A New Convex Optimization Model for Multiplicative Noise and Blur Removal

Zhao, Xi-Le; Wang, Fan; Ng, Michael K.

doi:10.1137/13092472x

Cited by 128 publications

(80 citation statements)

References 30 publications

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“…This could be a great advantage for real-world applications. We note finally that we have only considered additive noise in this paper, for images contaminated by multiplicative noise, some newly developed noise reduction filters, such as [22] may be applied, which can be our future work in this area. …”

Section: Discussionmentioning

confidence: 99%

A robust iterative algorithm for image restoration

Liu

2017

J Image Video Proc.

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We present a new image restoration method by combining iterative VanCittert algorithm with noise reduction modeling. Our approach enables decoupling between deblurring and denoising during the restoration process, so allows any well-established noise reduction operator to be implemented in our model, independent of the VanCittert deblurring operation. Such an approach has led to an analytic expression for error estimation of the restored images in our method as well as simple parameter setting for real applications, both of which are hard to attain in many regularization-based methods. Numerical experiments show that our method can achieve good balance between structure recovery and noise reduction, and perform close to the level of the state of the art method and favorably compared to many other methods.

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Section: Discussionmentioning

confidence: 99%

A robust iterative algorithm for image restoration

Liu

2017

J Image Video Proc.

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“…The symmetric alternating direction method with multipliers (symmetric ADMM) is an acceleration method of ADMM, which can be used to solve the constraint optimization formulation in image processing [34][35][36][37][38][39][40][41][42][43].…”

Section: Symmetric Admmmentioning

confidence: 99%

“…Many optimization methods can be applied to solve the proposed formulation (P2), such as the split Bregman method, alternating direction method with multipliers [35][36][37][38][39][40]42,43,49,50]. Here, we employ symmetric ADMM to solve (P2) due to its simplicity and efficiency [34].…”

Section: Optimization Algorithmmentioning

confidence: 99%

Double Reweighted Sparse Regression and Graph Regularization for Hyperspectral Unmixing

et al. 2018

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Hyperspectral unmixing, aiming to estimate the fractional abundances of pure spectral signatures in each mixed pixel, has attracted considerable attention in analyzing hyperspectral images. Plenty of sparse unmixing methods have been proposed in the literature that achieved promising performance. However, many of these methods overlook the latent geometrical structure of the hyperspectral data which limit their performance to some extent. To address this issue, a double reweighted sparse and graph regularized unmixing method is proposed in this paper. Specifically, a graph regularizer is employed to capture the correlation information between abundance vectors, which makes use of the property that similar pixels in a spectral neighborhood have higher probability to share similar abundances. In this way, the latent geometrical structure of the hyperspectral data can be transferred to the abundance space. In addition, a double weighted sparse regularizer is used to enhance the sparsity of endmembers and the fractional abundance maps, where one weight is introduced to promote the sparsity of endmembers as a hyperspectral image typically contains fewer endmembers compared to the overcomplete spectral library and the other weight is exploited to improve the sparsity of the abundance matrix. The weights of the double weighted sparse regularizer used for the next iteration are adaptively computed from the current abundance matrix. The experimental results on synthetic and real hyperspectral data demonstrate the superiority of our method compared with some state-of-the-art approaches.

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“…Nowadays, the TV regularization is widely extended to other fields, such as nature image restoration [42,43] and tensor completion [44]. Comparing with Tikhonov-like regularization, TV regularization has a better ability to effectively preserve sharp edges and promote piecewise smooth objects.…”

Section: Tv Regularizationmentioning

confidence: 99%

Stripe noise removal of remote sensing images by total variation regularization and group sparsity constraint

et al. 2017

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Remote sensing images have been used in many fields, such as urban planning, military, and environment monitoring, but corruption by stripe noise limits its subsequent applications. Most existing stripe noise removal (destriping) methods aim to directly estimate the clear images from the stripe images without considering the intrinsic properties of stripe noise, which causes the image structure destroyed. In this paper, we propose a new destriping method from the perspective of image decomposition, which takes the intrinsic properties of stripe noise and image characteristics into full consideration. The proposed method integrates the unidirectional total variation (TV) regularization, group sparsity regularization, and TV regularization together in an image decomposition framework. The first two terms are utilized to exploit the stripe noise properties by implementing statistical analysis, and the TV regularization is adopted to explore the spatial piecewise smooth structure of stripe-free image. Moreover, an efficient alternating minimization scheme is designed to solve the proposed model. Extensive experiments on simulated and real data demonstrate that our method outperforms several existing state-of-the-art destriping methods in terms of both quantitative and qualitative assessments.

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A New Convex Optimization Model for Multiplicative Noise and Blur Removal

Cited by 128 publications

References 30 publications

A robust iterative algorithm for image restoration

A robust iterative algorithm for image restoration

Double Reweighted Sparse Regression and Graph Regularization for Hyperspectral Unmixing

Stripe noise removal of remote sensing images by total variation regularization and group sparsity constraint

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