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 ℓ₁-based minimization algorithm needs more measurements than the ℓ₀-based ones. On the other hand, ℓ₀-based minimization is computational intractable and unstable. In this paper, we propose a hybrid total variation (HTV) which effectively integrates both ℓ₁-norm and ℓ₀-norm of the image gradient by introducing a threshold. The HTV minimization algorithm has the benefits of both the robustness of ℓ₁ and fewer measurements of ℓ₀. Simulations and in vivo experiments demonstrate the proposed method outperforms the conventional TV minimization algorithm.