A Weighted Two-Level Bregman Method with Dictionary Updating for Nonconvex MR Image Reconstruction

Area of Science:

• Medical Imaging
• Optimization Theory
• Signal Processing

Background:

• Nonconvex optimization offers advantages over l1 minimization for signal recovery using fewer measurements.
• Dictionary learning models are crucial for reconstructing signals from partial measurements.
• Efficient algorithms are needed to solve lp-norm minimization problems in compressed sensing.

Purpose of the Study:

• To propose two efficient numerical algorithms for solving lp optimization under dictionary learning models.
• To address the challenge of reconstructing magnetic resonance imaging (MRI) data from highly undersampled k-space measurements.
• To improve image reconstruction quality and efficiency in accelerated MRI.

Main Methods:

• Development of the weighted two-level Bregman method with dictionary updating (WTBMDU).
• Incorporation of iteratively reweighted norms into the two-level Bregman iteration method with dictionary updating (TBMDU).
• Application of a modified alternating direction method (ADM) to solve approximated lp-norm penalty models efficiently.

Main Results:

• The proposed algorithms converge rapidly, requiring a relatively small number of iterations.
• Reconstruction using iteratively reweighted l1 and l2 minimization formulations proved effective.
• Experimental results showed superior performance on MR image simulations and real data compared to state-of-the-art methods.

Conclusions:

• The WTBMDU method efficiently reconstructs MR images from highly undersampled k-space data.
• The proposed algorithms demonstrate significant advantages in terms of higher Peak Signal-to-Noise Ratio (PSNR) and lower High-Frequency Error Norm (HFEN) values.
• This approach offers a promising solution for accelerated MRI acquisition and reconstruction.