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Compressed Sensing and Its Application in CT and EEG

Compressed Sensing and Its Application in CT and EEG

Sajib Saha, Murat Tahtali
Copyright: © 2016 |Pages: 24
ISBN13: 9781466688117|ISBN10: 1466688114|EISBN13: 9781466688124
DOI: 10.4018/978-1-4666-8811-7.ch006
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MLA

Saha, Sajib, and Murat Tahtali. "Compressed Sensing and Its Application in CT and EEG." Biomedical Image Analysis and Mining Techniques for Improved Health Outcomes, edited by Wahiba Ben Abdessalem Karâa and Nilanjan Dey, IGI Global, 2016, pp. 123-146. https://doi.org/10.4018/978-1-4666-8811-7.ch006

APA

Saha, S. & Tahtali, M. (2016). Compressed Sensing and Its Application in CT and EEG. In W. Karâa & N. Dey (Eds.), Biomedical Image Analysis and Mining Techniques for Improved Health Outcomes (pp. 123-146). IGI Global. https://doi.org/10.4018/978-1-4666-8811-7.ch006

Chicago

Saha, Sajib, and Murat Tahtali. "Compressed Sensing and Its Application in CT and EEG." In Biomedical Image Analysis and Mining Techniques for Improved Health Outcomes, edited by Wahiba Ben Abdessalem Karâa and Nilanjan Dey, 123-146. Hershey, PA: IGI Global, 2016. https://doi.org/10.4018/978-1-4666-8811-7.ch006

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Abstract

Compressed sensing, also known as compressive sampling is a new technique being rapidly developed over the last few years. The theory states that when some prior information about the signal is available and appropriately incorporated into the signal reconstruction procedure, a signal can be accurately reconstructed even if the Shannon/ Nyquest sampling requirement is violated. The key idea of compressed sensing is to recover a sparse signal from very few non-adaptive, linear measurements by optimization technique. Following the discovery by Donoho in (2006), that sparsity could enable exact solution of ill-posed problems under certain conditions, there has been a tremendous growth on efficient application of sparsity constraints for solving ill-posed problems. The theoretical foundation of compressed sensing has already become a key concept in various areas of applied mathematics, computer science, and electrical engineering. In this chapter we will detail the application of compressed sensing in X-ray computed tomography (CT) and Electroencephalography. Starting from the very basic principles we will provide theoretical justifications on why and how sparsity prior is used in CT and in EEG.

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