Directional Total Generalized Variation Regularization for Impulse Noise Removal

Kongskov, Rasmus Dalgas; Dong, Yiqiu

doi:10.1007/978-3-319-58771-4_18

Cited by 17 publications

(23 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Similar versions of the directional total variation have been used before [17,19,29] and it is related to other anisotropic priors [14,30,31] and the notion of parallel level sets [32][33][34]. Note that the directional total variation generalizes the usual total variation (7) for ξ = 0 and other versions of the directional total variation [35,36] where the direction ξ is constant and not depending in the pixel location i. With the isotropic choice P i = w i I, 0 ≤ w i ≤ 1 it reduces to weighted total variation [18,29,[37][38][39].…”

Section: Image Regularizationmentioning

confidence: 92%

Blind image fusion for hyperspectral imaging with the directional total variation

et al. 2018

View full text Add to dashboard Cite

Hyperspectral imaging is a cutting-edge type of remote sensing used for mapping vegetation properties, rock minerals and other materials. A major drawback of hyperspectral imaging devices is their intrinsic low spatial resolution. In this paper, we propose a method for increasing the spatial resolution of a hyperspectral image by fusing it with an image of higher spatial resolution that was obtained with a different imaging modality. This is accomplished by solving a variational problem in which the regularization functional is the directional total variation. To accommodate for possible mis-registrations between the two images, we consider a non-convex blind super-resolution problem where both a fused image and the corresponding convolution kernel are estimated. Using this approach, our model can realign the given images if needed. Our experimental results indicate that the non-convexity is negligible in practice and that reliable solutions can be computed using a variety of different optimization algorithms. Numerical results on real remote sensing data from plant sciences and urban monitoring show the potential of the proposed method and suggests that it is robust with respect to the regularization parameters, mis-registration and the shape of the kernel.AMS classification scheme numbers: 49M37, 65K10, 90C30, 90C90 PACS numbers: 42.30. Va, 42.68.Wt, 95.75.Pq, 95.75.Rs Figure 1. Three example data for image fusion in remote sensing. They each consist of a hyperspectral image (small image, only one channel shown) and an image of higher spatial resolution (large image). The goal is to create an image that has both high spatial and high spectral resolution.

show abstract

Section: Image Regularizationmentioning

confidence: 92%

Blind image fusion for hyperspectral imaging with the directional total variation

et al. 2018

View full text Add to dashboard Cite

show abstract

“…, (ω m,1 , ω m,2 ) ∈ R 2 \ πZ 2 ∪ {0}. Figure 2: Elements from the kernel of discrete oscillation TGV according to (24) for the choice ω 1 = sin( kπ 8 ), ω 2 = cos( kπ 8 ) and c according to (38) and constants C 1 = C 2 = 1.…”

Section: Discrete Kernel Representationmentioning

confidence: 99%

“…There, one can see that the restored images with 4 and 6 directions lose some textures, whereas the majority of textures is recovered using 8, 10 and 12 directions. Hence, the choice of 8 directions in (38) indeed offers a good balance between performance and complexity of the model.…”

Section: Cartoon/texture Decomposition and Image Denoisingmentioning

confidence: 99%

“…Disadvantages are, of course, the bias of this regularization approach towards certain directions and the fact that we cannot expect to recover texture that is not composed of different line structures. In [38], Kongskov and Dong proposed a new directional total generalized variation (DTGV) functional to capture the directional information of an image, which can be considered as a special case of ICTGV.Another approach to decompose an image is to compute sparse representations based on dictionaries. The basic idea is to find two suitable dictionaries, one adapted to represent textures, and the other to represent the cartoon part.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Infimal Convolution of Oscillation Total Generalized Variation for the Recovery of Images with Structured Texture

Gao¹,

Bredies²

2018

SIAM J. Imaging Sci.

