A Guide to the TV Zoo

Burger, Martin; Osher, Stanley

doi:10.1007/978-3-319-01712-9_1

Cited by 91 publications

(121 citation statements)

References 180 publications

(225 reference statements)

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“…In order to obtain smooth and denoised maps we employ a variant of Total-Variation (TV) smoothing for vectorial data. The basic concept of TV regularization for image denoising was originally proposed by Rudin, Osher and Fatemi with their ROF model [12], which is an an edge-preserving noise-removal method endowed with a L 2 data fidelity term [3]. Given that I Γ ∈ R 2 and the inherent shape and scale coupling, we use Vectorial Rudin-Osher-Fatemi (VROF) [2] for joint smoothing of shape and scale.…”

Section: Probabilistic Graph Distancementioning

confidence: 99%

RF Ultrasound Distribution-Based Confidence Maps

Klein

Wells

2015

Lecture Notes in Computer Science

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Abstract.Ultrasound is becoming an ever increasingly important modality in medical care. However, underlying physical acquisition principles are prone to image artifacts and result in overall quality variation. Therefore processing medical ultrasound data remains a challenging task. We propose a novel distribution-based measure of assessing the confidence in the signal, which emphasizes uncertainty in attenuated as well as shadow regions. In contrast to the similar recently proposed method that relies on image intensities, the new approach makes use of the enveloped-detected radio-frequency data, facilitating the use of Nakagami speckle statistics. Employing J-divergence as distance measure for the random-walk based algorithm, provides a natural measure of similarity, yielding a more reliable estimate of confidence. For evaluation of the model's performance, tests are conducted on the application of shadow detection. Additionally, computed maps are presented for different organs such as neck, liver and prostate, showcasing the properties of the model. The probabilistic approach is shown to have beneficial features for image processing tasks.

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Section: Probabilistic Graph Distancementioning

confidence: 99%

RF Ultrasound Distribution-Based Confidence Maps

Klein

Wells

2015

Lecture Notes in Computer Science

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“…Note that we use multi-index notation for all kernel and image spaces, that is, for instance, R m = R m1×m2 . In this work, we consider the case of super-resolution n < m. Data fidelity is measured in terms of the Euclidean / Frobenius norm x 2 2 := i x 2 i and an optimal image / kernel pair is regularized through the (directional) total variation functionals dTV v [2][3][4] and TV [5], weighted by parameters λ u , λ k > 0, respectively. Letting ∇u ∈ R m×2 denote the discrete gradient of u ∈ R m with forward differences and periodic boundary conditions, the directional total variation dTV v (u) of u with respect to a structural prior v ∈ R m is defined as…”

Section: Mathematical Modelmentioning

confidence: 99%

Robust Blind Image Fusion for Misaligned Hyperspectral Imaging Data

Bungert

Ehrhardt

Reisenhofer

2018

Proc Appl Math and Mech

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The low spatial resolution of hyperspectral imaging can be significantly improved by fusing the hyperspectral image with a high resolution photograph. In most practical cases, however, the exact alignment between the fused images is not known a priori. In this work, we study how including a blind deconvolution approach in the mathematical model can help resolve translational misalignments. In particular, we investigate the influence of different initialization strategies. The efficiency of the proposed model is validated by numerical experiments using both simulated and real remote sensing data.

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“…Moreover, we model the tracer's regularity with the total variation. 33,34 Thus, the prior function ψ becomes…”

Section: Mathematical Model For Pet Reconstructionmentioning

confidence: 99%

Faster PET reconstruction with a stochastic primal-dual hybrid gradient method

Ehrhardt

Markiewicz

Chambolle

et al. 2017

Wavelets and Sparsity XVII

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Image reconstruction in positron emission tomography (PET) is computationally challenging due to Poisson noise, constraints and potentially non-smooth priors-let alone the sheer size of the problem. An algorithm that can cope well with the first three of the aforementioned challenges is the primal-dual hybrid gradient algorithm (PDHG) studied by Chambolle and Pock in 2011. However, PDHG updates all variables in parallel and is therefore computationally demanding on the large problem sizes encountered with modern PET scanners where the number of dual variables easily exceeds 100 million. In this work, we numerically study the usage of SPDHG-a stochastic extension of PDHG-but is still guaranteed to converge to a solution of the deterministic optimization problem with similar rates as PDHG. Numerical results on a clinical data set show that by introducing randomization into PDHG, similar results as the deterministic algorithm can be achieved using only around 10 % of operator evaluations. Thus, making significant progress towards the feasibility of sophisticated mathematical models in a clinical setting.

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A Guide to the TV Zoo

Cited by 91 publications

References 180 publications

RF Ultrasound Distribution-Based Confidence Maps

RF Ultrasound Distribution-Based Confidence Maps

Robust Blind Image Fusion for Misaligned Hyperspectral Imaging Data

Faster PET reconstruction with a stochastic primal-dual hybrid gradient method

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