Undersampling the k-space is an efficient way to speed up the magnetic resonance imaging (MRI). Recently emerged compressed sensing MRI shows promising results. However, most of them only enforce the sparsity of images in single transform, e.g. total variation, wavelet, etc. In this paper, based on the principle of basis pursuit, we propose a new framework to combine sparsifying transforms in compressed sensing MRI. Each transform can efficiently represent specific feature that the other can not. This framework is implemented via the state-of-art smoothed ℓ0 norm in overcomplete sparse decomposition. Simulation results demonstrate that the proposed method can improve image quality when comparing to single sparsifying transform.
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