View full text Add to dashboard Cite

We propose a new type of regularization functional for images called oscillation total generalized variation (TGV) which can represent structured textures with oscillatory character in a specified direction and scale. The infimal convolution of oscillation TGV with respect to several directions and scales is then used to model images with structured oscillatory texture. Such functionals constitute a regularizer with good texture preservation properties and can flexibly be incorporated into many imaging problems. We give a detailed theoretical analysis of the infimal-convolution-type model with oscillation TGV in function spaces. Furthermore, we consider appropriate discretizations of these functionals and introduce a first-order primaldual algorithm for solving general variational imaging problems associated with this regularizer. Finally, numerical experiments are presented which show that our proposed models can recover textures well and are competitive in comparison to existing state-of-the-art methods.Mathematics subject classification: 94A08, 68U10, 26A45, 90C90. component u belonging to BV(Ω) and a noise or small-scale texture component in L 2 (Ω). In [42], Y. Meyer pointed out some limitations of the above model and introduced a new space G(Ω) = W −1,∞ (Ω), which is larger than L 2 (Ω), to model oscillating patterns that are typical for structured texture: minwhere G(Ω) denotes the spaceand again, J(u) = Ω |Du|. In this model, u represents a piecewise constant function, consisting of homogeneous regions with sharp boundaries and is usually called cartoon component. The other part v in G(Ω) contains oscillating patterns, like textures and noise. This model can be considered as the original cartoon-texture decomposition model. However, the G-space may be difficult to handle in implementations. Vese and Osher [52] approximated the G-space by a Sobolev space of negative differentiability order W −1,p (Ω), which can, in practice, more easily be implemented by partial differential equations. Later, Aujol et al. [4] made a modification to the G-norm term in (2) which is replaced by constrainingAs a consequence, the problem can be solved alternatingly by Chambolle's projection method [23] with respect to the two variables u and v. Certainly, the aim of above models is to find an appropriate norm to describe textures. However, in general, the above norms can represent all kinds of oscillatory parts. As a consequence, since noise can be regarded as small-scale oscillating texture, these models do not deal well with noise. In order to tackle this disadvantage, in [47], Schaeffer and Osher incorporated robust principal component analysis (PCA) [22] into cartoon-texture decomposition models based on the patch method. For the texture part, the authors suggest to decompose the image into small, non-overlapping patches, written as vectors. The collection of the patch vectors is assumed to be (highly) linearly dependent and thus to have low rank. This suggests to minimize the nuclear norm of the patch-vector matrix. Howeve...

show abstract

“…Furthermore, it is not adapted to situations where clear local directional texture may appear, as it happens for instance in fiber and seismic imaging applications. For the mentioned problems the use of some dominant [26,2] or local [55] anisotropy information can strongly improve the quality of the reconstruction.…”

Section: Introductionmentioning

confidence: 99%

A Flexible Space-Variant Anisotropic Regularization for Image Restoration with Automated Parameter Selection

Calatroni¹,

Lanza²,

Pragliola³

et al. 2019

SIAM J. Imaging Sci.

View full text Add to dashboard Cite

We propose a new space-variant anisotropic regularisation term for variational image restoration, based on the statistical assumption that the gradients of the target image distribute locally according to a bivariate generalised Gaussian distribution. The highly flexible variational structure of the corresponding regulariser encodes several free parameters which hold the potential for faithfully modelling the local geometry in the image and describing local orientation preferences. For an automatic estimation of such parameters, we design a robust maximum likelihood approach and report results on its reliability on synthetic data and natural images. For the numerical solution of the corresponding image restoration model, we use an iterative algorithm based on the Alternating Direction Method of Multipliers (ADMM). A suitable preliminary variable splitting together with a novel result in multivariate non-convex proximal calculus yield a very efficient minimisation algorithm. Several numerical results showing significant quality-improvement of the proposed model with respect to some related state-of-the-art competitors are reported, in particular in terms of texture and detail preservation.

show abstract

Directional Total Generalized Variation Regularization for Impulse Noise Removal

Cited by 17 publications

References 22 publications

Blind image fusion for hyperspectral imaging with the directional total variation

Blind image fusion for hyperspectral imaging with the directional total variation

Infimal Convolution of Oscillation Total Generalized Variation for the Recovery of Images with Structured Texture

A Flexible Space-Variant Anisotropic Regularization for Image Restoration with Automated Parameter Selection

Contact Info

Product

Resources

About