Monotone FISTA with Variable Acceleration for Compressed Sensing Magnetic Resonance Imaging

Area of Science:

• Applied Mathematics
• Medical Imaging
• Optimization Algorithms

Background:

• Compressed sensing (CS) is crucial for accelerating magnetic resonance imaging (MRI) acquisition.
• Existing algorithms like monotone fast iterative shrinkage-thresholding algorithm (MFISTA) face limitations in reconstruction time.
• The need for faster convergence in iterative algorithms for MRI reconstruction is significant.

Purpose of the Study:

• To enhance the convergence speed of the MFISTA algorithm for compressed sensing MRI.
• To reduce the overall reconstruction time in MRI scans.
• To extend FISTA-like methods to complex variables for broader applicability.

Main Methods:

• Introduced an extra term, a multiple of the proximal-gradient step, into the MFISTA momentum formula.
• Modified the algorithm to select the next iterate from improved points using methods like arbitrary shifts or line searches.
• Provided a careful extension of FISTA-like methods to functions of several complex variables.

Main Results:

• The modified MFISTA algorithm demonstrates accelerated convergence compared to the original MFISTA.
• Improved theoretical convergence bounds were established for the enhanced algorithm.
• The modified algorithm offers greater flexibility in parameter selection.

Conclusions:

• The proposed MFISTA modification effectively reduces reconstruction time in compressed sensing MRI.
• The enhanced algorithm provides superior convergence properties and flexibility.
• The extension to complex variables broadens the potential applications of these methods.