Ambiguity in Solving Imaging Inverse Problems with Deep-Learning-Based Operators.

Area of Science:

• Computer Vision
• Artificial Intelligence
• Image Processing

Background:

• Convolutional neural networks (CNNs) excel at image deblurring but struggle with noise sensitivity.
• Image deblurring is an ill-posed inverse problem, challenging for neural networks, especially with noisy data.
• Current deep learning methods often neglect the mathematical underpinnings of imaging problems.

Purpose of the Study:

• To propose strategies for improving the stability of deep learning-based image deblurring methods.
• To maintain accuracy while enhancing robustness against noise and perturbations.
• To address the limitations of existing neural network approaches in handling noisy image data.

Main Methods:

• Development of a compact neural network architecture to reduce training time and noise amplification.
• Introduction of a unified framework incorporating a pre-processing step to stabilize neural network deblurring.
• Implementation of two pre-processors: a parameter-free denoiser and a variational-model-based regularizer.
• Formal mathematical analysis of the proposed framework.

Main Results:

• The proposed small neural architecture reduces execution time and noise amplification.
• The unified framework with pre-processing significantly improves network stability in the presence of noise.
• Numerical experiments confirm enhanced accuracy and stability compared to standard deep learning methods.
• The model-based framework offers a robust trade-off between visual fidelity and noise resilience.

Conclusions:

• The developed strategies effectively enhance the stability of deep learning-based image deblurring.
• The unified framework, particularly the model-based approach, provides a reliable solution for deblurring noisy images.
• The findings contribute to more robust and efficient deep learning applications in image restoration.