Constrained and unconstrained deep image prior optimization models with automatic regularization.

Area of Science:

• Computer Vision
• Machine Learning
• Image Processing

Background:

• Deep Image Prior (DIP) is an efficient unsupervised deep learning method for ill-posed inverse imaging problems.
• DIP utilizes implicit regularization through generative Convolutional Neural Network (CNN) architectures.
• Existing DIP models require accurate regularization parameter estimation for optimal solutions.

Purpose of the Study:

• To develop novel DIP models that automatically estimate local regularization parameters.
• To introduce a constrained formulation for broader regularizer applicability, inspired by Morozov's discrepancy principle.
• To enhance the robustness and applicability of DIP for inverse imaging problems.

Main Methods:

• A locally adapted regularized unconstrained model with automatic parameter estimation for separable regularizers.
• A novel constrained formulation analogous to Morozov's discrepancy principle.
• Proximal gradient descent-ascent for solving both unconstrained and constrained models.

Main Results:

• The proposed models automatically estimate local regularization parameters, overcoming limitations of previous methods.
• The constrained formulation allows for a wider array of regularizers.
• Demonstrated robustness across various image contents, noise levels, and hyperparameters.
• Successful application in denoising and deblurring of simulated and real-world images, including natural and medical images.

Conclusions:

• The novel unconstrained and constrained DIP models offer robust and automatic regularization parameter estimation.
• These advancements improve the performance and applicability of unsupervised deep learning for inverse imaging problems.
• The methods show significant potential for enhancing image quality in various imaging applications.