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

Affiliation(s)

Department of Mathematics, University of Idaho, Moscow, USA.

HRL Laboratories, LLC, Malibu, USA.

School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, USA.

Department of Mathematics, George Washington University, Washington DC, USA.

Department of Mathematics, University of Idaho, Moscow, USA.

HRL Laboratories, LLC, Malibu, USA.

School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, USA.

Department of Mathematics, George Washington University, Washington DC, USA.

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.

Cite this paper

S. Datta, K. Ni, P. Mahanti and S. Roudenko, "Stability of Efficient Deterministic Compressed Sensing for Images with Chirps and Reed-Muller Sequences,"*Applied Mathematics*, Vol. 4 No. 1, 2013, pp. 183-196. doi: 10.4236/am.2013.41A029.

S. Datta, K. Ni, P. Mahanti and S. Roudenko, "Stability of Efficient Deterministic Compressed Sensing for Images with Chirps and Reed-Muller Sequences,"

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