Compressed sensing MRI via fast linearized preconditioned alternating direction method of multipliers

Area of Science:

• Medical Imaging
• Magnetic Resonance Imaging (MRI)
• Computational Imaging

Background:

• Compressed sensing MRI reconstructs images from undersampled k-space data.
• Total variation (TV) regularization preserves edges but leads to complex nonlinear, nonsmooth optimization problems.
• Efficient algorithms are crucial for large-scale TV-regularized problems.

Purpose of the Study:

• To develop an efficient algorithm for solving augmented TV-regularized models in compressed sensing MRI.
• To address the challenges of nonlinear and nonsmooth optimization in image reconstruction.

Main Methods:

• Proposed the fast linearized preconditioned alternating direction method of multipliers (FLPADMM).
• Augmented the TV-regularized model with a quadratic term for image smoothness.
• Decomposed the problem into two subproblems solvable via augmented Lagrangian function.
• Incorporated a linearized strategy and multistep weighted scheme for enhanced recovery.

Main Results:

• FLPADMM demonstrated improved accuracy and efficiency over existing methods.
• Experiments on in vivo data showed higher signal-to-noise ratio (SNR).
• Achieved lower relative error (Rel.Err) and better structural similarity (SSIM) index.

Conclusions:

• The proposed FLPADMM algorithm offers superior performance in accuracy and efficiency.
• Outperforms conventional compressed sensing MRI algorithms.
• Validates effectiveness on in vivo medical imaging data.