You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
Recent advances in photographic sensing technologies have made it possible to achieve light detection in terms of a single photon. Photon counting sensors are being increasingly used in many diverse applications. We address the problem of jointly recovering spatial and temporal scene radiance from very few photon counts. Our ConvNet-based scheme effectively combines spatial and temporal information present in measurements to reduce noise. We demonstrate that using our method one can acquire videos at a high frame rate and still achieve good quality signal-to-noise ratio. Experiments show that the proposed scheme performs quite well in different challenging scenarios while the existing approaches are unable to handle them.

Cited Abstract(s):
[1]: Image denoising is a central problem in image processing and it is often a necessary step prior to higher level analysis such as segmentation, reconstruction, or super-resolution. The nonlocal means (NL-means) perform denoising by exploiting the natural redundancy of patterns inside an image; they perform a weighted average of pixels whose neighborhoods (patches) are close to each other. This reduces significantly the noise while preserving most of the image content. While it performs well on flat areas and textures, it suffers from two opposite drawbacks: it might over-smooth low-contrasted areas or leave a residual noise around edges and singular structures. Denoising can also be performed by total variation minimization-the Rudin, Osher and Fatemi model-which leads to restore regular images, but it is prone to over-smooth textures, staircasing effects, and contrast losses. We introduce in this paper a variational approach that corrects the over-smoothing and reduces the residual noise of the NL-means by adaptively regularizing nonlocal methods with the total variation. The proposed regularized NL-means algorithm combines these methods and reduces both of their respective defaults by minimizing an adaptive total variation with a nonlocal data fidelity term. Besides, this model adapts to different noise statistics and a fast solution can be obtained in the general case of the exponential family. We develop this model for image denoising and we adapt it to video denoising with 3D patches.

[2]: We propose an effective video denoising method based on highly sparse signal representation in local 3D transform domain. A noisy video is processed in blockwise manner and for each processed block we form a 3D data array that we call “group” by stacking together blocks found similar to the currently processed one. This grouping is realized as a spatio-temporal predictive-search block-matching, similar to techniques used for motion estimation. Each formed 3D group is filtered by a 3D transform-domain shrinkage (hard-thresholding and Wiener filtering), the result of which are estimates of all grouped blocks. This filtering — that we term “collaborative filtering” — exploits the correlation between grouped blocks and the corresponding highly sparse representation of the true signal in the transform domain. Since, in general, the obtained block estimates are mutually overlapping, we aggregate them by a weighted average in order to form a non-redundant estimate of the video. Significant improvement of this approach is achieved by using a two-step algorithm where an intermediate estimate is produced by grouping and collaborative hard-thresholding and then used both for improving the grouping and for applying collaborative empirical Wiener filtering. We develop an efficient realization of this video denoising algorithm. The experimental results show that at reasonable computational cost it achieves state-of-the-art denoising performance in terms of both peak signal-to-noise ratio and subjective visual quality.

[3]: This paper presents a new patch-based video restoration scheme. By grouping similar patches in the spatiotemporal domain, we formulate the video restoration problem as a joint sparse and low-rank matrix approximation problem. The resulting nuclear norm and @math norm related minimization problem can also be efficiently solved by many recently developed numerical methods. The effectiveness of the proposed video restoration scheme is illustrated on two applications: video denoising in the presence of random-valued noise, and video in-painting for archived films. The numerical experiments indicate that the proposed video restoration method compares favorably against many existing algorithms.

[4]: The ability to generate intermediate frames between two given images in a video sequence is an essential task for video restoration and video post-processing. In addition, restoration requires robust denoising algorithms, must handle corrupted frames and recover from impaired frames accordingly. In this paper we present a unified framework for all these tasks. In our approach we use a variant of the TV-L1 denoising algorithm that operates on image sequences in a space-time volume. The temporal derivative is modified to take the pixels' movement into account. In order to steer the temporal gradient in the desired direction we utilize optical flow to estimate the velocity vectors between consecutive frames. We demonstrate our approach on impaired movie sequences as well as on benchmark datasets where the ground-truth is known.

[5]: In this paper, we consider denoising of image sequences that are corrupted by zero-mean additive white Gaussian noise. Relative to single image denoising techniques, denoising of sequences aims to also utilize the temporal dimension. This assists in getting both faster algorithms and better output quality. This paper focuses on utilizing sparse and redundant representations for image sequence denoising. In the single image setting, the K-SVD algorithm is used to train a sparsifying dictionary for the corrupted image. This paper generalizes the above algorithm by offering several extensions: i) the atoms used are 3-D; ii) the dictionary is propagated from one frame to the next, reducing the number of required iterations; and iii) averaging is done on patches in both spatial and temporal neighboring locations. These modifications lead to substantial benefits in complexity and denoising performance, compared to simply running the single image algorithm sequentially. The algorithm's performance is experimentally compared to several state-of-the-art algorithms, demonstrating comparable or favorable results.

