Nonlinear approximation based image recovery using adaptive sparse reconstructions and iterated denoising-part II: adaptive algorithms

Guleryuz, Onur G.

doi:10.1109/tip.2005.863055

Cited by 139 publications

(116 citation statements)

References 9 publications

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“…We define a maximum a posteriori probability (MAP) estimator as the minimizer of a well-defined global penalty term. Its numerical solution leads to a simple iterated patch-by-patch sparse coding and averaging algorithm that is closely related to the ideas explored in [38]- [40] and generalizes them.…”

mentioning

confidence: 99%

Image Denoising Via Sparse and Redundant Representations Over Learned Dictionaries

Elad

Aharon

2006

IEEE Trans. on Image Process.

4,827

3,580

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Abstract-We address the image denoising problem, where zero-mean white and homogeneous Gaussian additive noise is to be removed from a given image. The approach taken is based on sparse and redundant representations over trained dictionaries. Using the K-SVD algorithm, we obtain a dictionary that describes the image content effectively. Two training options are considered: using the corrupted image itself, or training on a corpus of high-quality image database. Since the K-SVD is limited in handling small image patches, we extend its deployment to arbitrary image sizes by defining a global image prior that forces sparsity over patches in every location in the image. We show how such Bayesian treatment leads to a simple and effective denoising algorithm. This leads to a state-of-the-art denoising performance, equivalent and sometimes surpassing recently published leading alternative denoising methods.Index Terms-Bayesian reconstruction, dictionary learning, discrete cosine transform (DCT), image denoising, K-SVD, matching pursuit, maximum a posteriori (MAP) estimation, redundancy, sparse representations.

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confidence: 99%

Image Denoising Via Sparse and Redundant Representations Over Learned Dictionaries

Elad

Aharon

2006

IEEE Trans. on Image Process.

4,827

3,580

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“…Having posed the problem this way, all the above discussion on denosing and deblurring becomes relevant, and in fact leads to an effective solution of the problem. There are several algorithms proposed for the inpainting problem along the above lines, some of which adopt the global approach of handling the image as a whole [27], and others that operate on patches [33], [34], [40]. Due to their close resemblance to deblurring algorithms, we shall not dwell further on this topic, and simply show typical examples.…”

Section: Image Inpaintingmentioning

confidence: 99%

On the Role of Sparse and Redundant Representations in Image Processing

2010

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Abstract-Much of the progress made in image processing in the past decades can be attributed to better modeling of image content, and a wise deployment of these models in relevant applications. This path of models spans from the simple ℓ2-norm smoothness, through robust, thus edge preserving, measures of smoothness (e.g. total variation), and till the very recent models that employ sparse and redundant representations. In this paper, we review the role of this recent model in image processing, its rationale, and models related to it. As it turns out, the field of image processing is one of the main beneficiaries from the recent progress made in the theory and practice of sparse and redundant representations. We discuss ways to employ these tools for various image processing tasks, and present several applications in which state-of-the-art results are obtained.

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“…Again, due to the fact that (I − AA T )s is orthogonal to At for any s and t, by (36) and (37) we have…”

Section: Convergence In the Transformed Domainmentioning

confidence: 99%

“…The problem of restoration from incomplete data in the image domain is referred to as image inpainting. Many useful techniques have been proposed in recent years to address the problem, see, for examples, [1,2,22,23,34,36].…”

Section: Introductionmentioning

confidence: 99%

Simultaneously inpainting in image and transformed domains

et al. 2009

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In this paper, we focus on the restoration of images that have incomplete data in either the image domain or the transformed domain or in both. The transform used can be any orthonormal or tight frame transforms such as orthonormal wavelets, tight framelets, the discrete Fourier transform, the Gabor transform, the discrete cosine transform, and the discrete local cosine transform. We propose an iterative algorithm that can restore the incomplete data in both domains simultaneously. We prove the convergence of the algorithm and derive the optimal properties of its limit. The algorithm generalizes, unifies, and simplifies the inpainting algorithm in image domains given in [8] and the inpainting algorithms in the transformed domains given in [7,16,19]. Finally, applications of the new algorithm to super-resolution image reconstruction with different zooms are presented.

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Nonlinear approximation based image recovery using adaptive sparse reconstructions and iterated denoising-part II: adaptive algorithms

Cited by 139 publications

References 9 publications

Image Denoising Via Sparse and Redundant Representations Over Learned Dictionaries

Image Denoising Via Sparse and Redundant Representations Over Learned Dictionaries

On the Role of Sparse and Redundant Representations in Image Processing

Simultaneously inpainting in image and transformed domains

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