Trainable Nonlinear Reaction Diffusion: A Flexible Framework for Fast and Effective Image Restoration (1508.02848v2)

Abstract: Image restoration is a long-standing problem in low-level computer vision with many interesting applications. We describe a flexible learning framework based on the concept of nonlinear reaction diffusion models for various image restoration problems. By embodying recent improvements in nonlinear diffusion models, we propose a dynamic nonlinear reaction diffusion model with time-dependent parameters (\ie, linear filters and influence functions). In contrast to previous nonlinear diffusion models, all the parameters, including the filters and the influence functions, are simultaneously learned from training data through a loss based approach. We call this approach TNRD -- \textit{Trainable Nonlinear Reaction Diffusion}. The TNRD approach is applicable for a variety of image restoration tasks by incorporating appropriate reaction force. We demonstrate its capabilities with three representative applications, Gaussian image denoising, single image super resolution and JPEG deblocking. Experiments show that our trained nonlinear diffusion models largely benefit from the training of the parameters and finally lead to the best reported performance on common test datasets for the tested applications. Our trained models preserve the structural simplicity of diffusion models and take only a small number of diffusion steps, thus are highly efficient. Moreover, they are also well-suited for parallel computation on GPUs, which makes the inference procedure extremely fast.

• The paper introduces the TNRD model, a trainable nonlinear reaction diffusion framework that jointly learns filters and influence functions for state-of-the-art image restoration.
• The model achieves notable PSNR improvements across tasks like Gaussian denoising, single image super resolution, and JPEG deblocking, outperforming classical and contemporary methods.
• Its efficiency on parallel architectures and adaptability to various restoration tasks underscore the TNRD framework's potential for real-time, scalable image processing applications.

Trainable Nonlinear Reaction Diffusion: A Flexible Framework for Fast and Effective Image Restoration

Image restoration remains a cornerstone within low-level computer vision due to its wide array of applications and the challenging nature of its problem domain. The paper "Trainable Nonlinear Reaction Diffusion: A Flexible Framework for Fast and Effective Image Restoration" by Chen and Pock introduces a substantial advancement in learning-based approaches for image restoration tasks. Central to this methodology is the concept of nonlinear reaction diffusion (NRD) models, which have been dynamically adapted, parameterized, and optimized using a supervised learning framework.

Model Formulation and Training

The authors propose the Trainable Nonlinear Reaction Diffusion (TNRD) model, which integrates recent improvements in NRD models and enhances them through trainable parameters. The TNRD model consists of time-dependent parameters—filter kernels and influence functions—both of which are optimized concurrently from the training dataset. The framework stems from the nonlinear diffusion process expressed mathematically as:

u_t = u_{t-1} - (Σ_i (k_i^t)^T φ_i^t(k_i^t * u_{t-1}) + ψ^t(u_{t-1}, f))

where k_i^t represents linear filters, φ_i^t denotes influence functions, and ψ^t is the reaction term. This model distinguishes itself from prior NRD methods by allowing all parameters to be jointly learned, optimizing performance specifically for tasks such as Gaussian denoising, single image super resolution (SISR), and JPEG deblocking.

Numerical Results and Performance

In a series of comprehensive experiments, the authors demonstrate the efficacy of their TNRD model across multiple image restoration tasks:

1. Gaussian Denoising: The TNRD model achieves state-of-the-art results, outperforming classical methods such as BM3D and contemporary approaches like CSF and WNNM. For noise level σ = 25, the TNRD model reaches an average PSNR of 28.92 dB, notably higher than 28.60 dB of the CSF model with similar configurations.
2. Single Image Super Resolution: The TNRD framework is robust across various upscaling factors (×2, ×3, ×4). For instance, the model yielded a significant improvement in PSNR for the Set14 dataset with an average PSNR of 29.46 dB for ×3 upscaling, surpassing methods such as ANR, SR-CNN, and RFL.
3. JPEG Deblocking: The application extends to handling non-smooth data terms, crucial for suppressing block artifacts in JPEG compressed images. Here, the PSNR scores for quality factors of q = 10, 20, and 30 were elevated to 27.85 dB, 30.06 dB, and 31.41 dB respectively, indicative of superior performance relative to other advanced techniques.

Implications and Future Work

The proposed TNRD model offers several noteworthy practical and theoretical implications:

• Efficiency: The model is inherently efficient for parallel architectures such as GPUs. This facilitates real-time processing even for high-resolution images, a substantial practical advantage.
• Generality: By training both the filters and the influence functions, the model can adapt to various restoration tasks, marking a significant theoretical advancement over fixed-function models.
• Scalability: Though the framework is shown to be effective with current datasets, the potential for large-scale deployment remains an interesting domain for future exploration. The scalability in conjunction with deeper learning strategies warrants further investigation.

The paper propounds future directions, including adaptations for other image processing tasks like image inpainting and optical flow. The promising results and the flexibility of the TNRD model suggest widespread applicability and further improvements through broader training datasets and optimized learning algorithms.

Overall, the work by Chen and Pock presents a meticulously developed, efficient, and highly effective approach to image restoration by introducing a dynamically trainable nonlinear reaction diffusion framework that sets a new benchmark in the field.