Due to the sheer volume of data involved, video coding is an important application of lossy source coding, and has received wide industrial interest and support as evidenced by the development and success of a series of video coding standards. All MPEG-series and H-series video coding standards proposed so far are based upon a video coding paradigm called predictive video coding, where video source frames Xᵢ,i=1,2,...,N, are encoded in a frame by frame manner, the encoder and decoder for each frame Xᵢ, i =1, 2, ..., N, enlist help only from all previous encoded frames Sj, j=1, 2, ..., i-1. In this thesis, we will look further beyond all existing and proposed video coding standards, and introduce a new coding paradigm called causal video coding, in which the encoder for each frame Xᵢ can use all previous original frames Xj, j=1, 2, ..., i-1, and all previous encoded frames Sj, while the corresponding decoder can use only all previous encoded frames. We consider all studies, comparisons, and designs on causal video coding from an information theoretic point of view. Let R*c(D₁,...,D_N) (R*p(D₁,...,D_N), respectively) denote the minimum total rate required to achieve a given distortion level D₁,...,D_N > 0 in causal video coding (predictive video coding, respectively). A novel computation approach is proposed to analytically characterize, numerically compute, and compare the minimum total rate of causal video coding R*c(D₁,...,D_N) required to achieve a given distortion (quality) level D₁,...,D_N > 0. Specifically, we first show that for jointly stationary and ergodic sources X₁, ..., X_N, R*c(D₁,...,D_N) is equal to the infimum of the n-th order total rate distortion function R_{c,n}(D₁,...,D_N) over all n, where R_{c,n}(D₁,...,D_N) itself is given by the minimum of an information quantity over a set of auxiliary random variables. We then present an iterative algorithm for computing R_{c,n}(D₁,...,D_N) and demonstrate the convergence of the algorithm to the global minimum. The global convergence of the algorithm further enables us to not only establish a single-letter characterization of R*c(D₁,...,D_N) in a novel way when the N sources are an independent and identically distributed (IID) vector source, but also demonstrate a somewhat surprising result (dubbed the more and less coding theorem)---under some conditions on source frames and distortion, the more frames need to be encoded and transmitted, the less amount of data after encoding has to be actually sent. With the help of the algorithm, it is also shown by example that R*c(D₁,...,D_N) is in general much smaller than the total rate offered by the traditional greedy coding method by which each frame is encoded in a local optimum manner based on all information available to the encoder of the frame. As a by-product, an extended Markov lemma is established for correlated ergodic sources. From an information theoretic point of view, it is interesting to compare causal video coding and predictive video coding, which all existing video coding standards proposed so far are based upon. In this thesis, by fixing N=3, we first derive a single-letter characterization of R*p(D₁,D₂,D₃) for an IID vector source (X₁,X₂,X₃) where X₁ and X₂ are independent, and then demonstrate the existence of such X₁,X₂,X₃ for which R*p(D₁,D₂,D₃)>R*c(D₁,D₂,D₃) under some conditions on source frames and distortion. This result makes causal video coding an attractive framework for future video coding systems and standards. The design of causal video coding is also considered in the thesis from an information theoretic perspective by modeling each frame as a stationary information source. We first put forth a concept called causal scalar quantization, and then propose an algorithm for designing optimum fixed-rate causal scalar quantizers for causal video coding to minimize the total distortion among all sources. Simulation results show that in comparison with fixed-rate predictive scalar quantization, fixed-rate causal scalar quantization offers as large as 16% quality improvement (distortion reduction).

