Représentations parcimonieuses pour les signaux multivariés

Dans cette thèse, nous étudions les méthodes d'approximation et d'apprentissage qui fournissent des représentations parcimonieuses. Ces méthodes permettent d'analyser des bases de données très redondantes à l'aide de dictionnaires d'atomes appris. Etant adaptés aux données étudiées, ils sont plus performants en qualité de représentation que les dictionnaires classiques dont les atomes sont définis analytiquement. Nous considérons plus particulièrement des signaux multivariés résultant de l'acquisition simultanée de plusieurs grandeurs, comme les signaux EEG ou les signaux de mouvements 2D et 3D. Nous étendons les méthodes de représentations parcimonieuses au modèle multivarié, pour prendre en compte les interactions entre les différentes composantes acquises simultanément. Ce modèle est plus flexible que l'habituel modèle multicanal qui impose une hypothèse de rang 1. Nous étudions des modèles de représentations invariantes : invariance par translation temporelle, invariance par rotation, etc. En ajoutant des degrés de liberté supplémentaires, chaque noyau est potentiellement démultiplié en une famille d'atomes, translatés à tous les échantillons, tournés dans toutes les orientations, etc. Ainsi, un dictionnaire de noyaux invariants génère un dictionnaire d'atomes très redondant, et donc idéal pour représenter les données étudiées redondantes. Toutes ces invariances nécessitent la mise en place de méthodes adaptées à ces modèles. L'invariance par translation temporelle est une propriété incontournable pour l'étude de signaux temporels ayant une variabilité temporelle naturelle. Dans le cas de l'invariance par rotation 2D et 3D, nous constatons l'efficacité de l'approche non-orientée sur celle orientée, même dans le cas où les données ne sont pas tournées. En effet, le modèle non-orienté permet de détecter les invariants des données et assure la robustesse à la rotation quand les données tournent. Nous constatons aussi la reproductibilité des décompositions parcimonieuses sur un dictionnaire appris. Cette propriété générative s'explique par le fait que l'apprentissage de dictionnaire est une généralisation des K-means. D'autre part, nos représentations possèdent de nombreuses invariances, ce qui est idéal pour faire de la classification. Nous étudions donc comment effectuer une classification adaptée au modèle d'invariance par translation, en utilisant des fonctions de groupement consistantes par translation.In this thesis, we study approximation and learning methods which provide sparse representations. These methods allow to analyze very redundant data-bases thanks to learned atoms dictionaries. Being adapted to studied data, they are more efficient in representation quality than classical dictionaries with atoms defined analytically. We consider more particularly multivariate signals coming from the simultaneous acquisition of several quantities, as EEG signals or 2D and 3D motion signals. We extend sparse representation methods to the multivariate model, to take into account interactions between the different components acquired simultaneously. This model is more flexible that the common multichannel one which imposes a hypothesis of rank 1. We study models of invariant representations: invariance to temporal shift, invariance to rotation, etc. Adding supplementary degrees of freedom, each kernel is potentially replicated in an atoms family, translated at all samples, rotated at all orientations, etc. So, a dictionary of invariant kernels generates a very redundant atoms dictionary, thus ideal to represent the redundant studied data. All these invariances require methods adapted to these models. Temporal shift-invariance is an essential property for the study of temporal signals having a natural temporal variability. In the 2D and 3D rotation invariant case, we observe the efficiency of the non-oriented approach over the oriented one, even when data are not revolved. Indeed, the non-oriented model allows to detect data invariants and assures the robustness to rotation when data are revolved. We also observe the reproducibility of the sparse decompositions on a learned dictionary. This generative property is due to the fact that dictionary learning is a generalization of K-means. Moreover, our representations have many invariances that is ideal to make classification. We thus study how to perform a classification adapted to the shift-invariant model, using shift-consistent pooling functions.SAVOIE-SCD - Bib.électronique (730659901) / SudocGRENOBLE1/INP-Bib.électronique (384210012) / SudocGRENOBLE2/3-Bib.électronique (384219901) / SudocSudocFranceF

