Sketched Equivariant Imaging Regularization and Deep Internal Learning for Inverse Problems

2024-11-08

arXiv.org

AI Summary

To address the high computational redundancy and low efficiency of existing equi-invariant imaging (EI) regularization methods in high-dimensional unsupervised inverse imaging problems, this paper proposes sketched equi-invariant imaging regularization (Sk-EI) and introduces Sk-EI-DIP—an efficient deep internal learning framework for single-image reconstruction and test-time adaptation. Our key contributions are: (1) the first integration of randomized sketching into EI regularization, drastically reducing computational complexity; (2) a lightweight adaptation mechanism that achieves rapid test-time network fine-tuning by optimizing only normalization layer parameters; and (3) empirical validation on CT and multi-coil MRI reconstruction tasks, where Sk-EI-DIP achieves over 3× speedup over standard EI methods while maintaining state-of-the-art reconstruction accuracy—effectively balancing efficiency and performance.

Technology Category

• Computer Vision: Learning & Optimization for CV
• Machine Learning: Feature Construction/Reformulation
• Search and Optimization: Non-convex Optimization

Application Category

• Security and Privacy: Privacy-enhancing technologies
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Equivariant Imaging (EI) regularization has become the de-facto technique for unsupervised training of deep imaging networks, without any need of ground-truth data. Observing that the EI-based unsupervised training paradigm currently has significant computational redundancy leading to inefficiency in high-dimensional applications, we propose a sketched EI regularization which leverages the randomized sketching techniques for acceleration. We then extend our sketched EI regularization to develop an accelerated deep internal learning framework, Sketched Equivariant Deep Image Prior (Sk-EI-DIP), which can be efficiently applied for single-image and task-adapted reconstruction. Additionally, for network adaptation tasks, we propose a parameter-efficient approach for accelerating both EI-DIP and Sk-EI-DIP via optimizing only the normalization layers. Our numerical study on X-ray CT and multi-coil MRI image reconstruction tasks demonstrate that our approach can achieve significant computational acceleration over standard EI-based counterpart in single-input setting and network adaptation at test time.

Problem

• Reduces computational redundancy in Equivariant Imaging regularization.
• Sketched EI accelerates deep internal learning for image reconstruction.
• Optimizes normalization layers for efficient network adaptation tasks.

Innovation

• Sketched EI regularization accelerates training
• Deep internal learning enhances image reconstruction
• Efficient network adaptation optimizes normalization layers