Depuis les années 50, la récupération de la phase d’un faisceau optique diffracté par un objet quelconque, est un sujet important dans plusieurs domaines scientifiques, comme la microscopie, l’astronomie et bien d’autres. Généralement, les méthodes qui le permettent se divisent en deux grandes catégories : les méthodes interférométriques et les méthodes itératives basées sur la propagation du faisceau. L’intérêt de ces dernières, réside dans le fait qu’elles sont moins sensibles au bruit, et leur implémentation expérimentale est plus simple. Aussi, le développement des techniques informatiques a rendu cette approche plus rapide et plus intéressante. Cependant, même si l’efficacité de ces méthodes a été démontrée dans plusieurs domaines, leur utilisation est restée limitée à cause de certaines exigences sur les conditions expérimentales, et à la non-convergence de leur algorithme vers une solution unique dans un grand nombre de cas. Ceci est encore plus vrai pour les objets dits "objets complexes", possédant une amplitude et une phase, ce qui réduit fortement leur champ d’application. Afin de surmonter ces problèmes de convergence, diverses stratégies expérimentales ont été développées. Elles ont toutes comme principe d’introduire de nouvelles contraintes bien connues dans le plan de l’objet. Cela permet d’augmenter le nombre de spectres acquis, et donc accroitre et diversifier les sources d’informations sur l’objet de base, ce qui va aider l’algorithme itératif à converger plus rapidement vers une solution finale et unique. Comme exemple de ces stratégies expérimentales, on peut acquérir plusieurs spectres provenant de différentes zones de l’objet, ou moduler la longueur d’onde du faisceau incident, ou même enregistrer les spectres dans des plans parallèles, connectés entre eux par la transformée de Fresnel. Dans ce contexte, le présent travail vise à démontrer expérimentalement une technique connue sous SSPR (Spread Spectrum Phase Retrieval), proposé en 2007 par Zhang, tout en lui introduisant un certain nombre de modifications, afin de la rendre plus pratique. L’idée consiste à moduler le front d’onde de l’objet par M phases aléatoires, générées avec un modulateur spatial de lumière à base de cristaux liquides (LC-SLM), puis enregistrer dans le plan de Fourier les M spectres correspondants. Ces M spectres seront ensuite utilisés dans un algorithme itératif permettant de remonter au front d’onde de l’objet initial, en simulant la propagation du front d’onde entre les deux espaces, spatial et fréquentiel.La première partie de cette thèse comporte une étude détaillée sur les modulateurs spatiaux de lumière, afin de pouvoir choisir le mieux adapté à notre application. Une fois que le modulateur à base de cristaux liquides (LC-SLM) est sélectionné, on présentera ses caractéristiques techniques, ainsi que les tests et les étapes de calibrations nécessaires pour assurer son fonctionnement linéaire et optimal. Ensuite, on montrera plusieurs types d’applications possibles avec ce composant, et dans divers domaines scientifiques, comme l’holographie, la microscopie, l’optique adaptative ainsi que les méthodes interférométriques permettant de reconstruire la phase d’un faisceau lumineux. Dans la deuxième grande partie, on concentre notre travail autour de la méthode itérative SSPR. On montrera comment on peut rendre l’application de cette méthode plus simple en utilisant un modulateur spatial de lumière à base de cristaux liquides, et en travaillant dans le plan de Fourier à la place du plan de Fresnel. Cependant, après avoir appliqué expérimentalement cette méthode, on remarque que les résultats obtenus sont très mauvais par rapport aux résultats des simulations. On effectue donc, une étude détaillée concernant les sources de bruits pouvant être responsable de la dégradation de la qualité des reconstructions obtenues. [...] / Since the 50s, recovering the phase information of a diffracted beam has a major interest in several fields such as microscopy, astronomy and many others. Generally, the solutions fall into two broad categories: interferometric methods and iterative methods based on beam propagation. The advantage of the latter is that they are less sensitive to noise, and their experimental implementation is simpler. Also, the progress in computer technologies as well in digital imaging devices makes the application of this approach easier and more interesting. However, even if the effectiveness of these methods has been demonstrated in several fields, their use remained limited because of certain requirements on the experimental conditions and the non-convergence of their algorithm to a single solution in many cases. This is even more true for the so-called "complex objects", having an amplitude and a phase, which can greatly reduce their field of application. To overcome the convergence problems and improve the robustness of these methods, many experimental strategies have been employed. They are all based on the same principle, which consists of introducing new well-known constraints in the object plane. This increases the number of acquired spectrum, and therefore diversifies the sources of information about the starting object, which will help the iterative algorithm to converge more quickly towards the final solution. As examples of such experimental strategies, one can record several spectra from different areas of the object, or modulate the wavelength of the incident beam, or also acquire the spectrums across two or more parallel planes connected through Fresnel or Fourier transform.In this context, the present work aims to experimentally demonstrate a technique known as SSPR (Spread Spectrum Phase Retrieval), proposed in 2007 by Zhang, while modifying it in order to make it more flexible. The idea is to introduce, using a liquid crystal spatial light modulator M strong phase modulation into the object field, then record in the Fourier plane the M corresponding spectrums. These M acquisitions will then be used in an iterative algorithm what will allow us to recover the object wavefront by simulating the propagation of the light between spatial and frequency spaces. The first part of this thesis includes a complete study on spatial light modulators; in order to select which one will be best suited for our application. Once liquid crystal spatial light modulators are selected, we present their technical characteristics, as well as the calibration tests needed to ensure their linear and optimal functioning. Then we show several possible applications with this type of component, in various scientific fields, like holography, microscopy, adaptive optics and interferometric methods to reconstruct the phase of a beam.In the second part, we focus our work around the SSPR iterative method. We will show how to make the application of this method simpler by using a liquid crystal spatial light modulator, and by working in Fourier plane instead of Fresnel plane. However, after applying SSPR we have noticed that the quality of experimental results is very inferior to the quality of simulation results. Therefore, a detailed study of the noise sources is conducted. Each of these noise sources adds its own contribution, yet modulator cross-talk remains the factor that deteriorates the most the quality of reconstruction. In fact liquid crystal spatial light modulators are known to have a strong cross-talk between their pixels commonly recognized as fringing field effect. As the pixels are micrometric, each addressed one affects its neighbors, and thus, the phase retardation obtained from a pixel will not be uniform over its entire surface. This will result in a blurring effect of the desired sharp edge between the pixels; therefore, the real displayed phase map will be very different from the addressed one. [...]

