Deep learning methods for inverse problems.

Area of Science:

• Computer Science
• Machine Learning
• Artificial Intelligence

Background:

• Inverse problems are prevalent in scientific and engineering fields.
• Deep learning offers promising solutions for inverse problems.
• Existing deep learning approaches lack a unified classification and comparative analysis.

Purpose of the Study:

• To classify and compare the robustness of different deep learning strategies for solving inverse problems.
• To evaluate the performance of these strategies under varying conditions, including noise and outliers.
• To provide guidance on selecting the most appropriate deep learning approach for specific inverse problem domains.

Main Methods:

• Categorization of deep learning solutions into Direct Mapping, Data Consistency Optimizer, and Deep Regularizer.
• Experimental validation on linear regression, image denoising, 3D human face inverse rendering, and object tracking.
• Statistical analysis of the robustness and performance differences across categories and problem types.

Main Results:

• Deep learning solution categories exhibit varying robustness depending on the inverse problem domain.
• The presence of measurement outliers significantly impacts the performance of different categories.
• No single category universally outperforms others; suitability is problem-dependent.

Conclusions:

• The choice of deep learning strategy for inverse problems should be informed by the specific problem characteristics, particularly the likelihood of measurement outliers.
• Direct Mapping, Data Consistency Optimizer, and Deep Regularizer approaches have distinct strengths and weaknesses.
• This research proposes the most robust solution category for each investigated inverse problem class based on empirical evidence.