PALMNUT: An Enhanced Proximal Alternating Linearized Minimization Algorithm with Application to Separate...

Area of Science:

• Optimization algorithms
• Image reconstruction
• Computational imaging

Background:

• Complex image reconstruction involves solving non-convex optimization problems.
• Separate regularization of image magnitude and phase is challenging.
• Existing methods like alternating minimization can be computationally intensive.

Purpose of the Study:

• Introduce a novel algorithm for complex image reconstruction.
• Enhance the proximal alternating linearized minimization (PALM) algorithm.
• Improve computational efficiency and convergence for non-convex optimization problems.

Main Methods:

• Implemented a novel proximal alternating linearized minimization (PALM) algorithm.
• Developed PALMNUT by integrating Nesterov's momentum and coordinatewise step sizes into PALM.
• Utilized coordinatewise Lipschitz-like bounds for step size determination.

Main Results:

• PALMNUT demonstrates computational advantages over alternating minimization in magnetic resonance imaging.
• A version of PALMNUT guarantees monotonic decrease of the objective function, ensuring convergence.
• Empirical results validate the effectiveness of the proposed algorithm.

Conclusions:

• PALMNUT offers an effective and computationally efficient solution for complex image reconstruction.
• The algorithm shows promise for applications involving separate magnitude and phase regularization.
• The approach may be applicable to other non-convex optimization problems with similar structures.