Data Compression and Compressed Sensing in Imaging Mass Spectrometry and Sporadic Communication
Andreas Bartels
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Andreas Bartels, Data Compression and Compressed Sensing in Imaging Mass Spectrometry and Sporadic Communication (2014), Logos Verlag, Berlin, ISBN: 9783832591663
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Beschreibung / Abstract
This thesis contributes to the fields of data compression and compressed sensing and their application to imaging mass spectrometry and sporadic communication. Compressed sensing is mainly built on the knowledge that most data is compressible or sparse, meaning that most of its content is redundant and not worth being measured. As a main result in this work, a compressed sensing model for imaging mass spectrometry is introduced. It combines peak-picking of the spectra and denoising of the m/z-images A robustness result for the reconstruction of compressed measured data is presented which generalizes known reconstruction guarantees.
Inhaltsverzeichnis
- BEGINN
- 1 Introduction
- 1.1 The big data problem
- 1.2 Data compression
- 1.3 What compressed sensing is about
- 1.4 Scientific contributions of the thesis
- 1.5 Organization of the thesis
- 2 Preliminaries and concepts
- 2.1 Notations
- 2.2 Proximity operators and algorithms
- 3 Data compression
- 3.1 What is compression?
- 3.2 Compression and quality measures
- 3.3 Mathematical techniques
- 4 Compressed Sensing
- 4.1 Introduction
- 4.2 Uniqueness, sparseness and other properties
- 4.3 Stable `1 minimization
- 4.4 Stable total variation minimization
- 4.5 Coherent and redundant dictionaries
- 4.6 Asymmetric restricted isometry property
- 5 Imaging mass spectrometry in a nutshell
- 5.1 Mass spectrometry
- 5.2 Imaging mass spectrometry
- 5.3 Datasets used in this thesis
- 6 Compression in imaging mass spectrometry
- 6.1 Introduction
- 6.2 Peak picking
- 6.3 Denoising
- 6.4 Nonnegative matrix factorization
- 6.5 Conclusion
- 7 Compressed sensing in imaging mass spectrometry
- 7.1 Introduction
- 7.2 The compressed sensing process
- 7.3 First assumption: compressible spectra
- 7.4 Second assumption: sparse image gradients
- 7.5 The final model
- 7.6 Robust recovery
- 7.7 Numerical results
- 7.8 Conclusion
- 8 Compressed sensing based multi-user detection
- 8.1 Introduction
- 8.2 Sporadic communication
- 8.3 Multi-user system modelling
- 8.4 The elastic-net
- 8.5 The multi-user test setup
- 8.6 A parameter choice rule: The C-curve criterion
- 8.7 An offline approach
- 8.8 Conclusion
- 9 Conclusion