Fast compressed sensing reconstruction using the least squares and signal correlation

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.