On Architecture Selection for Linear Inverse Problems with Untrained Neural Networks.

Area of Science:

• Computer Vision
• Machine Learning
• Signal Processing

Background:

• Neural network image priors, particularly pre-trained generative models, excel in linear inverse problems, surpassing traditional sparsity-based methods.
• Untrained neural networks also demonstrate potential as effective image priors across diverse imaging applications.

Purpose of the Study:

• To expand the understanding and application of untrained neural network priors.
• Investigate the interplay between neural network architecture, measurement models (inpainting, denoising, compressive sensing), and signal characteristics (smooth, erratic).

Main Methods:

• Theoretical motivation using statistical learning theory.
• Development of two practical algorithms for tuning architectural hyperparameters.
• Experimental evaluations across various tasks and signal types.

Main Results:

• Optimal hyperparameters for untrained neural network priors are task-dependent.
• Significant performance degradation occurs when hyperparameters are tuned for the incorrect task.
• Identified key hyperparameters and assessed their robustness to suboptimal settings.

Conclusions:

• The effectiveness of untrained neural network priors is sensitive to architectural choices and task-specific tuning.
• Careful hyperparameter selection is crucial for maximizing performance in image reconstruction tasks.
• Understanding these interactions is vital for advancing untrained neural network applications in imaging.