Magnetic Resonance Image Restoration by Utilizing Fractional-Order Total Variation and Recursive Filtering

Abstract

Total variation-based methods are effective for magnetic resonance image restoration. To eliminate impulse noise, the $\ell_0$-norm total variation model is a proven approach. However, traditional total variation image restoration often results in staircase artifacts, especially at high noise levels. In this paper, we propose an innovative magnetic resonance image restoration model that integrates fractional-order regularization and filtering techniques. Specifically, the first term uses the $\ell_0$-norm as the data fidelity term to effectively remove impulse noise. The second term introduces a fractional-order total variation regularizer, which preserves structural information while reducing staircase artifacts during deblurring. Due to its limitations in texture detail recovery, we employ recursive filtering for high-quality edge-preserving filtering. Finally, we solve the optimization model using the alternating direction method of multipliers. Experimental results demonstrate the effectiveness of our method in restoring magnetic resonance images.