In recent years, sparsity and compressive sensing have attracted significant attention in parameter estimation tasks, including frequency estimation, delay estimation, and localization. Parametric dictionaries collect signals for a sampling of the parameter space and can yield sparse representations for the signals of interest when the sampling is sufficiently dense. While this dense sampling can lead to high coherence in the dictionary, it is possible to leverage structured sparsity models to prevent highly coherent dictionary elements from appearing simultaneously in a signal representation, alleviating these coherence issues. However, the resulting approaches depend heavily on a careful setting of the maximum allowable coherence; furthermore, their guarantees apply to the coefficient vector recovery and do not translate in general to the parameter estimation task. We propose a new algorithm based on optimal sparse approximation measured by earth mover's distance (EMD). Theoretically, we show that EMD provides a better metric for the performance of parametric dictionary-based parameter estimation and $K$-median clustering algorithms has the potential to solve the EMD-optimal sparse approximation problems. Simulations show that the resulting compressive parameter estimation algorithm is better at addressing the coherence issuers without a careful setting of additional parameters.

Le nombre croissant d'approches de détection de texte proposé dans la littérature exige une évaluation rigoureuse de la performance. Un protocole d'évaluation repose sur trois éléments: une vérité terrain fiable, une stratégie d'appariement et enfin un ensemble de métriques. Peu de protocoles existent et ces protocoles manquent souvent de précision. Dans cette thèse, nous proposons un nouveau protocole d'évaluation qui résout la plupart des problèmes rencontrés dans les méthodes d'évaluation actuelles. Ce travail est axé sur trois contributions principales : tout d’abord, nous introduisons une représentation complexe de la vérité terrain qui ne contraint pas les détecteurs de texte à adopter un niveau de granularité de détection spécifique ou une représentation d'annotation ; d’autre part, nous proposons un ensemble de règles capables d'évaluer tous types de scénario qui peuvent se produire entre les objets de la vérité terrain et les détections correspondantes ; et enfin, nous montrons comment nous pouvons analyser un ensemble de résultats de détection, non seulement à travers un ensemble de mesures, mais aussi à travers une représentation visuelle intuitive. Un défi fréquent pour de nombreux systèmes de détection de texte est d'aborder la variété des caractéristiques de texte dans des images naturelles ou d’origine numérique pour lesquels les OCR actuels ne sont pas bien adaptées. Par exemple, des textes en perspective sont fréquemment présents dans les images réelles. Dans cette thèse, nous proposons également une procédure de rectification capable de corriger des textes hautement déformés, évalué sur un ensemble de données difficiles. / The growing number of text detection approaches proposed in the literature requires a rigorous performance evaluation and ranking. An evaluation protocol relies on three elements: a reliable text reference, a matching strategy and finally a set of metrics. The few existing evaluation protocols often lack accuracy either due to inconsistent matching or due to unrepresentative metrics. In this thesis we propose a new evaluation protocol that tackles most of the drawbacks faced by currently used evaluation methods. This work is focused on three main contributions: firstly, we introduce a complex text reference representation that does not constrain text detectors to adopt a specific detection granularity level or annotation representation; secondly, we propose a set of matching rules capable of evaluating any type of scenario that can occur between a text reference and a detection; and finally we show how we can analyze a set of detection results, not only through a set of metrics, but also through an intuitive visual representation. A frequent challenge for many Text Understanding Systems is to tackle the variety of text characteristics in born-digital and natural scene images for which current OCRs are not well adapted. For example, texts in perspective are frequently present in real-word images because the camera capture angle is not normal to the plane containing the text regions. Despite the ability of some detectors to accurately localize such text objects, the recognition stage fails most of the time. In this thesis we also propose a rectification procedure capable of correcting highly distorted texts evaluated on a very challenging dataset.

The Customer Success department at Visma handles about 200 000 customer chats each year, the chat dialogues are stored and contain both questions and answers. In order to get an idea of what customers ask about, the Customer Success department has to read a random sample of the chat dialogues manually. This thesis develops and investigates an analysis tool for the chat data, using the approach of clustering and summarization. The approach aims to decrease the time spent and increase the quality of the analysis. Models for clustering (K-means, DBSCAN and HDBSCAN) and extractive summarization (K-means, LSA and TextRank) are compared. Each algorithm is combined with three different text representations (TFIDF, S-BERT and FastText) to create models for evaluation. These models are evaluated against a test set, created for the purpose of this thesis. Silhouette Index and Adjusted Rand Index are used to evaluate the clustering models. ROUGE measure together with a qualitative evaluation are used to evaluate the extractive summarization models. In addition to this, the best clustering model is further evaluated to understand how different data sizes impact performance. TFIDF Unigram together with HDBSCAN or K-means obtained the best results for clustering, whereas FastText together with TextRank obtained the best results for extractive summarization. This thesis applies known models on a textual domain of customer chat dialogues, something that, to our knowledge, has previously not been done in literature.

Magnetic Resonance Imaging (MRI) is an essential healthcare technology, with diffusion MRI being a specialized technique. Diffusion MRI exploits the inherent diffusion of water molecules within the human body to produce a high-resolution tissue image. An MRI image contains information about a 3D volume in space, composed of 3D units called voxels. This thesis assumes the existence of a probability distribution for the diffusivity within a voxel, the diffusion tensor distribution (DTD), with the diffusivity described by a family of diffusion tensors. In 2D, these tensors can be described by 2x2 symmetric positive semidefinite matrices. The objective is to estimate the DTD of a voxel with neural networks for both 1D and 2D diffusion tensors. We assume the DTD to be a discrete distribution, with a finite set of diffusion tensors. The MRI signal is influenced by several experimental parameters, which for diffusion measurements are summarized in the measurement tensor B. To determine the diffusivity of a voxel, multiple measurement tensors are utilized, producing various MRI signals. From these signals, the network estimates the corresponding DTD of the voxel. The network seeks to employ the earth mover's distance (EMD) as its loss function, given the established use of EMD as a distance between probability distributions. Due to the difficulty of expressing the EMD as a differentiable loss function, the Sinkhorn distance, an entropic regularized approximation of the EMD, is used instead. Different network configurations are explored through simulations to identify optimal settings, assessed by the EMD loss and the closeness of the Sinkhorn loss to the EMD. The results indicate that the network achieves satisfactory accuracy when approximating DTDs with a small number of diffusivities, but struggles when the number increases. Future work could explore alternative loss functions and advanced neural network architectures. Despite the challenges encountered, this thesis offers relevant insight into the estimation of diffusion tensor distributions.