Joint image edge reconstruction and its application in multi-contrast MRI
For multi-contrast MRI reconstruction, this method offers a more efficient and accurate approach, though it is an incremental improvement over existing regularization techniques.
The paper proposes a joint image reconstruction method that recovers edges directly from observed data, reformulating vectorial total-variation regularization as an l1 minimization problem. The method achieves an O(1/k^2) convergence rate and significantly improves reconstruction efficiency and accuracy over state-of-the-arts in multi-contrast MRI tests.
We propose a new joint image reconstruction method by recovering edge directly from observed data. More specifically, we reformulate joint image reconstruction with vectorial total-variation regularization as an $l_1$ minimization problem of the Jacobian of the underlying multi-modality or multi-contrast images. Derivation of data fidelity for Jacobian and transformation of noise distribution are also detailed. The new minimization problem yields an optimal $O(1/k^2)$ convergence rate, where $k$ is the iteration number, and the per-iteration cost is low thanks to the close-form matrix-valued shrinkage. We conducted numerical tests on a number multi-contrast magnetic resonance image (MRI) datasets, which show that the proposed method significantly improves reconstruction efficiency and accuracy compared to the state-of-the-arts.