MAP Image Recovery with Guarantees using Locally Convex Multi-Scale Energy (LC-MUSE) Model

Area of Science:

• Medical Imaging
• Machine Learning
• Applied Mathematics

Background:

• Inverse problems are crucial in scientific imaging.
• Existing methods for inverse problems often lack guaranteed convergence or robustness.
• Deep learning models offer potential but require careful formulation for stability.

Purpose of the Study:

• To introduce a novel multi-scale deep energy model for probability density representation.
• To apply this model to image-based inverse problems, particularly Magnetic Resonance (MR) image reconstruction.
• To ensure desirable properties like solution uniqueness, convergence guarantees, and robustness.

Main Methods:

• Developed a multi-scale deep energy model constrained to be locally convex.
• Parameterized the model using a Convolutional Neural Network (CNN) with a monotone gradient.
• Formulated the negative log-prior as this locally convex multi-scale energy model (LC-MuSE).

Main Results:

• The LC-MuSE model demonstrated strong convexity around the data manifold.
• In MR image reconstruction, the method achieved superior performance compared to convex regularizers.
• Performance was comparable to state-of-the-art plug-and-play and end-to-end trained methods.

Conclusions:

• The proposed LC-MuSE model provides a robust and theoretically sound approach for inverse problems.
• It offers significant advantages in MR image reconstruction over existing convex methods.
• The model's properties ensure reliable and accurate image reconstruction.