literature. A modiﬁed entropy functional approximating the absolute value function is deﬁned. This functional is also used to approximate the ℓ1 norm, which is the most widely used cost function in sparse signal processing problems. The modiﬁed entropy functional is continuously diﬀerentiable, and convex. As a result, it is possible to develop iterative, globally convergent algorithms for compressive sensing, denoising and restoration problems using the modiﬁed entropy functional. Iterative interval convex programming algorithms are constructed using Bregman’s D-Projection operator. In sparse signal processing, it is assumed that the signal can be represented using a sparse set of coeﬃcients in ...

Kose, Kivanc — Bilkent University

Group-Sparse Regression - With Applications in Spectral Analysis and Audio Signal Processing

This doctorate thesis focuses on sparse regression, a statistical modeling tool for selecting valuable predictors in underdetermined linear models. By imposing different constraints on the structure of the variable vector in the regression problem, one obtains estimates which have sparse supports, i.e., where only a few of the elements in the response variable have non-zero values. The thesis collects six papers which, to a varying extent, deals with the applications, implementations, modifications, translations, and other analysis of such problems. Sparse regression is often used to approximate additive models with intricate, non-linear, non-smooth or otherwise problematic functions, by creating an underdetermined model consisting of candidate values for these functions, and linear response variables which selects among the candidates. Sparse regression is therefore a widely used tool in applications such as, e.g., image processing, audio processing, seismological and biomedical modeling, but is ...

Kronvall, Ted — Lund University

This thesis deals with problems of Pattern Recognition in the framework of Machine Learning (ML) and, specifically, Statistical Learning Theory (SLT), using Support Vector Machines (SVMs). The focus of this work is on the geometric interpretation of SVMs, which is accomplished through the notion of Reduced Convex Hulls (RCHs), and its impact on the derivation of new, efficient algorithms for the solution of the general SVM optimization task. The contributions of this work is the extension of the mathematical framework of RCHs, the derivation of novel geometric algorithms for SVMs and, finally, the application of the SVM algorithms to the field of Medical Image Analysis and Diagnosis (Mammography). Geometric SVM Framework's extensions: The geometric interpretation of SVMs is based on the notion of Reduced Convex Hulls. Although the geometric approach to SVMs is very intuitive, its usefulness was restricted by ...

Mavroforakis, Michael — University of Athens

Constrained Non-negative Matrix Factorization for Vocabulary Acquisition from Continuous Speech

One desideratum in designing cognitive robots is autonomous learning of communication skills, just like humans. The primary step towards this goal is vocabulary acquisition. Being different from the training procedures of the state-of-the-art automatic speech recognition (ASR) systems, vocabulary acquisition cannot rely on prior knowledge of language in the same way. Like what infants do, the acquisition process should be data-driven with multi-level abstraction and coupled with multi-modal inputs. To avoid lengthy training efforts in a word-by-word interactive learning process, a clever learning agent should be able to acquire vocabularies from continuous speech automatically. The work presented in this thesis is entitled \emph{Constrained Non-negative Matrix Factorization for Vocabulary Acquisition from Continuous Speech}. Enlightened by the extensively studied techniques in ASR, we design computational models to discover and represent vocabularies from continuous speech with little prior knowledge of the language to ...

Sun, Meng — Katholieke Universiteit Leuven

The task of robust regression is of particular importance in signal processing, statistics and machine learning. Ordinary estimators, such as the Least Squares (LS) one, fail to achieve sufficiently good performance in the presence of outliers. Although the problem has been addressed many decades ago and several methods have been established, it has recently attracted more attention in the context of sparse modeling and sparse optimization techniques. The latter is the line that has been followed in the current dissertation. The reported research, led to the development of a novel approach in the context of greedy algorithms. The model adopts the decomposition of the noise into two parts: a) the inlier noise and b) the outliers, which are explicitly modeled by employing sparse modeling arguments. Based on this rationale and inspired by the popular Orthogonal Matching Pursuit (OMP), two novel ...