Sparsity & [and] dictionaries - algorithms & [and] design

With the flood of information available today the question how to deal with high dimensional data/signals, which are cumbersome to handle, to calculate with and to store, is highly important. One approach to reducing this flood is to find sparse signal representations, as a signal that is the linear combination of a few elements from a pool of building blocks, can be reduced to the few coefficients of this representation. If these building blocks form a basis, finding the sparse representation poses no problem but unfortunately not many signal classes are sparse in a basis. Taking more building blocks, i.e. a redundant dictionary, increases the chances of having sparse representations, but actually finding them becomes very hard. This led to the development of numerous strategies and algorithms for finding sparse representations, with varying complexity and success rate. The first part of the thesis deals with two of those algorithms, Thresholding and Matching Pursuit, from a more theoretical point of view. It is shown that both those greedy algorithms can be improved with a little trick, that does not increase their complexity, and that when considering their average instead of their worst case performance they perform quite well in comparison to more complex methods. The second part of thesis treats questions concerning the whole dictionary and its properties. First it gives more evidence that sparsity is useful by extending the concept of compressed sensing to signals that are sparse not in a basis but in a redundant dictionary. Thus to record a sparse signal it is not necessary to make as many measurements as the dimension of the signal but only a multiple of the number of dictionary elements used to represent it. Next we show that dictionaries cannot only provide sparse representations but that their geometric properties can also be exploited to model data structures. Here we explain how to model different subclasses of a class of signals by incoherent subspaces, present an algorithm to learn a dictionary made out of these subspaces and then use it for classification of faces. Finally we turn back to the sparse representation problem and study the fundamental question how to find a dictionary providing sparse representations. We pick up the idea to learn a dictionary via minimisation of a continuous cost function and provide conditions, guaranteeing that the decomposition of a collection of training signals into a dictionary and a coefficient matrix constitutes a local minimum. We also analyse statistically when these conditions are fulfilled with high probability

Compressed Sensing for Open-ended Waveguide Non-Destructive Testing and Evaluation

Ph. D. ThesisNon-destructive testing and evaluation (NDT&E) systems using open-ended waveguide (OEW) suffer from critical challenges. In the sensing stage, data acquisition is time-consuming by raster scan, which is difficult for on-line detection. Sensing stage also disregards demand for the latter feature extraction process, leading to an excessive amount of data and processing overhead for feature extraction. In the feature extraction stage, efficient and robust defect region segmentation in the obtained image is challenging for a complex image background. Compressed sensing (CS) demonstrates impressive data compression ability in various applications using sparse models. How to develop CS models in OEW NDT&E that jointly consider sensing & processing for fast data acquisition, data compression, efficient and robust feature extraction is remaining challenges. This thesis develops integrated sensing-processing CS models to address the drawbacks in OEW NDT systems and carries out their case studies in low-energy impact damage detection for carbon fibre reinforced plastics (CFRP) materials. The major contributions are: (1) For the challenge of fast data acquisition, an online CS model is developed to offer faster data acquisition and reduce data amount without any hardware modification. The images obtained with OEW are usually smooth which can be sparsely represented with discrete cosine transform (DCT) basis. Based on this information, a customised 0/1 Bernoulli matrix for CS measurement is designed for downsampling. The full data is reconstructed with orthogonal matching pursuit algorithm using the downsampling data, DCT basis, and the customised 0/1 Bernoulli matrix. It is hard to determine the sampling pixel numbers for sparse reconstruction when lacking training data, to address this issue, an accumulated sampling and recovery process is developed in this CS model. The defect region can be extracted with the proposed histogram threshold edge detection (HTED) algorithm after each recovery, which forms an online process. A case study in impact damage detection on CFRP materials is carried out for validation. The results show that the data acquisition time is reduced by one order of magnitude while maintaining equivalent image quality and defect region as raster scan. (2) For the challenge of efficient data compression that considers the later feature extraction, a feature-supervised CS data acquisition method is proposed and evaluated. It reserves interested features while reducing the data amount. The frequencies which reveal the feature only occupy a small part of the frequency band, this method finds these sparse frequency range firstly to supervise the later sampling process. Subsequently, based on joint sparsity of neighbour frame and the extracted frequency band, an aligned spatial-spectrum sampling scheme is proposed. The scheme only samples interested frequency range for required features by using a customised 0/1 Bernoulli measurement matrix. The interested spectral-spatial data are reconstructed jointly, which has much faster speed than frame-by-frame methods. The proposed feature-supervised CS data acquisition is implemented and compared with raster scan and the traditional CS reconstruction in impact damage detection on CFRP materials. The results show that the data amount is reduced greatly without compromising feature quality, and the gain in reconstruction speed is improved linearly with the number of measurements. (3) Based on the above CS-based data acquisition methods, CS models are developed to directly detect defect from CS data rather than using the reconstructed full spatial data. This method is robust to texture background and more time-efficient that HTED algorithm. Firstly, based on the histogram is invariant to down-sampling using the customised 0/1 Bernoulli measurement matrix, a qualitative method which only gives binary judgement of defect is developed. High probability of detection and accuracy is achieved compared to other methods. Secondly, a new greedy algorithm of sparse orthogonal matching pursuit (spOMP)-based defect region segmentation method is developed to quantitatively extract the defect region, because the conventional sparse reconstruction algorithms cannot properly use the sparse character of correlation between the measurement matrix and CS data. The proposed algorithms are faster and more robust to interference than other algorithms.China Scholarship Counci

