High resolution 3D images are of high interest in military operations, where data can be used to classify and identify targets. The Swedish defence research agency (FOI) is interested in the latest research and technologies in this area. A draw- back with normal 3D-laser systems are the lack of high resolution for long range measurements. One technique for high long range resolution laser radar is based on time correlated single photon counting (TCSPC). By repetitively sending out short laser pulses and measure the time of flight (TOF) of single reflected pho- tons, extremely accurate range measurements can be done. A drawback with this method is that it is hard to create single photon detectors with many pixels and high temporal resolution, hence a single detector is used. Scanning an entire scene with one detector is very time consuming and instead, as this thesis is all about, the entire scene can be measured with less measurements than the number of pixels. To do this a technique called compressed sensing (CS) is introduced. CS utilizes that signals normally are compressible and can be represented sparse in some basis representation. CS sets other requirements on the sampling compared to the normal Shannon-Nyquist sampling theorem. With a digital micromirror device (DMD) linear combinations of the scene can be reflected onto the single photon detector, creating scalar intensity values as measurements. This means that fewer DMD-patterns than the number of pixels can reconstruct the entire 3D-scene. In this thesis a computer model of the laser system helps to evaluate different CS reconstruction methods with different scenarios of the laser system and the scene. The results show how many measurements that are required to reconstruct scenes properly and how the DMD-patterns effect the results. CS proves to enable a great reduction, 85 − 95 %, of the required measurements com- pared to pixel-by-pixel scanning system. Total variation minimization proves to be the best choice of reconstruction method. / Högupplösta 3D-bilder är väldigt intressanta i militära operationer där data kan utnyttjas för klassificering och identifiering av mål. Det är av stort intresse hos Totalförsvarets forskningsinstitut (FOI) att undersöka de senaste teknikerna in- om detta område. Ett stort problem med vanliga 3D-lasersystem är att de saknar hög upplösning för långa mätavstånd. En teknik som har hög avståndsupplös- ning är tidskorrelerande enfotonräknare, som kan räkna enstaka fotoner med extremt bra noggrannhet. Ett sådant system belyser en scen med laserljus och mäter sedan reflektionstiden för enstaka fotoner och kan på så sätt mäta avstånd. Problemet med denna metod är att göra detektion av många pixlar när man bara kan använda en detektor. Att skanna en hel scen med en detektor tar väldigt lång tid och istället handlar det här exjobbet om att göra färre mätningar än antalet pixlar, men ändå återskapa hela 3D-scenen. För att åstadkomma detta används en ny teknik kallad Compressed Sensing (CS). CS utnyttjar att mätdata normalt är komprimerbar och skiljer sig från det traditionella Shannon-Nyquists krav på sampling. Med hjälp av ett Digital Micromirror Device (DMD) kan linjärkombi- nationer av scenen speglas ner på enfotondetektorn och med färre DMD-mönster än antalet pixlar kan hela 3D-scenen återskapas. Med hjälp av en egenutvecklad lasermodell evalueras olika CS rekonstruktionsmetoder och olika scenarier av la- sersystemet. Arbetet visar att basrepresentationen avgör hur många mätningar som behövs och hur olika uppbyggnader av DMD-mönstren påverkar resultatet. CS visar sig möjliggöra att 85 − 95 % färre mätningar än antalet pixlar behövs för att avbilda hela 3D-scener. Total variation minimization visar sig var det bästa valet av rekonstruktionsmetod.

