Despite significant advances in image denoising, most algorithms rely on supervised learning, with their performance largely dependent on the quality and diversity of training data. It is widely assumed that digital image distortions are caused by spatially invariant Additive White Gaussian Noise (AWGN). However, the analysis of real-world data suggests that this assumption is invalid. Therefore, this paper tackles image corruption by real noise, providing a framework to capture and utilise the underlying structural information of an image along with the spatial information conventionally used for deep learning tasks. We propose a novel denoising loss function that incorporates topological invariants and is informed by textural information extracted from the image wavelet domain. The effectiveness of this proposed method was evaluated by training state-of-the-art denoising models on the BVI-Lowlight dataset, which features a wide range of real noise distortions. Adding a topological term to common loss functions leads to a significant increase in the LPIPS (Learned Perceptual Image Patch Similarity) metric, with the improvement reaching up to 25%. The results indicate that the proposed loss function enables neural networks to learn noise characteristics better. We demonstrate that they can consequently extract the topological features of noise-free images, resulting in enhanced contrast and preserved textural information.

Video restoration and enhancement are critical not only for improving visual quality, but also as essential pre-processing steps to boost the performance of a wide range of downstream computer vision tasks. This survey presents a comprehensive review of video restoration and enhancement techniques with a particular focus on unsupervised approaches. We begin by outlining the most common video degradations and their underlying causes, followed by a review of early conventional and deep learning methods-based, highlighting their strengths and limitations. We then present an in-depth overview of unsupervised methods, categorise by their fundamental approaches, including domain translation, self-supervision signal design and blind spot or noise-based methods. We also provide a categorization of loss functions employed in unsupervised video restoration and enhancement, and discuss the role of paired synthetic datasets in enabling objective evaluation. Finally, we identify key challenges and outline promising directions for future research in this field.

Although image denoising algorithms have attracted significant research attention, surprisingly few have been proposed for, or evaluated on, noise from imagery acquired under real low-light conditions. Moreover, noise characteristics are often assumed to be spatially invariant, leading to edges and textures being distorted after denoising. Here, we introduce a novel topological loss function which is based on persistent homology. The method performs in the space of image patches, where topological invariants are calculated and represented in persistent diagrams. The loss function is a combination of $\ell_1$ or $\ell_2$ losses with the new persistence-based topological loss. We compare its performance across popular denoising architectures and loss functions, training the networks on our new comprehensive dataset of natural images captured in low-light conditions -- BVI-LOWLIGHT. Analysis reveals that this approach outperforms existing methods, adapting well to complex structures and suppressing common artifacts.

Despite extensive research conducted in the field of image denoising, many algorithms still heavily depend on supervised learning and their effectiveness primarily relies on the quality and diversity of training data. It is widely assumed that digital image distortions are caused by spatially invariant Additive White Gaussian Noise (AWGN). However, the analysis of real-world data suggests that this assumption is invalid. Therefore, this paper tackles image corruption by real noise, providing a framework to capture and utilise the underlying structural information of an image along with the spatial information conventionally used for deep learning tasks. We propose a novel denoising loss function that incorporates topological invariants and is informed by textural information extracted from the image wavelet domain. The effectiveness of this proposed method was evaluated by training state-of-the-art denoising models on the BVI-Lowlight dataset, which features a wide range of real noise distortions. Adding a topological term to common loss functions leads to a significant increase in the LPIPS (Learned Perceptual Image Patch Similarity) metric, with the improvement reaching up to 25\%. The results indicate that the proposed loss function enables neural networks to learn noise characteristics better. We demonstrate that they can consequently extract the topological features of noise-free images, resulting in enhanced contrast and preserved textural information.