A Review of Convolutional Neural Networks for Inverse Problems in Imaging (1710.04011v1)

Abstract: In this survey paper, we review recent uses of convolution neural networks (CNNs) to solve inverse problems in imaging. It has recently become feasible to train deep CNNs on large databases of images, and they have shown outstanding performance on object classification and segmentation tasks. Motivated by these successes, researchers have begun to apply CNNs to the resolution of inverse problems such as denoising, deconvolution, super-resolution, and medical image reconstruction, and they have started to report improvements over state-of-the-art methods, including sparsity-based techniques such as compressed sensing. Here, we review the recent experimental work in these areas, with a focus on the critical design decisions: Where does the training data come from? What is the architecture of the CNN? and How is the learning problem formulated and solved? We also bring together a few key theoretical papers that offer perspective on why CNNs are appropriate for inverse problems and point to some next steps in the field.

• The paper demonstrates that CNN architectures effectively solve inverse imaging problems, enhancing image reconstruction quality over traditional methods.
• It emphasizes the critical role of realistic training data and appropriate cost functions to boost CNN performance in tasks like denoising and deconvolution.
• The review outlines promising future directions, including cross-task learning and iterative algorithm unrolling to further advance imaging applications.

Convolutional Neural Networks for Inverse Problems in Imaging: A Review

The paper "A Review of Convolutional Neural Networks for Inverse Problems in Imaging" explores the application of convolutional neural networks (CNNs) to address inverse problems prevalent in imaging fields such as denoising, deconvolution, super-resolution, and medical image reconstruction. These endeavors have emerged following the successful deployment of CNNs in tasks like object classification and segmentation, driven by the capability to train deep networks with substantial parameters. This essay provides a detailed analysis of the paper, focusing on the critical aspects of designing CNNs for inverse problems and highlighting key experimental results in the domain.

Background and Motivation

Inverse problems involve the reconstruction of an image from incomplete or noisy measurements, and traditional techniques have included methods like compressed sensing and convex optimization. The significant advance in computational power, particularly with GPUs, has catalyzed a resurgence of interest in neural networks, especially CNNs. The capability of CNNs to approximate complex, non-linear mappings efficiently positions them as viable tools for solving inverse problems, benefiting from their speed and reusability across varied tasks.

Design Strategies for CNNs in Inverse Problems

The paper explores the design considerations for employing CNNs in inverse problems:

1. Training Data: The selection of training data is fundamental, often sourced from simulations where clean images are corrupted to emulate real-world degradation (e.g., adding noise for denoising tasks). This approach underscores the importance of preprocessing and ensuring that the training data reflect realistic scenarios.
2. Network Architecture: The architecture can significantly influence performance, with options ranging from deep, complex designs to more straightforward layer stacks. Some architectures are inspired by successful networks from image classification and are refined for specific inverse problem tasks. The concept of unrolling iterative algorithms into network architectures is notably mentioned as a promising direction.
3. Formulation of the Learning Problem: The choice of cost functions (often Euclidean) aligns with the statistical nature of noise models. Nevertheless, the paper articulates the need for considering other cost functions and regularizations to handle overfitting and ensure robust parameter learning.
4. Optimization: Leveraging stochastic gradient descent and its variants, CNN training aims to reach local minima efficiently. The paper emphasizes the challenges in non-convex optimization posed by CNN training and points to software frameworks that facilitate this process.

Numerical Results and Comparisons

Recent applications of CNNs in inverse imaging problems have shown quantitative improvements, albeit modest in some cases. Importantly, these improvements are in heavily optimized fields, highlighting CNNs as potential candidates for achieving state-of-the-art results. The paper reviews various studies where CNNs have managed performance gains, usually yielding SNR enhancements or qualitative visual improvements over traditional methods.

Theoretical Considerations

The paper discusses the theoretical underpinnings of CNNs, such as universal approximation and the rationale behind using convolutional layers for image-based tasks. The notion that CNNs generalize established methods (e.g., iterative algorithms) gives a foundational understanding of their flexibility and potential in replacing or augmenting traditional techniques.

Challenges and Future Directions

The authors identify several challenges, including reproducibility concerns, overfitting mitigation, and the need for robust cross-validation strategies. They stress the importance of exploring cross-task learning, where knowledge gained in one domain (e.g., natural images) can be transferred to another (e.g., medical imaging), thereby enhancing the applicability of trained networks.

In conclusion, CNNs represent a powerful tool for solving inverse problems in imaging. While the numerical improvements may currently be incremental, the methodological advantages of CNNs, such as reduced requirement for domain-specific engineering and scalability, present a compelling case for their continued exploration and development in this rapidly evolving area.