Digital image acquisition can be a time consuming process for situations where high spatial resolution is required. As such, optimizing the acquisition mechanism is of high importance for many measurement applications. Acquiring such data through a dynamically small subset of measurement locations can address this problem. In such a case, the measured information can be regarded as incomplete, which necessitates the application of special reconstruction tools to recover the original data set. The reconstruction can be performed based on the concept of sparse signal representation. Recovering signals and images from their sub-Nyquist measurements forms the core idea of compressive sensing (CS). In this work, a CS-based data-guided statistical sparse measurements method is presented, implemented and evaluated. This method significantly improves image reconstruction from sparse measurements. In the data-guided statistical sparse measurements approach, signal sampling distribution is optimized for improving image reconstruction performance. The sampling distribution is based on underlying data rather than the commonly used uniform random distribution. The optimal sampling pattern probability is accomplished by learning process through two methods - direct and indirect. The direct method is implemented for learning a nonparametric probability density function directly from the dataset. The indirect learning method is implemented for cases where a mapping between extracted features and the probability density function is required. The unified model is implemented for different representation domains, including frequency domain and spatial domain. Experiments were performed for multiple applications such as optical coherence tomography, bridge structure vibration, robotic vision, 3D laser range measurements and fluorescence microscopy. Results show that the data-guided statistical sparse measurements method significantly outperforms the conventional CS reconstruction performance. Data-guided statistical sparse measurements method achieves much higher reconstruction signal-to-noise ratio for the same compression rate as the conventional CS. Alternatively, Data-guided statistical sparse measurements method achieves similar reconstruction signal-to-noise ratio as the conventional CS with significantly fewer samples.

Digital image acquisition can be a time consuming process for situations where high spatial resolution is required. As such, optimizing the acquisition mechanism is of high importance for many measurement applications. Acquiring such data through a dynamically small subset of measurement locations can address this problem. In such a case, the measured information can be regarded as incomplete, which necessitates the application of special reconstruction tools to recover the original data set. The reconstruction can be performed based on the concept of sparse signal representation. Recovering signals and images from their sub-Nyquist measurements forms the core idea of compressive sensing (CS). In this work, a CS-based data-guided statistical sparse measurements method is presented, implemented and evaluated. This method significantly improves image reconstruction from sparse measurements. In the data-guided statistical sparse measurements approach, signal sampling distribution is optimized for improving image reconstruction performance. The sampling distribution is based on underlying data rather than the commonly used uniform random distribution. The optimal sampling pattern probability is accomplished by learning process through two methods - direct and indirect. The direct method is implemented for learning a nonparametric probability density function directly from the dataset. The indirect learning method is implemented for cases where a mapping between extracted features and the probability density function is required. The unified model is implemented for different representation domains, including frequency domain and spatial domain. Experiments were performed for multiple applications such as optical coherence tomography, bridge structure vibration, robotic vision, 3D laser range measurements and fluorescence microscopy. Results show that the data-guided statistical sparse measurements method significantly outperforms the conventional CS reconstruction performance. Data-guided statistical sparse measurements method achieves much higher reconstruction signal-to-noise ratio for the same compression rate as the conventional CS. Alternatively, Data-guided statistical sparse measurements method achieves similar reconstruction signal-to-noise ratio as the conventional CS with significantly fewer samples.

Le codage parcimonieux permet la reconstruction d'un signal à partir de quelques projections linéaires de celui-ci, sous l'hypothèse que le signal se décompose de manière parcimonieuse, c'est-à-dire avec peu de coefficients, sur un dictionnaire connu. Le codage est simple, et la complexité est déportée sur la reconstruction. Après une explication détaillée du fonctionnement du codage parcimonieux, une présentation de quelques résultats théoriques et quelques simulations pour cerner les performances envisageables, nous nous intéressons à trois problèmes : d'abord, l'étude de conception d'un système permettant le codage d'un signal par une matrice binaire, et des avantages apportés par une telle implémentation. Ensuite, nous nous intéressons à la détermination du dictionnaire de représentation parcimonieuse du signal par des méthodes d'apprentissage. Enfin, nous discutons la possibilité d'effectuer des opérations comme la classification sur le signal sans le reconstruire. / Compressed sensing allows to reconstruct a signal from a few linear projections, under the assumption that the signal can be sparsely represented, that is, with only a few coefficients, on a known dictionary. Coding is very simple and all the complexity is gathered on the reconstruction. After more detailed explanations of the principle of compressed sensing, some theoretic resultats from literature and a few simulations allowing to get an idea of expected performances, we focusson three problems: First, the study for the building of a system using compressed sensing with a binary matrix and the obtained benefits. Then, we have a look at the building of a dictionary for sparse representations of the signal. And lastly, we discuss the possibility of processing signal without reconstruction, with an example in classification.