Phase-contrast imaging (PCI) is a modality of medical x-ray imaging that can solve one of the main limitations with conventional attenuation-based imaging: the imaging of materials with low attenuation coefficients, such as soft tissues. A modality of PCI, Propagation-based phase-contrast imaging (PBI), was used in this project. This method does not require any optical elements than those used in the conventional imaging; it does, however, require more processing compared to other kinds of PCI. In addition to the reduced image quality, the required image reconstruction process, with PCI, also requires several manual adjustments, which in turn results in a lot of time consuming. In order to achieve that, a simple iterative image reconstruction method that combines Simultaneous Iterative Reconstruction Technique (SIRT) and propagation-based phase-contrast imaging was developed. The proposed method was compared with another commonly used phase-retrieval method, Paganin's algorithm. The obtained results showed higher resolution and reduced blur artefacts compared with Paganin's method. The developed method also appeared to be less sensitive to error in the input parameters, such as the attenuation coefficient, but also more time-consumption than the non-iterative Paganin's method, due to the higher data processing. / Faskontrastavbildning är en ny medicinsk röntgenavbildningsteknik, som har utvecklats för att ge bättre kontrast än konventionell röntgenavbildning, särskilt för objekt med låg attenuationskoefficient, såsom mjuk vävnad. I detta projekt användes s.k. propagationsbaserad faskonstrantavbildning, som är en av de enkla metoder som möjliggör faskontrastavbildningen, utan extra optiska element än det som ingår i en konventionell avbildning. Metoden kräver dock mer avancerad bildbehandling. Två av de huvudsakliga problemen som oftast uppstår vid faskontrastavbildning är minskad bildkvalité efter den väsentliga bildrekonstruktionen, samt att den är tidskrävande p.g.a. manuella justeringar som måste göras. I det här projektet implementerades en enkel metod baserad på en kombination av den iterativa algoritmen för bildrekonstruktion, Simultaneous Iterative Reconstruction Technique (SIRT), med propagationsbaserad faskonstrantavbildning. Resultaten jämfördes med en annan fasåterhämtningsmetod, som är välkänd och ofta används inom detta område, Paganinsmetod. Efter jämförelsen konstaterades att upplösningen blev högre och artefakter som suddighet reducerades. Det noterades också att den utvecklade metoden var mindre känslig för manuell inmatning av parametern för attenuationskoefficient. Metoden visade sig dock vara mer tidskrävande än Paganin-metoden.

Cílem disertační práce je navrhnout efektivně pracující algoritmus, který na základě bezfázového měření v blízkém poli antény bude schopen zrekonstruovat komplexní blízké pole antény resp. vyzařovací diagram antény ve vzdáleném poli. Na základě těchto úvah byly zkoumány vlastnosti minimalizačního algoritmu. Zejména byl analyzován a vhodně zvolen minimalizační přistup, optimalizační metoda a v neposlední řadě i optimalizační funkce tzv. funkcionál. Dále pro urychlení celého minimalizačního procesu byly uvažovány prvotní odhady. A na závěr byla do minimalizačního algoritmu zahrnuta myšlenka nahrazující hledané elektrické pole několika koeficienty. Na základě předchozích analýz byla navržená bezfázová metoda pro charakterizaci vyzařovacích vlastností antén. Tato metoda kombinuje globální optimalizaci s obrazovou kompresní metodou a s lokální metodou ve spojení s konvečním amplitudovým měřením na dvou površích. V našem případě je globální optimalizace použita k nalezení globálního minima minimalizovaného funkcionálu, kompresní metoda k redukci neznámých proměnných na apertuře antény a lokální metoda zajišťuje přesnější nalezení minima. Navržená metoda je velmi robustní a mnohem rychlejší než jiné dostupné minimalizační algoritmy. Další výzkum byl zaměřen na možnosti využití měřených amplitud pouze z jednoho měřícího povrchu pro rekonstrukci vyzařovacích charakteristik antén a využití nového algoritmu pro rekonstrukci fáze na válcové geometrii.