Multi-Scale Energy (MuSE) framework for inverse problems in imaging.

Area of Science:

• Computational imaging
• Machine learning for inverse problems
• Medical image analysis

Background:

• Traditional single-scale energy models face limitations in accuracy and convergence for image reconstruction.
• Inverse problems in imaging require robust methods for deriving estimates and sampling posterior distributions.

Purpose of the Study:

• To introduce and evaluate multi-scale energy models (MuSE) for learning image priors.
• To improve Maximum A Posteriori (MAP) estimation accuracy and convergence in inverse problems.
• To enable posterior sampling and uncertainty quantification in image reconstruction.

Main Methods:

• Development of two multi-scale energy strategies: explicit (e-MuSE) and implicit (i-MuSE).
• e-MuSE utilizes a sequence of explicit energies approximating the negative log-prior.
• i-MuSE employs a single energy function with scale-specific gradient matching.

Main Results:

• Both e-MuSE and i-MuSE significantly improve MAP estimation accuracy and convergence over single-scale models.
• i-MuSE demonstrates simpler formulation, faster convergence, and superior performance.
• MuSE models achieve MAP reconstruction quality comparable to End-to-End (E2E) trained models in MR image recovery.
• i-MuSE enables posterior sampling for uncertainty map estimation.

Conclusions:

• Multi-scale energy models offer a powerful framework for solving inverse problems in imaging.
• The implicit multi-scale energy (i-MuSE) approach provides a robust, efficient, and simpler alternative.
• MuSE models, particularly i-MuSE, are effective for Magnetic Resonance image reconstruction and uncertainty quantification.