Ces dernières années, la théorie mathématique de l'échantillonnage compressé (CS) a émergé en tant que nouvel outil en traitement d'images, permettant notamment de dépasser certaines limites établies par la théorie de l'échantillonnage de Nyquist. En particulier, la théorie du CS établit qu'un signal (une image, une séquence vidéo, etc.) peut être reconstruit à partir d'un faible nombre de mesures linéaires non-adaptatives et aléatoires, pourvu qu'il présente une structure parcimonieuse. Dans la mesure où cette hypothèse se vérifie pour une large classe d'images naturelles, plusieurs applications d'imagerie ont d'ores-et-déjà bénéficié à des titres divers des résultats issus de cette théorie. Le but du travail doctoral présent est d'étudier comment la théorie du CS - et plus généralement les idées et méthodes en relation avec les problèmes de reconstruction de signaux parcimonieux - peuvent être utilisés pour concevoir des dispositifs d'acquisition optiques à haute-résolution spatiale et temporelle pour des applications en imagerie biologique. Nous étudions tout d'abord quelques questions pratiques liées à l'étape de reconstruction nécessairement associée aux systèmes d'acquisition exploitant le CS, ainsi qu'à la sélection des paramètres d'échantillonnage. Nous examinons ensuite comment le CS peut être utilisé dans le cadre d'applications d'échantillonnage de signaux vidéo. Enfin, avec dans l'idée l'utilisation dans des problèmes de débruitage de méthodes inspirées du CS, nous abordons la question de l'estimation d'erreur dans les problèmes de débruitage d'images acquises en conditions de faible luminosité, notamment dans le cadre d'applications de microscopie. / In the past few years, the mathematical theory of compressed sensing (CS) has emerged as a new tool in the image processing field, leading to some progress in surpassing the limits stated by the Nyquist sampling theory. In particular, the CS theory establishes that a signal (image, video, etc.) can be reconstructed from a relatively small subset of non-adaptive linear random measurements, assuming that it presents a sparse structure. As this hypothesis actually holds for a large number of natural images, several imaging applications have already benefited from this theory in various aspects. The goal of the present PhD work is to investigate how the CS theory - and more generally the ideas and methods developed in relation with sparse signal reconstruction problematics - can be used to design efficient optical sensing devices with high spatial and temporal resolution for biological imaging applications. We first investigate some practical issues related to the post-processing stage required by CS acquisition schemes, and to the selection of sampling parameters. We then examine how CS can benefit to video sampling applications. Finally, with the application of CS methods for denoising tasks in mind, we focus on the error estimation issue in image denoising problems for low-light microscopy applications.

La radio impulsionnelle UWB (IR-UWB) est une technologie de communication relativement récente, qui apporte une solution intéressante au problème de l’encombrement du spectre RF, et qui répond aux exigences de haut débit et localisation précise d’un nombre croissant d’applications, telles que les communications indoor, les réseaux de capteurs personnels et corporels, l’IoT, etc. Ses caractéristiques uniques sont obtenues par la transmission d’impulsions de très courte durée (inférieure à 1 ns), occupant une largeur de bande allant jusqu’à 7,5 GHz, et ayant une densité spectrale de puissance extrêmement faible (inférieure à -43 dBm/MHz). Les meilleures performances d’un système IR-UWB sont obtenues avec des récepteurs cohérents de type Rake, au prix d’une complexité accrue, due notamment à l’étape d’estimation du canal UWB, caractérisé par de nombreux trajets multiples. Cette étape de traitement nécessite l’estimation d’un ensemble de composantes spectrales du signal reçu, sans pouvoir faire appel aux techniques d’échantillonnage usuelles, en raison d’une limite de Nyquist particulièrement élevée (plusieurs GHz).Dans le cadre de cette thèse, nous proposons de nouvelles approches, à faible complexité, pour l’estimation du canal UWB, basées sur la représentation parcimonieuse du signal reçu, la théorie de l’acquisition compressée, et les méthodes de reconstruction des signaux à taux d’innovation fini. La réduction de complexité ainsi obtenue permet de diminuer de manière significative le coût d’implémentation du récepteur IR-UWB et sa consommation. D’abord, deux schémas d’échantillonnage compressé, monovoie (filtre SoS) et multivoie (MCMW) identifiés dans la littérature sont étendus au cas des signaux UWB ayant un spectre de type passe-bande, en tenant compte de leur implémentation réelle dans le circuit. Ces schémas permettent