Preprint
MAP Image Recovery with Guarantees using Locally Convex Multi-Scale Energy (LC-MUSE) Model
ArXiV.org
Cornell University
02/05/2025
DOI: 10.48550/arxiv.2502.03302
Abstract
We propose a multi-scale deep energy model that is strongly convex in the
local neighbourhood around the data manifold to represent its probability
density, with application in inverse problems. In particular, we represent the
negative log-prior as a multi-scale energy model parameterized by a
Convolutional Neural Network (CNN). We restrict the gradient of the CNN to be
locally monotone, which constrains the model as a Locally Convex Multi-Scale
Energy (LC-MuSE). We use the learned energy model in image-based inverse
problems, where the formulation offers several desirable properties: i)
uniqueness of the solution, ii) convergence guarantees to a minimum of the
inverse problem, and iii) robustness to input perturbations. In the context of
parallel Magnetic Resonance (MR) image reconstruction, we show that the
proposed method performs better than the state-of-the-art convex regularizers,
while the performance is comparable to plug-and-play regularizers and
end-to-end trained methods.
Details
- Title: Subtitle
- MAP Image Recovery with Guarantees using Locally Convex Multi-Scale Energy (LC-MUSE) Model
- Creators
- Jyothi Rikhab ChandMathews Jacob
- Resource Type
- Preprint
- Publication Details
- ArXiV.org
- DOI
- 10.48550/arxiv.2502.03302
- ISSN
- 2331-8422
- Publisher
- Cornell University; Ithaca, New York
- Language
- English
- Date posted
- 02/05/2025
- Academic Unit
- Electrical and Computer Engineering; Iowa Technology Institute
- Record Identifier
- 9984787261702771
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