Fast compressed sensing reconstruction using the least squares and signal correlation

• Published in: IET Intelligent Signal Processing Conference 2013 (ISP 2013) p. 1.1
• Main Authors: Hotrakool, W, Abhayaratne, C
• Format: Conference Proceeding
• Language: English
• Published: Stevenage, UK IET 2013
• Subjects: Interpolation and function approximation (numerical analysis); Optimisation techniques; Signal processing and detection; Signal processing theory; least squares approximations; compressed sensing; temporal correlation; spatial correlation; l1-minimisation; signal correlation; fast compressed sensing reconstruction; least squares method; reconstruction error; signal reconstruction; minimisation; correlated reference; correlation methods
• ISBN: 1849197741; 9781849197748
• DOI: 10.1049/cp.2013.2039

A fast compressed sensing reconstruction using least squares method with the signal correlation is presented in this paper. It is well known that the complexity of l1-minimisation is very high and is undesirable for many practical applications. The least squares method, on the other hand, has a much lower complexity. However, least squares does not promote the sparsity of signal and therefore cannot provide acceptable reconstructed results. The main contribution of this paper is to show that by exploiting signal correlation, the reconstruction error of least squares is greatly improved. Moreover, the correlated reference used in this method is very flexible, and can contain many kinds of correlation, such as spatial or temporal correlation. Experimental results show that the performance of this method is comparable to the state-of-the-art algorithms, whilst having a much lower complexity. It also shows that this method can be applied to both sparse and redundant signal reconstruction.