[6]: Although the recent advances in the sparse representations of images have achieved outstanding denosing results, removing real, structured noise in digital videos remains a challenging problem. We show the utility of reliable motion estimation to establish temporal correspondence across frames in order to achieve high-quality video denoising. In this paper, we propose an adaptive video denosing framework that integrates robust optical flow into a nonlocal means (NLM) framework with noise level estimation. The spatial regularization in optical flow is the key to ensure temporal coherence in removing structured noise. Furthermore, we introduce approximate K-nearest neighbor matching to significantly reduce the complexity of classical NLM methods. Experimental results show that our system is comparable with the state of the art in removing AWGN, and significantly outperforms the state of the art in removing real, structured noise.

[7]: Most existing video denoising algorithms assume a single statistical model of image noise, e.g. additive Gaussian white noise, which often is violated in practice. In this paper, we present a new patch-based video denoising algorithm capable of removing serious mixed noise from the video data. By grouping similar patches in both spatial and temporal domain, we formulate the problem of removing mixed noise as a low-rank matrix completion problem, which leads to a denoising scheme without strong assumptions on the statistical properties of noise. The resulting nuclear norm related minimization problem can be efficiently solved by many recently developed methods. The robustness and effectiveness of our proposed denoising algorithm on removing mixed noise, e.g. heavy Gaussian noise mixed with impulsive noise, is validated in the experiments and our proposed approach compares favorably against some existing video denoising algorithms.

[8]: We propose a powerful video filtering algorithm that exploits temporal and spatial redundancy characterizing natural video sequences. The algorithm implements the paradigm of nonlocal grouping and collaborative filtering, where a higher dimensional transform-domain representation of the observations is leveraged to enforce sparsity, and thus regularize the data: 3-D spatiotemporal volumes are constructed by tracking blocks along trajectories defined by the motion vectors. Mutually similar volumes are then grouped together by stacking them along an additional fourth dimension, thus producing a 4-D structure, termed group, where different types of data correlation exist along the different dimensions: local correlation along the two dimensions of the blocks, temporal correlation along the motion trajectories, and nonlocal spatial correlation (i.e., self-similarity) along the fourth dimension of the group. Collaborative filtering is then realized by transforming each group through a decorrelating 4-D separable transform and then by shrinkage and inverse transformation. In this way, the collaborative filtering provides estimates for each volume stacked in the group, which are then returned and adaptively aggregated to their original positions in the video. The proposed filtering procedure addresses several video processing applications, such as denoising, deblocking, and enhancement of both grayscale and color data. Experimental results prove the effectiveness of our method in terms of both subjective and objective visual quality, and show that it outperforms the state of the art in video denoising.

[9]: State of the art movie restoration methods either estimate motion and filter out the trajectories, or compensate the motion by an optical flow estimate and then filter out the compensated movie. Now, the motion estimation problem is ill posed. This fact is known as the aperture problem: trajectories are ambiguous since they could coincide with any promenade in the space-time isophote surface. In this paper, we try to show that, for denoising, the aperture problem can be taken advantage of. Indeed, by the aperture problem, many pixels in the neighboring frames are similar to the current pixel one wishes to denoise. Thus, denoising by an averaging process can use many more pixels than just the ones on a single trajectory. This observation leads to use for movies a recently introduced image denoising method, the NL-means algorithm. This static 3D algorithm outperforms motion compensated algorithms, as it does not lose movie details. It involves the whole movie isophote and not just a trajectory.
Video denoising has been widely studied for many years and different kinds of algorithms have been proposed. Because of the vastness of the topic, we restrict our discussion to some of the popular and recent works. When compared with applying image denoising on each frame, video denoising has an advantage because the high temporal coherence can be leveraged to make a better prediction. Consequently, denoising algorithms adopt different strategies such as non-local means [9] [1] , motion estimation [6] [4] , 3D dictionary representations [1]4 etc. [8] propose a denoising method popularly known as VBM4D and is based on the collaborative filtering scheme (VBM3D) [1]1 . They apply this filtering scheme to a stack of 3-D spatio-temporal volumes that are obtained through non-local grouping. , [1] develop a variational denoising scheme by adaptively combining nonlocal means with total variation on spatio-temporal volumes. Their method adapts to different noise levels. The authors in [1]5 propose a denoising method for the scenario of mixed noise (like Gaussian noise mixed with impulsive noise). They formulate the denoising problem as low-rank matrix completion problem. This work has been extended in [1]8 to avoid pre-detection of outliers.