A hybrid total-variation minimization approach to compressed sensing
Compressed sensing (CS) has been successfully applied to accelerate conventional magnetic resonance imaging (MRI) with Fourier encoding. Total variation (TV) is usually used as the regularization function for image reconstruction. However, it is know that such ℓ<sub>1</sub>-based minimization algorithm needs more measurements than the ℓ<sub>0</sub>-based ones. On the other hand, ℓ<sub>0</sub>-based minimization is computational intractable and unstable. In this paper, we propose a hybrid total variation (HTV) which effectively integrates both ℓ<sub>1</sub>-norm and ℓ<sub>0</sub>-norm of the image gradient by introducing a threshold. The HTV minimization algorithm has the benefits of both the robustness of ℓ<sub>1</sub> and fewer measurements of ℓ<sub>0</sub>. Simulations and in vivo experiments demonstrate the proposed method outperforms the conventional TV minimization algorithm.