A Nonlocal Structure Tensor-Based Approach for Multicomponent Image Recovery Problems

Chierchia, Giovanni; Pustelnik, Nelly; Pesquet‐Popescu, Béatrice; Pesquet, Jean-Christophe

doi:10.1109/tip.2014.2364141

Cited by 67 publications

(47 citation statements)

References 104 publications

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“…Among the most efficient regularizer of this category is the nonlocal TV functional (NLTV) [28]. Discrete-domain extensions of NLTV for vector-valued images are studied in [17,18].…”

mentioning

confidence: 99%

Structure Tensor Total Variation

Lefkimmiatis¹,

Roussos²,

Maragos³

et al. 2015

SIAM J. Imaging Sci.

117

129

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Abstract. We introduce a novel generic energy functional that we employ to solve inverse imaging problems within a variational framework. The proposed regularization family, termed as structure tensor total variation (STV), penalizes the eigenvalues of the structure tensor and is suitable for both grayscale and vector-valued images. It generalizes several existing variational penalties, including the total variation seminorm and vectorial extensions of it. Meanwhile, thanks to the structure tensor's ability to capture first-order information around a local neighborhood, the STV functionals can provide more robust measures of image variation. Further, we prove that the STV regularizers are convex while they also satisfy several invariance properties w.r.t. image transformations. These properties qualify them as ideal candidates for imaging applications. In addition, for the discrete version of the STV functionals we derive an equivalent definition that is based on the patch-based Jacobian operator, a novel linear operator which extends the Jacobian matrix. This alternative definition allow us to derive a dual problem formulation. The duality of the problem paves the way for employing robust tools from convex optimization and enables us to design an efficient and parallelizable optimization algorithm. Finally, we present extensive experiments on various inverse imaging problems, where we compare our regularizers with other competing regularization approaches. Our results are shown to be systematically superior, both quantitatively and visually.

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“…Among the most efficient regularizer of this category is the nonlocal TV functional (NLTV) [28]. Discrete-domain extensions of NLTV for vector-valued images are studied in [17,18].…”

mentioning

confidence: 99%

Structure Tensor Total Variation

Lefkimmiatis¹,

Roussos²,

Maragos³

et al. 2015

SIAM J. Imaging Sci.

117

129

View full text Add to dashboard Cite

show abstract

“…In this case, R is the 1 norm, and Ψ is a frame analysis operator, e.g., wavelet [30] and curvelet [31]. More involved regularization, such as nonlocal regularization [32]- [34], regularization using learned operators [35], [36] and plug-and-play regularization [37], [38], can also be handled in our formulation by setting Ψ to the corresponding nonlocal/learned analysis operator.…”

Section: Problem Formulationmentioning

confidence: 99%

Image Restoration with Multiple Hard Constraints on Data-Fidelity to Blurred/Noisy Image Pair

Takeyama¹,

Ono

Kumazawa

2017

IEICE Trans. Inf. & Syst.

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SUMMARYExisting image deblurring methods with a blurred/noisy image pair take a two-step approach: blur kernel estimation and image restoration. They can achieve better and much more stable blur kernel estimation than single image deblurring methods. On the other hand, in the image restoration step, they do not exploit the information on the noisy image, or they require ad hoc tuning of interdependent parameters. This paper focuses on the image restoration step and proposes a new restoration method of using a blurred/noisy image pair. In our method, the image restoration problem is formulated as a constrained convex optimization problem, where data-fidelity to a blurred image and that to a noisy image is properly taken into account as multiple hard constraints. This offers (i) high quality restoration when the blurred image also contains noise; (ii) robustness to the estimation error of the blur kernel; and (iii) easy parameter setting. We also provide an efficient algorithm for solving our optimization problem based on the so-called alternating direction method of multipliers (ADMM). Experimental results support our claims.

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“…Shu et al proposed the NLCS algorithm [17] and tried to group similar patches through NLS (nonlocal sparsity) regularization. The authors in [19] proposed a nonlocal total variation structure tensor (ST-NLTV) regularization approach for multicomponent image recovery from degraded observations, leading to significant improvements in terms of convergence speed over state-of-the-art methods such as the Alternating Direction Method of Multipliers (ADMM). Dong et al proposed the nonlocal low-rank regularization (NLR-CS) method [20] which explored the structured sparsity of the image patches for compressed sensing.…”

Section: B Other Related Workmentioning

confidence: 99%

A Douglas–Rachford Splitting Approach to Compressed Sensing Image Recovery Using Low-Rank Regularization

2015

IEEE Trans. on Image Process.

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In this paper, we study the compressed sensing (CS) image recovery problem. The traditional method divides the image into blocks and treats each block as an independent sub-CS recovery task. This often results in losing global structure of an image. In order to improve the CS recovery result, we propose a nonlocal (NL) estimation step after the initial CS recovery for denoising purpose. The NL estimation is based on the well-known NL means filtering that takes an advantage of self-similarity in images. We formulate the NL estimation as the low-rank matrix approximation problem, where the low-rank matrix is formed by the NL similarity patches. An efficient algorithm, nonlocal Douglas-Rachford (NLDR), based on Douglas-Rachford splitting is developed to solve this low-rank optimization problem constrained by the CS measurements. Experimental results demonstrate that the proposed NLDR algorithm achieves significant performance improvements over the state-of-the-art in CS image recovery.

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A Nonlocal Structure Tensor-Based Approach for Multicomponent Image Recovery Problems

Cited by 67 publications

References 104 publications

Structure Tensor Total Variation

Structure Tensor Total Variation

Image Restoration with Multiple Hard Constraints on Data-Fidelity to Blurred/Noisy Image Pair

A Douglas–Rachford Splitting Approach to Compressed Sensing Image Recovery Using Low-Rank Regularization

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