Papageorgiou, George — National and Kapodistrian University of Athens

Contributions to signal analysis and processing using compressed sensing techniques

Chapter 2 contains a short introduction to the fundamentals of compressed sensing theory, which is the larger context of this thesis. We start with introducing the key concepts of sparsity and sparse representations of signals. We discuss the central problem of compressed sensing, i.e. how to adequately recover sparse signals from a small number of measurements, as well as the multiple formulations of the reconstruction problem. A large part of the chapter is devoted to some of the most important conditions necessary and/or sufficient to guarantee accurate recovery. The aim is to introduce the reader to the basic results, without the burden of detailed proofs. In addition, we also present a few of the popular reconstruction and optimization algorithms that we use throughout the thesis. Chapter 3 presents an alternative sparsity model known as analysis sparsity, that offers similar recovery ...

Cleju, Nicolae — "Gheorghe Asachi" Technical University of Iasi

Automatic Detection, Classification and Restoration of Defects in Historical Images

Historical photos are significant attestations of the inheritance of the past. Since Photography is an art that is more than 150 years old, more and more diffuse are the photographic archives all over the world. Nevertheless, time and bad preservation corrupts physical supports, and many important historical documents risk to be ruined and their content lost. Therefore solutions must be implemented to preserve their state and to recover damaged information. This PhD thesis proposes a general methodology, and several applicative solutions, to handle these problems, by means of digitization and digital restoration. The purpose is to create a useful tool to support non-expert users in the restoration process of damaged historical images. The content of this thesis is outlined as follows: Chapter 1 gives an overview on the problems related to management and preservation of cultural repositories, and discusses about ...

Mazzola, Giuseppe — Università degli studi di Palermo - Dipartimento di Ingegneria Informatica

Learning from structured EEG and fMRI data supporting the diagnosis of epilepsy

Epilepsy is a neurological condition that manifests in epileptic seizures as a result of an abnormal, synchronous activity of a large group of neurons. Depending on the affected brain regions, seizures produce various severe clinical symptoms. Epilepsy cannot be cured and in many cases is not controlled by medication either. Surgical resection of the region responsible for generating the epileptic seizures might offer remedy for these patients. Electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) measure the changes of brain activity in time over different locations of the brain. As such, they provide valuable information on the nature, the timing and the spatial origin of the epileptic activity. Unfortunately, both techniques record activity of different brain and artefact sources as well. Hence, EEG and fMRI signals are characterised by low signal to noise ratio. Data quality and the vast amount ...

Hunyadi, Borbála — KU Leuven

Offline Signature Verification with User-Based and Global Classifiers of Local Features

Signature veriﬁcation deals with the problem of identifying forged signatures of a user from his/her genuine signatures. The difficulty lies in identifying allowed variations in a user’s signatures, in the presence of high intra-class and low inter-class variability (the forgeries may be more similar to a user’s genuine signature, compared to his/her other genuine signatures). The problem can be seen as a non-rigid object matching where classes are very similar. In the ﬁeld of biometrics, signature is considered a behavioral biometric and the problem possesses further difficulties compared to other modalities (e.g. ﬁngerprints) due to the added issue of skilled forgeries. A novel offline (image-based) signature veriﬁcation system is proposed in this thesis. In order to capture the signature’s stable parts and alleviate the difficulty of global matching, local features (histogram of oriented gradients, local binary patterns) are used, based ...

Yılmaz, Mustafa Berkay — Sabancı University

Video Content Analysis by Active Learning

Advances in compression techniques, decreasing cost of storage, and high-speed transmission have facilitated the way videos are created, stored and distributed. As a consequence, videos are now being used in many applications areas. The increase in the amount of video data deployed and used in today's applications reveals not only the importance as multimedia data type, but also led to the requirement of efficient management of video data. This management paved the way for new research areas, such as indexing and retrieval of video with respect to their spatio-temporal, visual and semantic contents. This thesis presents work towards a unified framework for semi-automated video indexing and interactive retrieval. To create an efficient index, a set of representative key frames are selected which capture and encapsulate the entire video content. This is achieved by, firstly, segmenting the video into its constituent ...

