Multi-scale blind motion deblurring using local minimum

Wang, Chao; Sun, Lifeng; Chen, Zhuoyuan; Zhang, Jianwei

doi:10.1088/0266-5611/26/1/015003

Cited by 26 publications

(14 citation statements)

References 34 publications

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“…However, despite these additional constraints, the cost function (2) still suffers from local minima. A different approach is a strategy proposed by Wang et al [22] that seeks for the desired local minimum by using downsampled reconstructed images as priors during the optimization in a multi-scale framework. Other methods use some variants of total variation that nonetheless share similar properties.…”

Section: Prior Workmentioning

confidence: 99%

Total Variation Blind Deconvolution: The Devil Is in the Details

Perrone

Favaro

2014

2014 IEEE Conference on Computer Vision and Pattern Recognition

237

194

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In this paper we study the problem of blind deconvolution. Our analysis is based on the algorithm of Chan and Wong [2] which popularized the use of sparse gradient priors via total variation. We use this algorithm because many methods in the literature are essentially adaptations of this framework. Such algorithm is an iterative alternating energy minimization where at each step either the sharp image or the blur function are reconstructed. Recent work of Levin et al. [14] showed that any algorithm that tries to minimize that same energy would fail, as the desired solution has a higher energy than the no-blur solution, where the sharp image is the blurry input and the blur is a Dirac delta. However, experimentally one can observe that Chan and Wong's algorithm converges to the desired solution even when initialized with the no-blur one. We provide both analysis and experiments to resolve this paradoxical conundrum. We find that both claims are right. The key to understanding how this is possible lies in the details of Chan and Wong's implementation and in how seemingly harmless choices result in dramatic effects. Our analysis reveals that the delayed scaling (normalization) in the iterative step of the blur kernel is fundamental to the convergence of the algorithm. This then results in a procedure that eludes the no-blur solution, despite it being a global minimum of the original energy. We introduce an adaptation of this algorithm and show that, in spite of its extreme simplicity, it is very robust and achieves a performance comparable to the state of the art.Blind deconvolution is the problem of recovering a signal and a degradation kernel from their noisy convolution. This problem is found in diverse fields such as astronomical imaging, medical imaging, (audio) signal processing, and image processing. Yet, despite over three decades of research in the field (see [11] and references therein), the design of a principled, stable and robust algorithm that can handle real images remains a challenge. However, presentday progress has shown that recent models for sharp images and blur kernels, such as total variation [18], can yield remarkable results [7,19,4,23,13].Many of these recent approaches are evolutions of the variational formulation [26]. A common element in these methods is the explicit use of priors for both blur and sharp image to encourage smoothness in the solution. Among these recent methods, total variation emerged as one of the most popular priors [2,25]. Such popularity is probably due to its ability to encourage gradient sparsity, a property that can describe many signals of interest well [10].However, recent work by Levin et al. [14] has shown that the joint optimization of both image and blur kernel can have the no-blur solution as its global minimum. That is to say, a wide selection of prior work in blind image deconvolution either is a local minimizer and, hence, requires a lucky initial guess, or it cannot depart too much from the noblur solution. Nonetheless, several algorithms base...

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Section: Prior Workmentioning

confidence: 99%

Total Variation Blind Deconvolution: The Devil Is in the Details

Perrone

Favaro

2014

2014 IEEE Conference on Computer Vision and Pattern Recognition

237

194

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“…He et al [15] have incorporated the above constraints in a variational model, claiming that this enhances the stability of the algorithm. A different approach is a strategy proposed by Wang et al [17] that seeks for the desired local minimum by using downsampled reconstructed images as priors during the optimization in a multi-scale framework. TV regularization has been widely popularized because it models natural image gradients well [10].…”

Section: Prior Workmentioning

confidence: 99%

“…The total variation denoising algorithm (17) has been widely studied in the literature, and its analysis can give key insights on the behavior of the AM algorithm. In the next section we study this problem and present an important building block for the other results presented in the paper.…”

Section: The Alternating Minimization (Am) Algorithmmentioning

confidence: 99%

A Clearer Picture of Total Variation Blind Deconvolution

Perrone

Favaro

2016

IEEE Trans. Pattern Anal. Mach. Intell.

