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Open Access Article
1 - Noiselet Measurement Matrix Usage in CS Framework
Haybert Markarian Alireza Mohammad Zaki Sedigheh GhofraniTheory 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 inc MoreTheory 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%. Manuscript profile -
Open Access Article
2 - Randomness, Coherence and Noise Robustness in Compressive Sensing
Haybert Markarian Sedigheh GhofraniThe theory of compressive sensing (CS) in contrast with well-known Nyquist sampling theorem was proposed. Sensing matrix and sparse matrix have key roles in perfect signal reconstruction by using either greedy algorithms like orthogonal matching pursuit (OMP) or -norm b MoreThe theory of compressive sensing (CS) in contrast with well-known Nyquist sampling theorem was proposed. Sensing matrix and sparse matrix have key roles in perfect signal reconstruction by using either greedy algorithms like orthogonal matching pursuit (OMP) or -norm based methods. In this paper, different pairs as sensing and sparse matrices are evaluated in terms of randomness and coherence. Noiselet as a complex measurement matrix has low coherence with Haar wavelet, and so the recovered images by OMP in comparison with other measurement-sparse matrices are appropriate. But, because of complexity, it cannot be used for big size images. However, the pair structured random sensing matrix with values 0, 1 and Fourier sparse matrix which got the second rank in terms of coherence, approved to be a noise robust pair and showed a great potential to be used in CS. Manuscript profile
List of Articles Haybert Markarian
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