Fractional derivative based nonlinear diffusion model for image denoising

Kumar, Santosh; Alam, Khursheed; Chauhan, Akshansha

doi:10.1007/s40324-021-00255-0

Cited by 5 publications

(6 citation statements)

References 22 publications

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“…We show that the {u n }converges to u in C([0, T]; L 2 (Ω)), and it is the strong solution of the Equation (4). We observed from the estimate (16). That…”

Section: Convergent Iterative Schemementioning

confidence: 72%

“…Many other researchers have introduced a different‐different approach for image restoration, i.e., total variation (TV norm) models [ 9,10,11,12 ] and nonlinear anisotropic diffusion models. [ 13,14,15,16,17,18 ]…”

Section: Introductionmentioning

confidence: 99%

“…Many other researchers have introduced a different-different approach for image restoration, i.e., total variation (TV norm) models [9,10,11,12] and nonlinear anisotropic diffusion models. [13,14,15,16,17,18] In this article, we describe a PDEs-based nonlinear diffusion model for image denoising with two different diffusivities, i.e., total variation and Charbonnier, where the diffusivities are linked to the regulariser functional. In Section 2, we propose an approach for the image denoising algorithm.…”

Section: Introductionmentioning

confidence: 99%

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A Nonlinear Hybrid Diffusion Model for Image Denoising

Alam

Kumar

Kumar³

et al. 2023

Macromolecular Symposia

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In this paper, a denoising technique is proposed based on a nonlinear anisotropic diffusion model with two diffusivities parameters, i.e., Charbonnier and total variation. These diffusivities are dependent on the diffusivity function for balancing. Furthermore, proof of the existence and uniqueness theorem of the model are presented. The convergent iterative scheme is proposed for the diffusion model. To discretize the diffusion model, the finite difference method with forward-backward diffusivities is used. The numerical results are given in terms of peak signal-to-noise ratio (PSNR) as a metric.

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“…We show that the {u n }converges to u in C([0, T]; L 2 (Ω)), and it is the strong solution of the Equation (4). We observed from the estimate (16). That…”

Section: Convergent Iterative Schemementioning

confidence: 72%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Nonlinear Hybrid Diffusion Model for Image Denoising

Alam

Kumar

Kumar³

et al. 2023

Macromolecular Symposia

Self Cite

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“…In [26], a generalized fractional derivative (G-derivative) based anisotropic diffusion equations are proposed for image denoising. A fractional generalization of diffusion model is proposed in [27]. The proposed generalization is based on a conformable based fractional derivative operator.…”

Section: Introductionmentioning

confidence: 99%

High Performance Fractional Anisotropic Diffusion Filter forPortable Applications

AbdAlRahman¹,

Al-Atabany²,

Soltan³

et al. 2023

Preprint

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Anisotropic diffusion is one of the most effective methods used in image processing. It can be used to eliminate the small textures of an imagewhile preserving its significant edges. In this paper,a new anisotropic diffusion filter is proposed based on a fractional calculus kernel rather than an integer kernel to improve the overall performance of the filter. Integer and fractional anisotropic filters are implementedusing the Genesys-2 FPGA kit to utilize the efficiency of parallelism in FPGAs. Integer and fractional anisotropic filters are tested against the achievable PSNR value vs the number of iterations. The proposed fractional anisotropic filter has a better PSNR value using a smaller number of iterations, reducing the power and area compared to integer anisotropic filter.The proposed filter can be used in image smoothing,edge detection, image segmentation, image denoisingand cartooning. In addition, the proposed filter will save the power of applications with power constraints, such as portable devices, as it requires fewer iterations than integer anisotropic filters. The proposed filter reduces the required power consumption by 58.2%.

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“…[16] utilize Equation (1) to model the behavior of returns and derive a rather general phenomenological theory in financial markets. In addition, as a foundation for more complicated diffusion modeling, Equation (1) can also be developed into variable-order model [17], distributed-order model [18], random-order model [19], nonlinear model [20], and other forms [21] for better application.…”

Section: Introductionmentioning

confidence: 99%

A Preconditioner for Galerkin–Legendre Spectral All-at-Once System from Time-Space Fractional Diffusion Equation

Wang,

Zhang

2023

Symmetry

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As a model that possesses both the potentialities of Caputo time fractional diffusion equation (Caputo-TFDE) and symmetric two-sided space fractional diffusion equation (Riesz-SFDE), time-space fractional diffusion equation (TSFDE) is widely applied in scientific and engineering fields to model anomalous diffusion phenomena including subdiffusion and superdiffusion. Due to the fact that fractional operators act on both temporal and spatial derivative terms in TSFDE, efficient solving for TSFDE is important, where the key is solving the corresponding discrete system efficiently. In this paper, we derive a Galerkin–Legendre spectral all-at-once system from the TSFDE, and then we develop a preconditioner to solve this system. Symmetry property of the coefficient matrix in this all-at-once system is destroyed so that the deduced all-at-once system is more convenient for parallel computing than the traditional timing-step scheme, and the proposed preconditioner can efficiently solve the corresponding all-at-once system from TSFDE with nonsmooth solution. Moreover, some relevant theoretical analyses are provided, and several numerical results are presented to show competitiveness of the proposed method.

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Fractional derivative based nonlinear diffusion model for image denoising

Cited by 5 publications

References 22 publications

A Nonlinear Hybrid Diffusion Model for Image Denoising

A Nonlinear Hybrid Diffusion Model for Image Denoising

High Performance Fractional Anisotropic Diffusion Filter forPortable Applications

A Preconditioner for Galerkin–Legendre Spectral All-at-Once System from Time-Space Fractional Diffusion Equation

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