This abstract presents a novel hybrid total variation minimization algorithm to reconstruct MR images from reduced measurements. The method combines the benefits of both L1 and homotopic L0 minimization algorithms for sparse signal reconstruction in the sense that substantially fewer measurements are needed for exact reconstruction. The algorithm minimizes the conventional total variation when the gradient is small, and minimizes the L0 of gradient when the gradient is large. An auto-adaptive threshold determines the transition between L1 and L0 of the gradients. The experimental results show the proposed algorithm outperforms either L1 or homotopic L0 minimization when the same reduction factor is used.
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