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Abstract-Blind deconvolution is the problem of recovering a sharp image and a blur kernel from a noisy blurry image. Recently, there has been a significant effort on understanding the basic mechanisms to solve blind deconvolution. While this effort resulted in the deployment of effective algorithms, the theoretical findings generated contrasting views on why these approaches worked. On the one hand, one could observe experimentally that alternating energy minimization algorithms converge to the desired solution. On the other hand, it has been shown that such alternating minimization algorithms should fail to converge and one should instead use a so-called Variational Bayes approach. To clarify this conundrum, recent work showed that a good image and blur prior is instead what makes a blind deconvolution algorithm work. Unfortunately, this analysis did not apply to algorithms based on total variation regularization. In this manuscript, we provide both analysis and experiments to get a clearer picture of blind deconvolution. Our analysis reveals the very reason why an algorithm based on total variation works. We also introduce an implementation of this algorithm and show that, in spite of its extreme simplicity, it is very robust and achieves a performance comparable to the top performing algorithms.Index Terms-Deblurring, blind deconvolution, total variation. !Blind deconvolution is the problem of recovering a signal and a degradation kernel from their noisy convolution. This problem is found in diverse fields such as astronomical imaging, medical imaging, (audio) signal processing, and image processing. More recently, blind deconvolution has received renewed attention due to the emerging need for removing motion blur in images captured by mobile phones [1]. Yet, despite over three decades of research in the field (see [2] and references therein), the design and analysis of a principled, stable and robust algorithm that can handle real images remains a challenge. However, present-day progress has shown that recent models for sharp images and blur kernels can yield remarkable resultsMany of these recent approaches are evolutions of the variational formulation [7]. A common element in these methods is the explicit use of priors for both blur and sharp image to encourage smoothness in the solution. Among these recent methods, total variation emerged as one of the most popular priors [8], [9]. Such popularity is probably due to its ability to encourage gradient sparsity, a property that can describe many signals of interest well [10].However, recent work by Levin et al. [11] has shown that the joint optimization of both image and blur kernel can have the no-blur solution 1 as its global minimum. That is to say, blind deconvolution algorithms that use a total variation prior either are local minimizers and, hence, require a lucky initial guess, or they cannot depart too much from the initial blurry image. Nonetheless, algorithms based on the joint optimization This incongruence called for an in-depth analysis of tota...

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“…To overcome the limitations of TV, some methods relax the global prior assumption and impose that texture statistics should change smoothly across an image [18,21]. Some methods use wavelet bases that are specifically chosen to represent a natural image [13,16].…”

Section: Prior Workmentioning

confidence: 99%

Image Priors for Image Deblurring with Uncertain Blur

Perrone¹,

Ravichandran²,

Vidal³

et al. 2012

Procedings of the British Machine Vision Conference 2012

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We consider the problem of non-blind deconvolution of images corrupted by a blur that is not accurately known. We propose a method that exploits dictionary-based image priors and non Gaussian noise models to improve deblurring accuracy in the presence of an inexact blur. The proposed image priors express each image patch as a linear combination of atoms from a dictionary learned from patches extracted from the same image or from an image database. When applied to blurred images, this model imposes that patches that are similar in the blurred image retain the same similarity when deblurred. We perform image deblurring by imposing this prior model in an energy minimization scheme that also deals with outliers. Experimental results on publicly available databases show that our approach is able to remove artifacts such as oscillations, which are often introduced during the deblurring process when the correct blur is not known.

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Multi-scale blind motion deblurring using local minimum

Cited by 26 publications

References 34 publications

Total Variation Blind Deconvolution: The Devil Is in the Details

Total Variation Blind Deconvolution: The Devil Is in the Details

A Clearer Picture of Total Variation Blind Deconvolution

Image Priors for Image Deblurring with Uncertain Blur

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