Adaptive direction-guided structure tensor total variation

Demircan-Tureyen, Ezgi; Kamasak, Mustafa E.

doi:10.1016/j.image.2021.116497

Cited by 3 publications

(6 citation statements)

References 36 publications

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“…The following subsection starts with the explanation of the proposed regularizer. Since we used the term adaptive direction-guided STV (ADSTV) in [9] to refer the extended version of DSTV [8], which gained the ability of handling multi-directional images, the regularization term that we propose here will be called as nonlocal ADSTV (NLADSTV).…”

Section: Methodsmentioning

confidence: 99%

“…This neighborhood-awareness provides a better representation of the local image variations, and significantly boosts the performance. Recently in [8,9], we have shown that penalizing the summary of the directional gradients within a patch instead of the gradients increases the performance as long as the local directions are accurately estimated. In this paper, we design a nonlocal counterpart to our prior direction-guided regularizer, under the influence of the nonlocal STV (NLSTV [14]), so that the long-distance dependencies across the image can also be modelled.…”

Section: Introductionmentioning

confidence: 99%

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Nonlocal Adaptive Direction-Guided Structure Tensor Total Variation For Image Recovery

Demircan-Tureyen¹,

Kamasak²

2020

Preprint

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A common strategy in variational image recovery is utilizing the nonlocal self-similarity (NSS) property, when designing energy functionals. One such contribution is nonlocal structure tensor total variation (NLSTV), which lies at the core of this study. This paper is concerned with boosting the NLSTV regularization term through the use of directional priors. More specifically, NLSTV is leveraged so that, at each image point, it gains more sensitivity in the direction that is presumed to have the minimum local variation. The actual difficulty here is capturing this directional information from the corrupted image. In this regard, we propose a method that employs anisotropic Gaussian kernels to estimate directional features to be later used by our proposed model. The experiments validate that our entire two-stage framework achieves better results than the NLSTV model and two other competing local models, in terms of visual and quantitative evaluation.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Nonlocal Adaptive Direction-Guided Structure Tensor Total Variation For Image Recovery

Demircan-Tureyen¹,

Kamasak²

2020

Preprint

Self Cite

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“…In this section, we enrich the statistical and analytical study of the space-adaptive regularisers introduced in the previous sections by providing some insights helpful to understand their local behaviour from a geometrical point of view. To do so, we unify and expand some considerations from [6,83,112,50] and start recalling the dual definition of TV:…”

Section: Geometrical Interpretationmentioning

confidence: 99%

“…By this definition we can thus write the directional formulation of TV firstly used in [6] and later applied in several other works (see, e.g., [133,83,50]) for promoting TV smoothness along v. Note that the (WDTV sv p ) reduces to this definition by choosing…”

Section: Geometrical Interpretationmentioning

confidence: 99%

“…This choice, however, is very sensitive to noise oscillations and it may misguide the local directional behaviour if these are too large. Alternatively, as considered in [65,58,54,93] and more recently in [109,50], the dependence on the image to retrieve can be encoded explicitly in the definition of the regularisation by allowing θ i to be a function of the target image u (i.e. θ i = θ i (u)) using, for instance, information coming from the structure tensor.…”

Section: Geometrical Interpretationmentioning

confidence: 99%

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On and beyond Total Variation regularisation in imaging: the role of space variance

Pragliola¹,

Calatroni²,

Lanza³

et al. 2021

Preprint

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Over the last 30 years a plethora of variational regularisation models for image reconstruction has been proposed and thoroughly inspected by the applied mathematics community. Among them, the pioneering prototype often taught and learned in basic courses in mathematical image processing is the celebrated Rudin-Osher-Fatemi (ROF) model [118] which relies on the minimisation of the edge-preserving Total Variation (TV) semi-norm as regularisation term. Despite its (often limiting) simplicity, this model is still very much employed in many applications and used as a benchmark for assessing the performance of modern learning-based image reconstruction approaches, thanks to its thorough analytical and numerical understanding. Among the many extensions to TV proposed over the years, a large class is based on the concept of space variance. Space-variant models can indeed overcome the intrinsic inability of TV to describe local features (strength, sharpness, directionality) by means of an adaptive mathematical modelling which accommodates local regularisation weighting, variable smoothness and anisotropy. Those ideas can further be cast in the flexible Bayesian framework of generalised Gaussian distributions and combined with maximum likelihood and hierarchical optimisation approaches for efficient hyper-parameter estimation. In this work, we review and connect the major contributions in the field of space-variant TV-type image reconstruction models, focusing, in particular, on their Bayesian interpretation which paves the way to new exciting and unexplored research directions.

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Restoring Fluorescence Microscopy Images by Transfer Learning From Tailored Data

Demircan-Tureyen

Akbulut²,

Kamasak

2022

IEEE Access

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Adaptive direction-guided structure tensor total variation

Cited by 3 publications

References 36 publications

Nonlocal Adaptive Direction-Guided Structure Tensor Total Variation For Image Recovery

Nonlocal Adaptive Direction-Guided Structure Tensor Total Variation For Image Recovery

On and beyond Total Variation regularisation in imaging: the role of space variance

Restoring Fluorescence Microscopy Images by Transfer Learning From Tailored Data

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