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:
Numerous recent approaches attempt to remove image blur due to camera shake, either with one or multiple input images, by explicitly solving an inverse and inherently ill-posed deconvolution problem. If the photographer takes a burst of images, a modality available in virtually all modern digital cameras, we show that it is possible to combine them to get a clean sharp version. This is done without explicitly solving any blur estimation and subsequent inverse problem. The proposed algorithm is strikingly simple: it performs a weighted average in the Fourier domain, with weights depending on the Fourier spectrum magnitude. The method can be seen as a generalization of the align and average procedure, with a weighted average, motivated by hand-shake physiology and theoretically supported, taking place in the Fourier domain. The method’s rationale is that camera shake has a random nature, and therefore, each image in the burst is generally blurred differently. Experiments with real camera data, and extensive comparisons, show that the proposed Fourier burst accumulation algorithm achieves state-of-the-art results an order of magnitude faster, with simplicity for on-board implementation on camera phones. Finally, we also present experiments in real high dynamic range (HDR) scenes, showing how the method can be straightforwardly extended to HDR photography.

Cited Abstract(s):
[1]: Recovery of degraded images due to motion blurring is a challenging problem in digital imaging. Most existing techniques on blind deblurring are not capable of removing complex motion blurring from the blurred images of complex structures. One promising approach is to recover the clear image using multiple images captured for the scene. However, in practice it is observed that such a multi-frame approach can recover a high-quality clear image of the scene only after multiple blurred image frames are accurately aligned during pre-processing, which is a very challenging task even with user interactions. In this paper, by exploring the sparsity of the motion blur kernel and the clear image under certain domains, we propose an alternative iteration approach to simultaneously identify the blur kernels of given blurred images and restore a clear image. Our proposed approach is not only robust to image formation noises, but is also robust to the alignment errors among multiple images. A modified version of linearized Bregman iteration is then developed to efficiently solve the resulting minimization problem. Experiments show that our proposed algorithm is capable of accurately estimating the blur kernels of complex camera motions with minimal requirements on the accuracy of image alignment. As a result, our method is capable of automatically recovering a high-quality clear image from multiple blurred images.

[2]: This paper presents a robust algorithm to deblur two consecutively captured blurred photos from camera shaking. Previous dual motion deblurring algorithms succeeded in small and simple motion blur and are very sensitive to noise. We develop a robust feedback algorithm to perform iteratively kernel estimation and image deblurring. In kernel estimation, the stability and capability of the algorithm is greatly improved by incorporating a robust cost function and a set of kernel priors. The robust cost function serves to reject outliers and noise, while kernel priors, including sparseness and continuity, remove ambiguity and maintain kernel shape. In deblurring, we propose a novel and robust approach which takes two blurred images as input to infer the clear image. The deblurred image is then used as feedback to refine kernel estimation. Our method can successfully estimate large and complex motion blurs which cannot be handled by previous dual or single image motion deblurring algorithms. The results are shown to be significantly better than those of previous approaches.

[3]: This paper presents a robust algorithm for estimating a single latent sharp image given multiple blurry and or noisy observations. The underlying multi-image blind deconvolution problem is solved by linking all of the observations together via a Bayesian-inspired penalty function which couples the unknown latent image, blur kernels, and noise levels together in a unique way. This coupled penalty function enjoys a number of desirable properties, including a mechanism whereby the relative-concavity or shape is adapted as a function of the intrinsic quality of each blurry observation. In this way, higher quality observations may automatically contribute more to the final estimate than heavily degraded ones. The resulting algorithm, which requires no essential tuning parameters, can recover a high quality image from a set of observations containing potentially both blurry and noisy examples, without knowing a priori the degradation type of each observation. Experimental results on both synthetic and real-world test images clearly demonstrate the efficacy of the proposed method.

[4]: Blind deconvolution of motion blur is hard, but it can be made easier if multiple images are available. This observation, and an algorithm using two differently-blurred images of a scene are the subject of this paper. While this idea is not new, existing methods have so far not delivered very practical results. In practice, the PSFs corresponding to the two given images are estimated and assumed to be close to the latent motion blurs. But in actual fact, these estimated blurs are often far from the truth, for a simple reason: They often share a common, and unidentified PSF that goes unaccounted for. That is, the estimated PSFs are themselves "blurry". While this can be due to any number of other blur sources including shallow depth of field, out of focus, lens aberrations, diffraction effects, and the like, it is also a mathematical artifact of the ill-posedness of the deconvolution problem. In this paper, instead of estimating the PSFs directly and only once from the observed images, we first generate a rough estimate of the PSFs using a robust multichannel deconvolution algorithm, and then "deconvolve the PSFs" to refine the outputs. Simulated and real data experiments show that this strategy works quite well for motion blurred images, producing state of the art results.

[5]: Image deblurring to remove blur caused by camera shake has been intensively studied. Nevertheless, most methods are brittle and computationally expensive. In this paper we analyze multi-image approaches, which capture and combine multiple frames in order to make deblurring more robust and tractable. In particular, we compare the performance of two approaches: align-and-average and multi-image deconvolution. Our deconvolution is non-blind, using a blur model obtained from real camera motion as measured by a gyroscope. We show that in most situations such deconvolution outperforms align-and-average. We also show, perhaps surprisingly, that deconvolution does not benefit from increasing exposure time beyond a certain threshold. To demonstrate the effectiveness and efficiency of our method, we apply it to still-resolution imagery of natural scenes captured using a mobile camera with flexible camera control and an attached gyroscope.

[6]:
Close to our work are papers on multi-image blind deconvolution [3] [1] [2] [6] [4] . [1] the authors showed that given multiple observations, the sparsity of the image under a tight frame is a good measurement of the clearness of the recovered image. Having multiple input images improves the accuracy of identifying the motion blur kernels, reducing the illposedness of the problem. Most of these multi-image algorithms introduce cross-blur penalty functions between image pairs. However this has the problem of growing combinatorially with the number of images in the burst. This idea is extended in [3] using a Bayesian framework for coupling all the unknown blurring kernels and the latent image in a unique prior. Although this prior has numerous good mathematical properties, its optimization is very slow. The algorithm produces very good results but it may take several minutes or even hours for a typical burst of 8-10 images of several megapixels. The very recent work by Park and Levoy [5] relies on an attached gyroscope, now present in many phones and tablets, to align all the input images and to get an estimation of the blurring kernels. Then, a multi-image non-blind deconvolution algorithm is applied.