An accelerated alternating direction method of multiplier for MRI with TV regularisation

Area of Science:

• Medical Imaging
• Signal Processing
• Optimization Algorithms

Background:

• Compressed Sensing (CS) enables Magnetic Resonance Imaging (MRI) reconstruction from undersampled k-space data.
• Total Variation (TV) regularization enhances image sparsity in CS-MRI.
• Alternating Direction Multiplier Method (ADMM) is crucial for variational image processing.

Purpose of the Study:

• To enhance MRI image quality and reduce reconstruction time.
• To develop an efficient algorithm for solving the constrained optimization problem in CS-MRI.

Main Methods:

• Formulated CS-MRI as a constrained optimization problem using TV regularization.
• Developed an accelerated ADMM algorithm for variational image processing.
• Theoretically verified convergence rate of O1/k^2 under specific convexity conditions.

Main Results:

• The accelerated ADMM algorithm demonstrated improved running speed compared to existing methods.
• Experimental results showed superior reconstruction quality for the proposed method.
• Tested using five undersampled templates in MRI experiments.

Conclusions:

• The proposed accelerated ADMM method effectively improves CS-MRI reconstruction speed and quality.
• This advancement holds potential for more efficient and accurate MRI diagnostics.
• The algorithm's convergence properties are theoretically validated.