An Adaptive Diffusion Scheme for Image Restoration and Selective Smoothing

Prasath, V. B. Surya; Singh, Arindama

doi:10.1142/s0219467812500039

Cited by 15 publications

(13 citation statements)

References 34 publications

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“…Note here that we assume an additive Gaussian noise-corrupted image is given, that is, u 0 = u + n , where u 0 is the input noisy image, u is the original (unknown) true image that we are trying to find and n ∼ N (0, σ 2 n ) the normalized Gaussian noise with zero mean and σ n standard deviation. The spatially adaptive weight function ω is chosen typically as smoothed inverse gradient [7,11],…”

Section: Adaptive Total Variationmentioning

confidence: 99%

Structure tensor adaptive total variation for image restoration

Prasath¹,

Thanh²

2019

Turk J Elec Eng & Comp Sci

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Image denoising and restoration is one of the basic requirements in many digital image processing systems. Variational regularization methods are widely used for removing noise without destroying edges that are important visual cues. This paper provides an adaptive version of the total variation regularization model that incorporates structure tensor eigenvalues for better edge preservation without creating blocky artifacts associated with gradient-based approaches. Experimental results on a variety of noisy images indicate that the proposed structure tensor adaptive total variation obtains promising results and compared with other methods, gets better structure preservation and robust noise removal.

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Section: Adaptive Total Variationmentioning

confidence: 99%

Structure tensor adaptive total variation for image restoration

Prasath¹,

Thanh²

2019

Turk J Elec Eng & Comp Sci

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“…The edge maps given by these functions can inherit the traditional problems associated with gradient based functionals such as blocky artifacts [35], edge dislocations [25], corner smoothing [36], etc. To mitigate such problems we propose using the smoothed structure tensor (SST) to capture local structures,…”

Section: A Adaptive Smoothed Scale Space Structure Tensormentioning

confidence: 99%

“…To derive the PDE flow associated with the energy minimization in (9) we need to use the weight 1 p(x) , i.e., |∇u| p(x) p(x) dx, the derivation is straightforward using the Euler-Lagrange formulation [3] and is omitted here for brevity; (25) This is the p(x)-Laplacian which generalizes the traditional p-Laplacian and has been found useful in various scenarios, see the recent monograph [32]. We next turn our attention to the corresponding dynamic time-dependent version of the PDE given in (25),…”

Section: B Well-posedness Of the Pde Flowmentioning

confidence: 99%

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Multiscale Tikhonov-Total Variation Image Restoration Using Spatially Varying Edge Coherence Exponent

Prasath

Vorotnikov

Pelapur

et al. 2015

IEEE Trans. on Image Process.

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Edge preserving regularization using partial differential equation (PDE)-based methods although extensively studied and widely used for image restoration, still have limitations in adapting to local structures. We propose a spatially adaptive multiscale variable exponent-based anisotropic variational PDE method that overcomes current shortcomings, such as over smoothing and staircasing artifacts, while still retaining and enhancing edge structures across scale. Our innovative model automatically balances between Tikhonov and total variation (TV) regularization effects using scene content information by incorporating a spatially varying edge coherence exponent map constructed using the eigenvalues of the filtered structure tensor. The multiscale exponent model we develop leads to a novel restoration method that preserves edges better and provides selective denoising without generating artifacts for both additive and multiplicative noise models. Mathematical analysis of our proposed method in variable exponent space establishes the existence of a minimizer and its properties. The discretization method we use satisfies the maximum-minimum principle which guarantees that artificial edge regions are not created. Extensive experimental results using synthetic, and natural images indicate that the proposed multiscale Tikhonov-TV (MTTV) and dynamical MTTV methods perform better than many contemporary denoising algorithms in terms of several metrics, including signal-to-noise ratio improvement and structure preservation. Promising extensions to handle multiplicative noise models and multichannel imagery are also discussed.

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“…Despite its usefulness in image restoration, T V regularization is known to exhibit blocky or staircasing artifacts in solutions [47]. To avoid such artifacts various modifications has been studied in the recent years like higher order regularization [38,41] and adaptive or weighted T V regularization [64,62,56,52,57]. For example, consider the weighted T…”

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confidence: 99%

Color image processing by vectorial total variation with gradient channels coupling

Moreno¹,

Prasath²,

Neves³

2016

IPI

Self Cite

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We study a regularization method for color images based on the vectorial total variation approach along with channel coupling for color image processing, which facilitates the modeling of inter channel relations in multidimensional image data. We focus on penalizing channel gradient magnitude similarities by using L 2 differences, which allow us to explicitly couple all the channels along with a vectorial total variation regularization for edge preserving smoothing of multichannel images. By using matched gradients to align edges from different channels we obtain multichannel edge preserving smoothing and decomposition. A detailed mathematical analysis of the vectorial total variation with penalized gradient channels coupling is provided. We characterize some important properties of the minimizers of the model as well as provide geometrical results regarding the regularization parameter. We are interested in applying our model to color image processing and in particular to denoising and decomposition. A fast global minimization based on the dual formulation of the total variation is used and convergence of the iterative scheme is provided. Extensive experiments are given to show that our approach obtains good decomposition and denoising results in natural images. Comparison with previous color image decomposition and denoising methods demonstrate the advantages of our approach.

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An Adaptive Diffusion Scheme for Image Restoration and Selective Smoothing

Cited by 15 publications

References 34 publications

Structure tensor adaptive total variation for image restoration

Structure tensor adaptive total variation for image restoration

Multiscale Tikhonov-Total Variation Image Restoration Using Spatially Varying Edge Coherence Exponent

Color image processing by vectorial total variation with gradient channels coupling

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