A platform for research: civil engineering, architecture and urbanism
A platform for research: civil engineering, architecture and urbanism
Phase transition diagrams in compressive sensing - computation and analysis
Compressive Sensing (CS) is a relatively new area of research in the field of digital signal processing and enables accurate reconstruction of signals, sampled significantly below the Shannon-Nyquist-Rate, under certain conditions. The method is more complicated than conventional ones and there is, until now, no sufficient bound, which enables the prediction about the success of CS. To nevertheless, make such statements, so called phase transition diagrams (PTD) were introduced. These diagrams display the probability of success as function of the number of samples and nonzero coefficients of the signal. It depicts that two areas are formed, representing the probability of 0 and 1. Both are divided by a relatively sharp transition, which justifies the name of the diagrams. This work, besides theoretical foundations of CS and PTDs, contains two main parts. On the one side the conception design and implementation of an improved MATLAB-based algorithm to estimate PTDs and on the other side, its application to systematically test CS-based algorithms for their performance and dependence against certain parameters. This part depicts that the algorithms clearly differ, regarding their performance, speed and reliability. Although, the examination shows that the choice of parameters has a large influence on certain algorithms. These information are enormously important for scientists and engineers, concerned with compressive sensing. ; Compressive Sensing (CS) ist ein relativ neues Forschungsgebiet der digitalen Signalverarbeitung und ermöglicht, unter bestimmten Bedingungen, die fehlerfreie Rekonstruktion von Signalen, die weit unterhalb der Shannon-Nyquist-Rate abgetastet wurden. Das Verfahren ist komplizierter als bisherige und es gibt bis heute keine hinreichenden Schranken, die eine konkrete Vorhersage des Erfolgs von CS ermöglichen. Um solche Aussagen dennoch treffen zu können, wurden sogenannte Phasendiagramme (engl. Phase Transition Diagrams, Abk. PTD) eingeführt. Diese tragen die Erfolgswahrscheinlichkeit als ...
Phase transition diagrams in compressive sensing - computation and analysis
Compressive Sensing (CS) is a relatively new area of research in the field of digital signal processing and enables accurate reconstruction of signals, sampled significantly below the Shannon-Nyquist-Rate, under certain conditions. The method is more complicated than conventional ones and there is, until now, no sufficient bound, which enables the prediction about the success of CS. To nevertheless, make such statements, so called phase transition diagrams (PTD) were introduced. These diagrams display the probability of success as function of the number of samples and nonzero coefficients of the signal. It depicts that two areas are formed, representing the probability of 0 and 1. Both are divided by a relatively sharp transition, which justifies the name of the diagrams. This work, besides theoretical foundations of CS and PTDs, contains two main parts. On the one side the conception design and implementation of an improved MATLAB-based algorithm to estimate PTDs and on the other side, its application to systematically test CS-based algorithms for their performance and dependence against certain parameters. This part depicts that the algorithms clearly differ, regarding their performance, speed and reliability. Although, the examination shows that the choice of parameters has a large influence on certain algorithms. These information are enormously important for scientists and engineers, concerned with compressive sensing. ; Compressive Sensing (CS) ist ein relativ neues Forschungsgebiet der digitalen Signalverarbeitung und ermöglicht, unter bestimmten Bedingungen, die fehlerfreie Rekonstruktion von Signalen, die weit unterhalb der Shannon-Nyquist-Rate abgetastet wurden. Das Verfahren ist komplizierter als bisherige und es gibt bis heute keine hinreichenden Schranken, die eine konkrete Vorhersage des Erfolgs von CS ermöglichen. Um solche Aussagen dennoch treffen zu können, wurden sogenannte Phasendiagramme (engl. Phase Transition Diagrams, Abk. PTD) eingeführt. Diese tragen die Erfolgswahrscheinlichkeit als ...
Phase transition diagrams in compressive sensing - computation and analysis
Herrmann, Martin (author) / Roemer, Florian / Del Galdo, Giovanni
2015-05-12
Theses
Electronic Resource
English
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