Estimation of the Optimal Variational Parameter via SNR Analysis

Gilboa, Guy; Sochen, Nir; Zeevi, Yehoshua Y.

doi:10.1007/11408031_20

Cited by 7 publications

(5 citation statements)

References 11 publications

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“…We mention that alternative approaches for selecting λ is the method proposed by Gilboa-Sochen-Zeevi [20], where the authors choose λ in an optimal way, by maximizing an estimate of the SNR or by minimizing the correlation between u and f − u.…”

Section: Numerical Results For Image Restorationmentioning

confidence: 99%

Image Restoration and Decomposition via Bounded Total Variation and Negative Hilbert-Sobolev Spaces

Lieu

Vese

2008

Appl Math Optim

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We propose a new class of models for image restoration and decomposition by functional minimization. Following ideas of Y. Meyer in a total variation minimization framework of L. Rudin, S. Osher, and E. Fatemi, our model decomposes a given (degraded or textured) image u 0 into a sum u + v. Here u ∈ BV is a function of bounded variation (a cartoon component), while the noisy (or textured) component v is modeled by tempered distributions belonging to the negative Hilbert-Sobolev space H −s . The proposed models can be seen as generalizations of a model proposed by S. Osher, A. Solé, L. Vese and have been also motivated by D. Mumford and B. Gidas. We present existence, uniqueness and two characterizations of minimizers using duality and the notion of convex functions of measures with linear growth, following I. Ekeland and R. Temam, F. Demengel and R. Temam. We also give a numerical algorithm for solving the minimization problem, and we present numerical results of denoising, deblurring, and decompositions of both synthetic and real images.

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Section: Numerical Results For Image Restorationmentioning

confidence: 99%

Image Restoration and Decomposition via Bounded Total Variation and Negative Hilbert-Sobolev Spaces

Lieu

Vese

2008

Appl Math Optim

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“…For inverse problems, L-curve criteria have been suggested by Hansen [205]. More heuristic based type stopping criteria have been suggested for instance in [31,181,282], to mention a few recent publications.…”

Section: Recent Topics On Denoising With Variational Methodsmentioning

confidence: 99%

Variational Methods in Imaging

Scherzer¹,

Grasmair²,

Grossauer³

et al. 2009

Applied Mathematical Sciences

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“…Whereas cartoon-type images reach their peak SNR at high denoising levels ( ), noncartoon images degrade faster and require less denoising . For deeper analysis and some bounds on the resulting SNR of process denoising, see [13] and [14].…”

Section: A Automatic Texture Preserving Denoisingmentioning

confidence: 99%

Variational denoising of partly textured images by spatially varying constraints

Gilboa

Sochen

Zeevi

2006

IEEE Trans. on Image Process.

158

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Denoising algorithms based on gradient dependent regularizers, such as nonlinear diffusion processes and total variation denoising, modify images towards piecewise constant functions. Although edge sharpness and location is well preserved, important information, encoded in image features like textures or certain details, is often compromised in the process of denoising. We propose a mechanism that better preserves fine scale features in such denoising processes. A basic pyramidal structure-texture decomposition of images is presented and analyzed. A first level of this pyramid is used to isolate the noise and the relevant texture components in order to compute spatially varying constraints based on local variance measures. A variational formulation with a spatially varying fidelity term controls the extent of denoising over image regions. Our results show visual improvement as well as an increase in the signal-to-noise ratio over scalar fidelity term processes. This type of processing can be used for a variety of tasks in partial differential equation-based image processing and computer vision, and is stable and meaningful from a mathematical viewpoint.

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Estimation of the Optimal Variational Parameter via SNR Analysis

Cited by 7 publications

References 11 publications

Image Restoration and Decomposition via Bounded Total Variation and Negative Hilbert-Sobolev Spaces

Image Restoration and Decomposition via Bounded Total Variation and Negative Hilbert-Sobolev Spaces

Variational Methods in Imaging

Variational denoising of partly textured images by spatially varying constraints

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