A Complex Quasi-Newton Proximal Method for Image Reconstruction in Compressed Sensing MRI

Area of Science:

• Medical Imaging
• Optimization Algorithms
• Signal Processing

Background:

• Model-based methods are crucial for compressed sensing (CS) magnetic resonance imaging (MRI) reconstruction.
• These methods rely on regularizers to characterize image properties.
• Reconstruction is typically framed as a composite optimization problem, often tackled by accelerated proximal methods (APMs).

Purpose of the Study:

• To propose a novel complex quasi-Newton proximal method (CQNPM) for CS MRI reconstruction.
• To address the computational challenge of weighted proximal mappings (WPM) within CQNPM.
• To enhance the efficiency and practicality of advanced reconstruction techniques in MRI.

Main Methods:

• Development of a complex quasi-Newton proximal method (CQNPM).
• Integration of wavelet and total variation regularizers for CS MRI.
• Proposal of efficient algorithms for solving the weighted proximal mapping (WPM).

Main Results:

• CQNPM demonstrates faster convergence, requiring fewer iterations than traditional APMs.
• The proposed efficient WPM solvers make CQNPM computationally feasible.
• Numerical experiments confirm the effectiveness and efficiency of CQNPM for non-Cartesian MRI data reconstruction.

Conclusions:

• CQNPM offers a significant improvement in convergence speed for CS MRI reconstruction.
• Efficient WPM solutions are key to the practical application of CQNPM.
• The method proves effective and efficient for reconstructing complex, non-Cartesian MRI datasets.