Prior ensemble learning : Theory and application to MR image priors

Area of Science:

• Medical Imaging
• Computational Imaging
• Machine Learning

Background:

• Compressed sensing (CS) accelerates magnetic resonance (MR) imaging by reducing measurement time.
• Image priors are crucial for enhancing reconstruction precision in CS-based MR imaging.
• Developing optimal, hand-built priors is challenging and subject-dependent.

Purpose of the Study:

• To introduce Prior Ensemble Learning (PEL), a novel methodology for combining multiple weak priors to create a superior image prior.
• To approximate the Bayes optimal posterior mean (PM) estimate, minimizing mean squared error (MSE).
• To enhance image reconstruction precision in compressed sensing MR imaging.

Main Methods:

• Proposed Prior Ensemble Learning (PEL) theory, transitioning from exponential to mixture family for prior combination.
• Applied PEL to reconstruct undersampled (10%) multicoil MR images.
• Efficiently combined 136 diverse image priors, including norm-based and wavelet priors with varying regularization coefficients (RCs).

Main Results:

• Demonstrated PEL's superiority over CS-SENSE in terms of reconstructed image MSE using only two training samples.
• Showcased sparse combining weights, with only 18% of weak priors retained.
• Validated PEL's effectiveness in a practical MR image reconstruction scenario.

Conclusions:

• Theoretically decomposed the PM estimator into a sparse weighted sum of individual weak prior estimators.
• Reduced computational complexity for regularization coefficients from exponential to polynomial order relative to the number of weak priors.
• Confirmed PEL as a feasible and effective approach for MR image reconstruction.