One Network to Solve Them All --- Solving Linear Inverse Problems using Deep Projection Models (1703.09912v1)

Abstract: While deep learning methods have achieved state-of-the-art performance in many challenging inverse problems like image inpainting and super-resolution, they invariably involve problem-specific training of the networks. Under this approach, different problems require different networks. In scenarios where we need to solve a wide variety of problems, e.g., on a mobile camera, it is inefficient and costly to use these specially-trained networks. On the other hand, traditional methods using signal priors can be used in all linear inverse problems but often have worse performance on challenging tasks. In this work, we provide a middle ground between the two kinds of methods --- we propose a general framework to train a single deep neural network that solves arbitrary linear inverse problems. The proposed network acts as a proximal operator for an optimization algorithm and projects non-image signals onto the set of natural images defined by the decision boundary of a classifier. In our experiments, the proposed framework demonstrates superior performance over traditional methods using a wavelet sparsity prior and achieves comparable performance of specially-trained networks on tasks including compressive sensing and pixel-wise inpainting.

Insights on "One Network to Solve Them All: Solving Linear Inverse Problems Using Deep Projection Models"

This paper presents a novel approach to addressing linear inverse problems in image processing through a unified deep learning framework. The motivation behind this research stems from the inefficiency and redundancy associated with problem-specific deep neural networks commonly used to tackle inverse problems such as image inpainting and super-resolution. Traditional methods employing hand-crafted signal priors are generalizable but often underperform compared to specialized deep learning models. This work proposes a mid-ground strategy wherein a single deep neural network is leveraged to serve as a proximal operator within an optimization algorithm, capable of solving various linear inverse problems without the need for retraining.

Key Contributions

1. General Framework for Linear Inverse Problems: The authors propose a system where a single network acts as a proximal operator integrated within the ADMM (Alternating Direction Method of Multipliers) optimization algorithm. This network is trained to project signals onto the manifold of natural images defined by the decision boundary learned from a classifier network.
2. Convergence Guarantees: Through theoretical backing, the paper assures convergence to a stationary point under specific conditions, such as the Lipschitz continuity of gradients in the objective function, which are often challenging to ensure in nonconvex optimization landscapes typical of deep learning.
3. Network Architecture and Training: The architecture includes a projection network trained jointly with a classifier using adversarial learning, effectively learning the manifold of natural images. The network's structure of convolutional and deconvolutional layers is consistent with common design in autoencoders, further matched with virtual batch normalization and residual connections ensuring stability and performance.
4. Empirical Evaluation: Experiments conducted demonstrate the proposed framework's ability to accomplish tasks such as compressive sensing, inpainting, and super-resolution with performance comparable to specialized networks and superior robustness to changes in problem-specific structures like noise and variations in operators.

Implications and Future Directions

The utilization of a universal network for diverse linear inverse problems lowers the redundancy seen in deep learning models, potentially streamlining mobile and embedded systems dealing with a range of visual tasks. The mechanisms described could significantly improve resource efficiency in hardware deployment, crucial for devices with limited computational capabilities such as mobile phones and edge computing devices.

Future work could explore refining this universal approach to extend beyond linear inverse problems into nonlinear domains, thereby further unifying the framework's applicability across different types of imaging and signal processing challenges. Additionally, addressing the limitations in terms of convergence and ensuring broader theoretical guarantees remains an avenue for ongoing research.

Conclusion

This paper contributes an intelligent balance between traditionally distinct approaches for solving inverse problems, showcasing how deep learning can harness flexibility without losing generality or performance. It makes a strategic advance toward developing cost-effective and broadly applicable solutions in practical imaging applications, highlighting a significant step forward in deep learning's adaptability and efficiency.