BM3D Frames and Variational Image Deblurring

By Aram Danielyan, Vladimir Katkovnik, Karen O. Egiazarian. IEEE Transactions on Image Processing, 2011

686 citations recorded by the source corpus.

A family of the block matching 3-D (BM3D) algorithms for various imaging problems has been recently proposed within the framework of nonlocal patchwise image modeling , . In this paper, we construct analysis and synthesis frames, formalizing BM3D image modeling, and use these frames to develop novel iterative deblurring algorithms. We consider two different formulations of the deblurring problem, i.e., one given by the minimization of the single-objective function and another based on the generalized Nash equilibrium (GNE) balance of two objective functions. The latter results in the algorithm where deblurring and denoising operations are decoupled. The convergence of the developed algorithms is proved. Simulation experiments show that the decoupled algorithm derived from the GNE formulation demonstrates the best numerical and visual results and shows superiority with respect to the state of the art in the field, confirming a valuable potential of BM3D-frames as an advanced image modeling tool.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/1aef1b70d296c2991943090bf8a17fc4f7763119

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Citations in the corpus

Plug-and-Play Methods Provably Converge with Properly Trained Denoisers (2019, methodology): “(Danielyan et al., 2012; Egiazarian & Katkovnik, 2015) use the notion of Nash equilibrium to propose a scheme similar to PnP. (Danielyan et al., 2010) proposed an augmented Lagrangian method similar to PnP. (Romano et al., 2017; Reehorst & Schniter, 2019) presented Regularization by Denoising…”
Non-local Color Image Denoising with Convolutional Neural Networks (2016, background): “The non-local operator L : R 7→ RR·F described above bears strong resemblance to the BM3D analysis operator studied in [8].”
Nonlocally Centralized Sparse Representation for Image Restoration (2013, methodology): “The PSNR results for the 6 typical deblurring experiments presented in [36] and [41] are reported in Table III.”
Plug-and-Play Priors for Bright Field Electron Tomography and Sparse Interpolation (2015, methodology): “Li and Zeng [35] adapted a two stage approach similar to [36] and used the BM3D denoising algorithm for the problem of sparse image reconstruction.”
A Nonlocal Bayesian Image Denoising Algorithm (2013, background): “A very recent development of BM3D is presented in [22], [15], where it is generalized to become a generic image restoration tool, including deblurring.”
Denoising Diffusion Models for Plug-and-Play Image Restoration (2023, background): “Recent studies have demonstrated that plug-and-play Image Restoration (IR) methods can effectively handle a variety of low-level vision tasks, such as image denoising [5], image Super-Resolution (SR) [16, 17, 37], image deblurring [12] and image inpainting [27], with excellent results [6, 11, 54, 57”
Learning Proximal Operators: Using Denoising Networks for Regularizing Inverse Imaging Problems (2017, neutral): “49 IDD-BM3D [9] 24.”
Non-Local Recurrent Network for Image Restoration (2018, background): “Similar ideas are adopted for image deblurring [9].”
Denoising Prior Driven Deep Neural Network for Image Restoration (2018, methodology): “We compared the proposed method with several leading deblurring methods, i.e., three leading model-based deblurring methods (EPLL [16], IDDBM3D [7] and NCSR [8]) and the current state-of-the-art denoising-based deblurring methods with CNN denoisers [36] (denoted as DD-CNN).”
Blind Deblurring Using Internal Patch Recurrence (2014, background): “Such priors have led to state-of-the-art results in various inverse problems [16] including nonblind deblurring [3,22,4] (namely, deblurring with a known blur kernel).”
Learning Deep CNN Denoiser Prior for Image Restoration (2017, methodology): “In the following experiments, we simply plug the color denoisers into the HQS framework, whereas we separately handle each color channel for IDDBM3D and MLP. Note that MLP trained a speciﬁc model for the Gaussian blur kernel with noise level 2.”
The Little Engine That Could: Regularization by Denoising (RED) (2016, methodology): “This has been the logical path that has led to contributions such as [24, 25, 26, 27, 28, 29] and many others.”
An Analysis and Implementation of the BM3D Image Denoising Method (2012, background): “In the very recent developments of BM3D [11, 6], it is generalized to become a generic image restoration tool, including deblurring.”