Noiselet Measurement Matrix Usage in CS Framework

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  • Haybert Markarian1,
  • Alireza Mohammad Zaki1,
  • Sedigheh Ghofrani*1,
  1. Electrical Engineering Department South Tehran Branch, Islamic Azad University Tehran, Iran

Revised: 2017-10-27

Accepted: 2017-11-12

Published in Issue 2017-03-01

How to Cite

Markarian, H., Mohammad Zaki, A., & Ghofrani, S. (2017). Noiselet Measurement Matrix Usage in CS Framework. Signal Processing and Renewable Energy (SPRE), 1(1), 1-9. https://oiccpress.com/spre/article/view/7738

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Abstract

Theory of compressive sensing (CS) is an alternative to Shannon/Nyquist sampling theorem which explained the number of samples requirement in order to have the perfect reconstruction. Perfect reconstruction of undersampled data in CS framework is highly dependent to incoherence of measurement and sparsifying basis matrices which the posterior is usually fulfilled by selecting a random matrix. While Noiselets, as a measurement matrix, have very low coherence with wavelets which are the interest of CS, they have never been studied well and compared with other well known Gaussian and Bernoulli measurement matrices, which have been widely used in CS framework, from randomness view point. Therefore, the main contribution of this paper is introducing Noiselets and comparing them with other measurement matrices in two point of view; randomness and quality of recovered images. In case of randomness, the entropy is used as a criterion for computing the randomness. In case of recovered images, the OMP and PDIP algorithms are applied under sampling rates 30, 40, 60%.
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