Camara Chavez, Guillermo — Federal University of Minas Gerais

Parallel Magnetic Resonance Imaging reconstruction problems using wavelet representations

To reduce scanning time or improve spatio-temporal resolution in some MRI applications, parallel MRI acquisition techniques with multiple coils have emerged since the early 90’s as powerful methods. In these techniques, MRI images have to be reconstructed from ac- quired undersampled “k-space” data. To this end, several reconstruction techniques have been proposed such as the widely-used SENSitivity Encoding (SENSE) method. However, the reconstructed images generally present artifacts due to the noise corrupting the ob- served data and coil sensitivity profile estimation errors. In this work, we present novel SENSE-based reconstruction methods which proceed with regularization in the complex wavelet domain so as to promote the sparsity of the solution. These methods achieve ac- curate image reconstruction under degraded experimental conditions, in which neither the SENSE method nor standard regularized methods (e.g. Tikhonov) give convincing results. The proposed approaches relies on ...

Lotfi CHAARI — University Paris-Est

Digital Processing Based Solutions for Life Science Engineering Recognition Problems

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 ...

Hussein, Walid — Technische Universität München

Density-based shape descriptors and similarity learning for 3D object retrieval

Next generation search engines will enable query formulations, other than text, relying on visual information encoded in terms of images and shapes. The 3D search technology, in particular, targets specialized application domains ranging from computer aided-design and manufacturing to cultural heritage archival and presentation. Content-based retrieval research aims at developing search engines that would allow users to perform a query by similarity of content. This thesis deals with two fundamentals problems in content-based 3D object retrieval: (1) How to describe a 3D shape to obtain a reliable representative for the subsequent task of similarity search? (2) How to supervise the search process to learn inter-shape similarities for more effective and semantic retrieval? Concerning the first problem, we develop a novel 3D shape description scheme based on probability density of multivariate local surface features. We constructively obtain local characterizations of 3D ...

Akgul, Ceyhun Burak — Bogazici University and Telecom ParisTech

Robust Methods for Sensing and Reconstructing Sparse Signals

Compressed sensing (CS) is a recently introduced signal acquisition framework that goes against the traditional Nyquist sampling paradigm. CS demonstrates that a sparse, or compressible, signal can be acquired using a low rate acquisition process. Since noise is always present in practical data acquisition systems, sensing and reconstruction methods are developed assuming a Gaussian (light-tailed) model for the corrupting noise. However, when the underlying signal and/or the measurements are corrupted by impulsive noise, commonly employed linear sampling operators, coupled with Gaussian-derived reconstruction algorithms, fail to recover a close approximation of the signal. This dissertation develops robust sampling and reconstruction methods for sparse signals in the presence of impulsive noise. To achieve this objective, we make use of robust statistics theory to develop appropriate methods addressing the problem of impulsive noise in CS systems. We develop a generalized Cauchy distribution (GCD) ...

Carrillo, Rafael — University of Delaware

Learning to recognise : a study on one-class classification and active learning

The thesis treats classification problems which are undersampled or where there exist an unbalance between classes in the sampling. The thesis is divided into three parts. The first two parts treat the problem of one-class classification. In the one-class classification problem, it is assumed that only examples of one of the classes, the target class, are available. The fact that no (or almost no) examples of other classes are available makes the one-class classification an example of an extremely unbalance problem. Therefore, such problem can not be described accurately by existing multi-class classifiers. However, a need to solve such classification rises from many theoretical and practical problems, e.g. the concept learning, machine fault detection and face recognition. In the third part of the thesis, we treat classification problems which are undersampled but not necessary unbalanced. In such problems, additional examples ...

Juszczak, Piotr — Delft University of Technology

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