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

Jyothi Rikhab Chand^1,2, Mathews Jacob²

¹Department of Electrical and Computer Engineering, University of Iowa, IA, USA.

Proceedings of the ... IEEE International Conference on Acoustics, Speech, and Signal Processing. ICASSP (Conference)

|March 12, 2026

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We developed a novel multi-scale deep energy model for inverse problems, ensuring unique solutions and convergence. This Locally Convex Multi-Scale Energy (LC-MuSE) model enhances Magnetic Resonance image reconstruction.

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.

Keywords:

Energy model Locally convex regularizer Parallel MR image reconstruction

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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.