Joint image edge reconstruction and its application in multi-contrast MRI

TL;DR

This paper introduces a novel joint image reconstruction method for multi-contrast MRI that directly recovers edges from observed data using vectorial total-variation regularization, achieving fast convergence and improved accuracy.

Contribution

It reformulates joint image reconstruction as an $l_1$ minimization of the Jacobian, providing a new efficient algorithm with proven convergence rate and low per-iteration cost.

Findings

Significantly improves reconstruction accuracy over existing methods.

Achieves an optimal $O(1/k^2)$ convergence rate.

Demonstrates efficiency and effectiveness on multi-contrast MRI datasets.

Abstract

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.