Deep Model-Based Super-Resolution with Non-uniform Blur

TL;DR

The work tackles single-image super-resolution under spatially varying blur, formalized as $y = (Hx)\downarrow_s + \epsilon$ with a non-uniform $H$. It introduces a deep unfolding network built from a linearized ADMM-based deep plug-and-play solver that learns hyperparameters end-to-end, enabling joint deblurring and upscaling. The method achieves state-of-the-art results on synthetic non-uniform blur and demonstrates robust generalization to real-world defocus and motion blur scenarios, without per-kernel retraining. This approach offers practical impact for devices and microscopy where blur varies across the image and is difficult to model precisely.

Abstract

We propose a state-of-the-art method for super-resolution with non-uniform blur. Single-image super-resolution methods seek to restore a high-resolution image from blurred, subsampled, and noisy measurements. Despite their impressive performance, existing techniques usually assume a uniform blur kernel. Hence, these techniques do not generalize well to the more general case of non-uniform blur. Instead, in this paper, we address the more realistic and computationally challenging case of spatially-varying blur. To this end, we first propose a fast deep plug-and-play algorithm, based on linearized ADMM splitting techniques, which can solve the super-resolution problem with spatially-varying blur. Second, we unfold our iterative algorithm into a single network and train it end-to-end. In this way, we overcome the intricacy of manually tuning the parameters involved in the optimization scheme. Our algorithm presents remarkable performance and generalizes well after a single training to a large family of spatially-varying blur kernels, noise levels and scale factors.

Figures (7)

• Figure 1: Super-resolution with scale factor 2 in the presence of spatially-varying blur. The foreground is not blurred while the background is blurred using isotropic Gaussian kernel.
• Figure 2: (a) Background objects are moving with respect to the camera, so they appear blurry, whereas foreground objects are sharp. (b) Restoration problems that are addressed by previous articles or that can be potentially solved by available architectures: SR=single image Super-Resolution; UB = Uniform Blur; SVB = Spatially Varying Blur; MB = Motion Blur. Brackets stand for potential use case of the architecture that have not been tested in the literature to our knowledge.
• Figure 3: Model architecture, the low-resolution image is upsampled and alternately fed to the prior module $\mathcal{P}$, the data module $\mathcal{D}$ and the update module $\mathcal{U}$ during $N$ iterations
• Figure 4: Example of data generated by our pipeline
• Figure 5: Super-resolution with scale factor s=2 on real-world defocused images