An empirical study on compressed sensing MRI using fast composite splitting algorithm and combined sparsifying transforms

The problem of compressed sensing magnetic resonance imaging (CS-MRI) reconstruction is often formulated as minimizing a linear combination of two terms, including data fidelity and prior regularization. Several prior regularizations can be chosen, including traditional sparsity regularizations such as Total Variance (TV) and wavelet transform, and notably some recently emerging methods such as curvelet and contourlet transforms. Moreover, combinations of multiple different sparsity regularizations are also used in various reconstruction algorithms. Currently, Fast Composite Splitting Algorithm (FCSA) is arguably regarded as one of the most outstanding reconstruction algorithms. This article performs an overall empirical study on using FCSA as the reconstruction algorithm and on different combinations of sparsifying transforms as the regularization terms for CS MRI reconstruction. Experimental results show that (1) the sparsity regularization using the combination of wavelet, curvelet and contourlet yields the best reconstructed image quality but has almost the highest running time in most cases; (2) the combination of wavelet, TV and contourlet can significantly reduce the running time at the cost of slightly compromised reconstruction accuracy; and (3) using contourlet transform solely can also achieve comparable reconstruction accuracy with less running time compared with the combination of TV, wavelet and contourlet.