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E. J. Candès and J. Romberg, “Sparsity and Incoherence in Compressive Sampling,” Inverse Problems, Vol. 23, No. 3, 2007, pp. 969-985. doi:10.1088/0266-5611/23/3/008

has been cited by the following article:

• TITLE: Stability of Efficient Deterministic Compressed Sensing for Images with Chirps and Reed-Muller Sequences

  AUTHORS: Somantika Datta, Kangyu Ni, Prasun Mahanti, Svetlana Roudenko

  KEYWORDS: Compressed Sensing; Reed-Muller Sequences; Chirps; Image Reconstruction

  JOURNAL NAME: Applied Mathematics, Vol.4 No.1A, January 30, 2013

  ABSTRACT: We explore the stability of image reconstruction algorithms under deterministic compressed sensing. Recently, we have proposed [1-3] deterministic compressed sensing algorithms for 2D images. These algorithms are suitable when Daubechies wavelets are used as the sparsifying basis. In the initial work, we have shown that the algorithms perform well for images with sparse wavelets coefficients. In this work, we address the question of robustness and stability of the algorithms, specifically, if the image is not sparse and/or if noise is present. We show that our algorithms perform very well in the presence of a certain degree of noise. This is especially important for MRI and other real world applications where some level of noise is always present.