Sparse Representation-Based Framework for Preprocessing Brain MRI

This thesis addresses the use of sparse representations, specifically Dictionary Learning and Sparse Coding, for pre-processing brain MRI, so that the processed image retains the fine details of the original image, to improve the segmentation of brain structures, to assess whether there is any relationship between alterations in brain structures and the behavior of young offenders. Denoising an MRI while keeping fine details is a difficult task; however, the proposed method, based on sparse representations, NLM, and SVD can filter noise while prevents blurring, artifacts, and residual noise. Segmenting an MRI is a non-trivial task; because normally the limits between regions in these images may be neither clear nor well defined, due to the problems which affect MRI. However, this method, from both the label matrix of the segmented MRI and the original image, yields a new improved label matrix in which improves the limits among regions.DoctoradoDoctor en Ingeniería de Sistemas y Computació

New approaches for unsupervised transcriptomic data analysis based on Dictionary learning

The era of high-throughput data generation enables new access to biomolecular profiles and exploitation thereof. However, the analysis of such biomolecular data, for example, transcriptomic data, suffers from the so-called "curse of dimensionality". This occurs in the analysis of datasets with a significantly larger number of variables than data points. As a consequence, overfitting and unintentional learning of process-independent patterns can appear. This can lead to insignificant results in the application. A common way of counteracting this problem is the application of dimension reduction methods and subsequent analysis of the resulting low-dimensional representation that has a smaller number of variables. In this thesis, two new methods for the analysis of transcriptomic datasets are introduced and evaluated. Our methods are based on the concepts of Dictionary learning, which is an unsupervised dimension reduction approach. Unlike many dimension reduction approaches that are widely applied for transcriptomic data analysis, Dictionary learning does not impose constraints on the components that are to be derived. This allows for great flexibility when adjusting the representation to the data. Further, Dictionary learning belongs to the class of sparse methods. The result of sparse methods is a model with few non-zero coefficients, which is often preferred for its simplicity and ease of interpretation. Sparse methods exploit the fact that the analysed datasets are highly structured. Indeed, a characteristic of transcriptomic data is particularly their structuredness, which appears due to the connection of genes and pathways, for example. Nonetheless, the application of Dictionary learning in medical data analysis is mainly restricted to image analysis. Another advantage of Dictionary learning is that it is an interpretable approach. Interpretability is a necessity in biomolecular data analysis to gain a holistic understanding of the investigated processes. Our two new transcriptomic data analysis methods are each designed for one main task: (1) identification of subgroups for samples from mixed populations, and (2) temporal ordering of samples from dynamic datasets, also referred to as "pseudotime estimation". Both methods are evaluated on simulated and real-world data and compared to other methods that are widely applied in transcriptomic data analysis. Our methods convince through high performance and overall outperform the comparison methods

Towards Fast and High-quality Biomedical Image Reconstruction

Department of Computer Science and EngineeringReconstruction is an important module in the image analysis pipeline with purposes of isolating the majority of meaningful information that hidden inside the acquired data. The term ???reconstruction??? can be understood and subdivided in several specific tasks in different modalities. For example, in biomedical imaging, such as Computed Tomography (CT), Magnetic Resonance Image (MRI), that term stands for the transformation from the, possibly fully or under-sampled, spectral domains (sinogram for CT and k-space for MRI) to the visible image domains. Or, in connectomics, people usually refer it to segmentation (reconstructing the semantic contact between neuronal connections) or denoising (reconstructing the clean image). In this dissertation research, I will describe a set of my contributed algorithms from conventional to state-of-the-art deep learning methods, with a transition at the data-driven dictionary learning approaches that tackle the reconstruction problems in various image analysis tasks.clos

Connected Attribute Filtering Based on Contour Smoothness

A new attribute measuring the contour smoothness of 2-D objects is presented in the context of morphological attribute filtering. The attribute is based on the ratio of the circularity and non-compactness, and has a maximum of 1 for a perfect circle. It decreases as the object boundary becomes irregular. Computation on hierarchical image representation structures relies on five auxiliary data members and is rapid. Contour smoothness is a suitable descriptor for detecting and discriminating man-made structures from other image features. An example is demonstrated on a very-high-resolution satellite image using connected pattern spectra and the switchboard platform