Learning Proximal Operators: Using Denoising Networks for Regularizing Inverse Imaging Problems (1704.03488v2)

Abstract: While variational methods have been among the most powerful tools for solving linear inverse problems in imaging, deep (convolutional) neural networks have recently taken the lead in many challenging benchmarks. A remaining drawback of deep learning approaches is their requirement for an expensive retraining whenever the specific problem, the noise level, noise type, or desired measure of fidelity changes. On the contrary, variational methods have a plug-and-play nature as they usually consist of separate data fidelity and regularization terms. In this paper we study the possibility of replacing the proximal operator of the regularization used in many convex energy minimization algorithms by a denoising neural network. The latter therefore serves as an implicit natural image prior, while the data term can still be chosen independently. Using a fixed denoising neural network in exemplary problems of image deconvolution with different blur kernels and image demosaicking, we obtain state-of-the-art reconstruction results. These indicate the high generalizability of our approach and a reduction of the need for problem-specific training. Additionally, we discuss novel results on the analysis of possible optimization algorithms to incorporate the network into, as well as the choices of algorithm parameters and their relation to the noise level the neural network is trained on.

• The paper replaces handcrafted proximal operators with learned CNN denoisers, improving image reconstruction adaptability and effectiveness.
• It integrates these denoising networks within optimization frameworks like PDHG and ADMM, ensuring robust convergence across various tasks.
• Experimental results show significant PSNR gains in deblurring and demosaicking, highlighting the method's practical impact in inverse imaging.

Learning Proximal Operators: Using Denoising Networks for Regularizing Inverse Imaging Problems

The paper "Learning Proximal Operators: Using Denoising Networks for Regularizing Inverse Imaging Problems" presents a novel approach to solving linear inverse problems in imaging by integrating learned denoising functions within established convex optimization frameworks. Traditionally, inverse imaging tasks, such as deblurring or demosaicking, have been addressed using variational methods that rely on handcrafted regularization terms to ensure stable solutions. However, these methods often fall short in adapting to varying problem specifics like noise level or fidelity requirements without significant reconfiguration.

Main Contributions

The primary contribution of the paper lies in the substitution of explicit proximal operators, which are typically derived from model-based regularizers, with learned denoising networks. This substitution allows for the capture of complex image priors more effectively than classical regularizers. The authors deploy convolutional neural networks (CNNs) as universal denoising operators within algorithms like the Primal-Dual Hybrid Gradient (PDHG) method, showcasing improved flexibility and adaptability across different imaging tasks.

Key contributions include:

• Replacement of Proximal Operators: Utilizing CNNs trained for denoising tasks as proximal operators, providing implicit and problem-agnostic regularization for diverse image reconstruction tasks.
• Algorithmic Integration and Analysis: Demonstrating the integration of these networks within established optimization algorithms such as ADMM and PDHG, while analyzing convergence properties and parameter influences.
• Performance Evaluation: Evidencing state-of-the-art performance in deconvolution and demosaicking tasks with a single trained network, thereby reducing the necessity for task-specific retrainings.

Numerical Results and Claims

The paper reports robust quantitative improvements in reconstruction quality over traditional methods for both image deblurring and demosaicking. For instance, experiments show that using a denoising CNN achieves significant PSNR enhancements across standard imaging benchmarks. The approach is evaluated extensively, revealing consistent performance across different noise and blur levels without the need for architecture or parameter modifications. The adaptability without retraining on problem-specific data showcases superior generalizability of the learned proximal operator strategy.

Theoretical and Practical Implications

Theoretically, this work challenges the constraints of variational models by incorporating data-driven priors, setting a precedent for hybrid methods in inverse problem-solving. Theoretically, the results suggest that learned denoisers serve as viable replacements for implicitly defined regularization functions under the MAP estimation framework. Convergence analyses further support the stability of combining learned priors with various optimization algorithms, contributing to the theoretical understanding of denoising as a regularization tool.

Practically, the implications are profound in the field of image processing, where plug-and-play adaptability is highly valued. The reduction of retraining efforts not only expedites the deployment of imaging solutions but also opens the door for utilizing robust priors in less understood or articulated physical models, something traditional model-based methods struggle with.

Future Directions

The research paves the way for future exploration into the application of learned proximal operators beyond imaging and into domains where inverse problems are prevalent, such as medical imaging and scientific computing. Further investigation into the optimization and parameter tuning could enhance the applicability and efficiency of the method, potentially leading to real-time solutions.

In closing, this paper underscores the potential of integrating machine learning with optimization-based frameworks, presenting a strategy that broadens the horizon for solving complex inverse imaging problems with enhanced efficacy and adaptability.