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 đť‘™ ! -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-theart algorithms, whilst having a much lower complexity. It also shows that this method can be applied to both sparse and redundant signal reconstruction.
Our recent work has shown that quality of compressed sensing reconstruction can be improved immensely by minimising the error between the signal and a correlated reference, as opposed to the conventional l 1 -minimisation of the data measurements. This paper introduces a method for online estimating suitable references for video sequences using the running Gaussian average. The proposed method can provide robustness to video content changes as well as reconstruction noise. The experimental results demonstrate the performance of this method to be superior to those of the state-of-the-art l 1 -min methods. The results are comparable to the lossless reference reconstruction approach.
The main task of Functional Magnetic Resonance Imaging (fMRI) is the localisation of brain activities, which depends on the detection of hemodynamic responses in the Blood Oxygenation-Level Dependent (BOLD) signal. While compressive sensing has been widely applied to improve the quality and resolution of MRI in general, its reconstruction noise overwhelms the small magnitude of hemodynamic responses. We propose a new reconstruction algorithm for the compressive sensing fMRI that exploits the temporal redundancy of the data, called Referenced Compressive Sensing, which works well in preserving fMRI analytical features. We also propose the use of the baselineindependent signal for analysis of reconstructed data. It is shown that the baseline-independent reconstructed data from Referenced Compressive Sensing is highly correlated to the lossless data, thus preserving more of the analytical features.
One of the approaches to exploit temporal redundancy in compressive sensing reconstruction of spatio-temporal signals is the Running Gaussian-based Referenced Compressive Sensing. It uses the weighted-average of all prior reconstructed instances as a reference to reconstruct the next instance with high accuracy. The performance of this approach depends on the weight called learning parameter. This work studies the relationship between the learning parameter and the reconstruction accuracy. We show that the small value of the learning parameter is more suitable for natural signals with dynamic sparse supports. We also propose a dynamic optimal learning parameter that provides good reconstruction accuracy for all signals. Out experimental results show that the proposed optimal learning parameter outperforms all fixed values of learning parameter in natural video sequences reconstruction.
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