l’acquisition des coefficients spectraux du signal reçu et l’échantillonnage à des fréquences très réduites ne dépendant pas de la bande passante des signaux, mais seulement du nombre des trajets multiples du canal UWB. L’efficacité des approches proposées est démontrée au travers de deux applications : l’estimation du canal UWB pour un récepteur Rake cohérent à faible complexité, et la localisation précise en environnement intérieur dans un contexte d’aide à la dépendance.En outre, afin de réduire la complexité de l’approche multivoie en termes de nombre de voies nécessaires pour l’estimation du canal UWB, nous proposons une architecture à nombre de voies réduit, en augmentant le nombre d’impulsions pilotes émises.Cette même approche permet aussi la réduction de la fréquence d’échantillonnage associée au schéma MCMW. Un autre objectif important de la thèse est constitué par l’optimisation des performances des approches proposées. Ainsi, bien que l’acquisition des coefficients spectraux consécutifs permette une mise en oeuvre simple des schémas multivoie, nous montrons que les coefficients ainsi choisis, ne donnent pas les performances optimales des algorithmes de reconstruction. Ainsi, nous proposons une méthode basée sur la cohérence des matrices de mesure qui permet de trouver l’ensemble optimal des coefficients spectraux, ainsi qu’un ensemble sous-optimal contraint où les positions des coefficients spectraux sont structurées de façon à faciliter la conception du schéma MCMW. Enfin, les approches proposées dans le cadre de cette thèse sont validées expérimentalement à l’aide d’une plateforme expérimentale UWB du laboratoire Lab-STICC CNRS UMR 6285. / Ultra-wideband impulse radio (IR-UWB) is a relatively new communication technology that provides an interesting solution to the problem of RF spectrum scarcity and meets the high data rate and precise localization requirements of an increasing number of applications, such as indoor communications, personal and body sensor networks, IoT, etc. Its unique characteristics are obtained by transmitting pulses of very short duration (less than 1 ns), occupying a bandwidth up to 7.5 GHz, and having an extremely low power spectral density (less than -43 dBm / MHz). The best performances of an IR-UWB system are obtained with Rake coherent receivers, at the expense of increased complexity, mainly due to the estimation of UWB channel, which is characterized by a large number of multipath components. This processing step requires the estimation of a set of spectral components for the received signal, without being able to adopt usual sampling techniques, because of the extremely high Nyquist limit (several GHz).In this thesis, we propose new low-complexity approaches for the UWB channel estimation, relying on the sparse representation of the received signal, the compressed sampling theory, and the reconstruction of the signals with finite rate of innovation. The complexity reduction thus obtained makes it possible to significantly reduce the IR-UWB receiver cost and consumption. First, two existent compressed sampling schemes, single-channel (SoS) and multi-channel (MCMW), are extended to the case of UWB signals having a bandpass spectrum, by taking into account realistic implementation constraints. These schemes allow the acquisition of the spectral coefficients of the received signal at very low sampling frequencies, which are not related anymore to the signal bandwidth, but only to the number of UWB channel multipath components. The efficiency of the proposed approaches is demonstrated through two applications: UWB channel estimation for low complexity coherent Rake receivers, and precise indoor localization for personal assistance and home care.Furthermore, in order to reduce the complexity of the MCMW approach in terms of the number of channels required for UWB channel estimation, we propose a reduced number of channel architecture by increasing the number of transmitted pilot pulses. The same approach is proven to be also useful for reducing the sampling frequency associated to the MCMW scheme.Another important objective of this thesis is the performance optimization for the proposed approaches. Although the acquisition of consecutive spectral coefficients allows a simple implementation of the MCMW scheme, we demonstrate that it not results in the best performance of the reconstruction algorithms. We then propose to rely on the coherence of the measurement matrix to find the optimal set of spectral coefficients maximizing the signal reconstruction performance, as well as a constrained suboptimal set, where the positions of the spectral coefficients are structured so as to facilitate the design of the MCMW scheme. Finally, the approaches proposed in this thesis are experimentally validated using the UWB equipment of Lab-STICC CNRS UMR 6285.