Iteratively Refined Image Reconstruction with Learned Attentive Regularizers.

Area of Science:

• Medical Imaging
• Computer Vision
• Applied Mathematics

Background:

• Deep learning models for image reconstruction lack interpretability and theoretical analysis.
• Classic sparsity-promoting models offer interpretability but may not match deep learning performance.

Purpose of the Study:

• To develop an interpretable regularization scheme for image reconstruction.
• To combine the strengths of deep learning and sparsity-promoting models.
• To provide theoretical guarantees for the proposed method.

Main Methods:

• A novel regularization scheme is proposed, leveraging deep learning and convex optimization.
• A series of convex problems are minimized, with spatially refined regularization masks generated iteratively.
• The existence of a fixed point for the update operator is proven, with convergence to a critical point shown for a specific mask generator.

Main Results:

• The proposed scheme achieves performance comparable to state-of-the-art learned variational models.
• Experimental results demonstrate the model's progressive attention to image structure.
• The method offers a balance between interpretability, theoretical guarantees, reliability, and performance.

Conclusions:

• The developed regularization scheme provides an interpretable and theoretically sound approach to image reconstruction.
• This method successfully integrates deep learning with classical sparsity priors.
• The approach represents a significant advancement in reliable and high-performance image reconstruction.