Frame-based compressive sensing MR image reconstruction with balanced regularization.

Area of Science:

• Medical Imaging
• Signal Processing
• Applied Mathematics

Background:

• Undersampled k-space measurements in MRI lead to image reconstruction challenges.
• Existing ℓ(1)-regularized methods (analysis-based and synthesis-based) have limitations with redundant transforms like frames.
• A gap exists between analysis-based and synthesis-based approaches under redundant transforms.

Purpose of the Study:

• To investigate and compare three frame-based ℓ(1)-regularized approaches for compressed sensing MRI reconstruction.
• To introduce and evaluate a balanced approach that bridges the gap between analysis-based and synthesis-based methods.
• To assess the performance of these methods in redundant frame domains.

Main Methods:

• Utilized frame-based ℓ(1)-regularized reconstruction for undersampled MR images.
• Developed a balanced approach by penalizing the distance between representation vectors and canonical frame coefficients.
• Employed variable splitting and the alternating direction method of multipliers (ADMM) to solve optimization problems.

Main Results:

• The balanced approach effectively reduces the gap between analysis-based and synthesis-based methods.
• Numerical simulations demonstrated the balanced approach's superiority over the other two methods under experimental conditions.
• The balanced method achieved better fidelity, sparsity, and smoothness in reconstructed MR images.

Conclusions:

• The balanced ℓ(1)-regularized approach offers improved performance for compressed sensing MRI reconstruction.
• This method provides a unified framework that balances key solution properties.
• The findings suggest the balanced approach is a promising technique for advanced MRI reconstruction.