Tangent vector-based gradient method with l₁₂-regularization: Iterative half thresholding algorithm for CS-MRI.

Area of Science:

• Medical Imaging
• Signal Processing
• Computational Science

Background:

• Compressed Sensing (CS) MRI enables faster image acquisition but requires sophisticated reconstruction algorithms.
• Standard CS reconstruction often relies on l1-regularization, which may not always yield optimal results.

Purpose of the Study:

• To introduce and evaluate a new tangent vector-based l12-regularization method for compressed sensing MRI reconstruction.
• To compare the performance of the proposed method against standard l1-regularization techniques.

Main Methods:

• The proposed l12-regularization method was applied to sparse signals, numerical phantoms, and in-vivo cardiac MRI datasets.
• Reconstructions were performed using both Cartesian and radial trajectories on a 3T scanner.
• Performance was evaluated using Root Mean Square Error (RMSE) and Peak Signal-to-Noise Ratio (PSNR) under different sub-sampling strategies (Cartesian and Gaussian random).

Main Results:

• The proposed l12-regularization method demonstrated significant improvements over standard l1-regularization, with a 54.8% reduction in RMSE and a 14.3% increase in PSNR.
• Image reconstruction using Gaussian random sub-sampling outperformed Cartesian sub-sampling.
• The method showed good sparse signal approximation and superior convergence behavior.

Conclusions:

• Tangent vector-based l12-regularization is a promising technique for cardiac MRI reconstruction.
• The proposed method offers superior performance compared to conventional CS algorithms.
• The findings suggest potential for improved efficiency and image quality in accelerated MRI acquisition.