On convergent finite difference schemes for variational–PDE-based image processing

Prasath, V. B. Surya; Moreno, Juan Carlos

doi:10.1007/s40314-016-0414-9

Cited by 9 publications

(7 citation statements)

References 55 publications

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“…The matrix A l = (a ijl ) ij corresponds to derivatives along the l-th coordinate axis. Note that this involves solving a linear system where the system matrix is tridiagonal and diagonally dominant, see [74,59] for more details. To avoid the directional (x-y axis) smoothing bias we adapted a multi-direction based modification [58] , and to be fair the same approach was used to compare all the PDEs here.…”

Section: Resultsmentioning

confidence: 99%

“…We do not use a notation for partial time derivative since we treat (59) as an ODE in a Banach space.…”

Section: Proof Of Theoremmentioning

confidence: 99%

“…The existence of solutions to (81) in class (60) is similar to the existence of solutions to (59) in the previous subsection. Note that, since condition (45) is violated in the logarithmic case, we do not work directly with (59). However, the a priori bounds (50), (51) and…”

Section: Weak and Strong Solutionsmentioning

confidence: 99%

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Analysis of adaptive forward-backward diffusion flows with applications in image processing

Prasath¹,

Urbano²,

Vorotnikov³

2015

Inverse Problems

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The nonlinear diffusion model introduced by Perona and Malik in 1990 is well suited to preserve salient edges while restoring noisy images. This model overcomes well-known edge smearing effects of the heat equation by using a gradient dependent diffusion function. Despite providing better denoising results, the analysis of the PM scheme is difficult due to the forward-backward nature of the diffusion flow. We study a related adaptive forward-backward diffusion equation which uses a mollified inverse gradient term engrafted in the diffusion term of a general nonlinear parabolic equation. We prove a series of existence, uniqueness and regularity results for viscosity, weak and dissipative solutions for such forward-backward diffusion flows. In particular, we introduce a novel functional framework for wellposedness of flows of total variation type. A set of synthetic and real image processing examples are used to illustrate the properties and advantages of the proposed adaptive forward-backward diffusion flows.

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Section: Resultsmentioning

confidence: 99%

“…We do not use a notation for partial time derivative since we treat (59) as an ODE in a Banach space.…”

Section: Proof Of Theoremmentioning

confidence: 99%

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Analysis of adaptive forward-backward diffusion flows with applications in image processing

Prasath¹,

Urbano²,

Vorotnikov³

2015

Inverse Problems

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“…(3), called structure tensor adaptive total variation (STATV), obtains better restoration results as we will in the experimental results (Section 3). There exist many convergent numerical implementations [12] for the TV regularization that can be adapted for the ATV model considered here. However, we utilize the well-known split Bregman algorithm [8] to solve the adaptive TV regularization in Eq.…”

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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“…Fixing a parameter with these standard parameter estimation methods can still lead to poor results, since the regularization needs to be reduced in the iterative implementation. Recently data adaptive methods (Fu, Zhang, 2010, Prasath, Singh, 2010, Wang et al, 2011, Prasath, 2011, Prasath, Moreno, 2018 are found to provide better solutions, though with higher computational overhead.…”

Section: Introductionmentioning

confidence: 99%

Simres-Tv: Noise and Residual Similarity for Parameter Estimation in Total Variation

Prasath

Hiền

Thanh

et al. 2021

Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci.

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Abstract. Image restoration with regularization models is very popular in the image processing literature. Total variation (TV) is one of the important edge preserving regularization models used, however, to obtain optimal restoration results the regularization parameter needs to be set appropriately. We propose here a new parameter estimation approach for total variation based image restoration. By utilizing known noise levels we compute the regularization parameter by reducing the similarity between residual and noise variances. We use the split Bregman algorithm for the total variation along with this automatic parameter estimation step to obtain a very fast restoration scheme. Experimental results indicate the proposed parameter estimation obtained better denoised images and videos in terms of PSNR and SSIM measures and the computational overload is less compared with other approaches.

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On convergent finite difference schemes for variational–PDE-based image processing

Cited by 9 publications

References 55 publications

Analysis of adaptive forward-backward diffusion flows with applications in image processing

Analysis of adaptive forward-backward diffusion flows with applications in image processing

Structure tensor adaptive total variation for image restoration

Simres-Tv: Noise and Residual Similarity for Parameter Estimation in Total Variation

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