Memory-efficient model-based deep learning with convergence and robustness guarantees.

Area of Science:

• Computational imaging
• Deep learning
• Inverse problems

Background:

• Compressed sensing (CS) revolutionized computational imaging with theoretical guarantees.
• Model-based deep learning offers powerful image recovery by integrating imaging physics and learned priors.
• Existing deep learning methods can be memory-intensive, limiting their application to complex datasets.

Purpose of the Study:

• Introduce a memory-efficient model-based algorithm for computational imaging.
• Provide theoretical guarantees for uniqueness, convergence, and stability comparable to CS methods.
• Develop a deep equilibrium formulation for enhanced image recovery.

Main Methods:

• An iterative algorithm alternating between gradient descent with a score function and conjugate gradient for data consistency.
• Modeling the score function using a monotone convolutional neural network.
• Two implementations of the MOL framework: strict monotone constraint and approximation.

Main Results:

• The monotone constraint is proven necessary and sufficient for fixed-point uniqueness and guarantees convergence robustness.
• Empirical studies show comparable convergence and robustness for both strict and approximate implementations.
• The approximate implementation demonstrates superior performance.

Conclusions:

• The proposed deep equilibrium model is significantly more memory-efficient than unrolled methods.
• This efficiency enables application to 3D or 2D+time problems intractable for current unrolled algorithms.
• The method provides a powerful and scalable solution for advanced computational imaging tasks.