000056045 001__ 56045
000056045 005__ 20190509132100.0
000056045 0247_ $$2doi$$a10.5075/epfl-thesis-3404
000056045 02470 $$2urn$$aurn:nbn:ch:bel-epfl-thesis3404-7
000056045 02471 $$2nebis$$a5050303
000056045 037__ $$aTHESIS
000056045 041__ $$aeng
000056045 088__ $$a3404
000056045 245__ $$aNonlinear approximation with redundant multi-component dictionaries
000056045 269__ $$a2006
000056045 260__ $$bEPFL$$c2006$$aLausanne
000056045 300__ $$a168
000056045 336__ $$aTheses
000056045 502__ $$aLaurent Daudet, Morten Nielsen, Anja Skrivervik Favre, Emre Telatar
000056045 520__ $$aThe problem of efficiently representing and approximating digital data is an open challenge and it is of paramount importance for many applications. This dissertation focuses on the approximation of natural signals as an organized combination of mutually connected elements, preserving and at the same time benefiting from their inherent structure. This is done by decomposing a signal onto a multi-component, redundant collection of functions (dictionary), built by the union of several subdictionaries, each of which is designed to capture a specific behavior of the signal. In this way, instead of representing signals as a superposition of sinusoids or wavelets many alternatives are available. In addition, since dictionaries we are interested in are overcomplete, the decomposition is non-unique. This gives us the possibility of adaptation, choosing among many possible representations the one which best fits our purposes. On the other hand, it also requires more complex approximation techniques whose theoretical decomposition capacity and computational load have to be carefully studied. In general, we aim at representing a signal with few and meaningful components. If we are able to represent a piece of information by using only few elements, it means that such elements can capture its main characteristics, allowing to compact the energy carried by a signal into the smallest number of terms. In such a framework, this work also proposes analysis methods which deal with the goal of considering the a priori information available when decomposing a structured signal. Indeed, a natural signal is not only an array of numbers, but an expression of a physical event about which we usually have a deep knowledge. Therefore, we claim that it is worth exploiting its structure, since it can be advantageous not only in helping the analysis process, but also in making the representation of such information more accessible and meaningful. The study of an adaptive image representation inspired and gave birth to this work. We often refer to images and visual information throughout the course of the dissertation. However, the proposed approximation setting extends to many different kinds of structured data and examples are given involving videos and electrocardiogram signals. An important part of this work is constituted by practical applications: first of all we provide very interesting results for image and video compression. Then, we also face the problem of signal denoising and, finally, promising achievements in the field of source separation are presented.
000056045 6531_ $$aImage and Video Coding
000056045 6531_ $$aMulti-Component Dictionaries
000056045 6531_ $$aNonlinear Approximation Theory
000056045 6531_ $$aWeighted Basis Pursuit
000056045 700__ $$0241529$$g141038$$aGranai, Lorenzo
000056045 720_2 $$aVandergheynst, Pierre$$edir.$$g120906$$0240428
000056045 8564_ $$uhttps://infoscience.epfl.ch/record/56045/files/EPFL_TH3404.pdf$$zTexte intégral / Full text$$s3396419$$yTexte intégral / Full text
000056045 909C0 $$xU10380$$0252392$$pLTS2
000056045 909CO $$pthesis$$pthesis-bn2018$$pDOI$$ooai:infoscience.tind.io:56045$$qDOI2$$qGLOBAL_SET$$pSTI
000056045 918__ $$bSTI-SEL$$cITS$$aSTI
000056045 919__ $$aLTS2
000056045 920__ $$b2005$$a2005-12-15
000056045 970__ $$a3404/THESES
000056045 973__ $$sPUBLISHED$$aEPFL
000056045 980__ $$aTHESIS