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Method for fractional order original duality for image noise elimination

A primitive dual, fractional-order technology, applied in the field of fractional-order primitive dual algorithm, can solve problems such as slow convergence speed, and achieve the effect of ensuring convergence, improving visual effects, and being easy to implement.

Inactive Publication Date: 2014-04-30
SHENYANG UNIV
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Problems solved by technology

The above methods have a certain influence in this field, and can effectively improve the visual effect of the image to varying degrees, but the numerical calculation methods used to solve the model all have the problem of slow convergence speed

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  • Method for fractional order original duality for image noise elimination
  • Method for fractional order original duality for image noise elimination
  • Method for fractional order original duality for image noise elimination

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Embodiment Construction

[0046] Below in conjunction with embodiment, the present invention is described in further detail.

[0047] First, combining the fractional-order calculus theory and dual theory, the fractional-order ROF model is equivalently transformed, and a fractional-order primal-dual denoising model is proposed.

[0048] Definition 1: For any , Represents a finite-dimensional vector space, and the discrete form of fractional divergence can be defined as:

[0049] , (10)

[0050] In the formula,

[0051] (11)

[0052] The fractional regularization term in the fractional ROF model can be equivalently transformed as follows,

[0053] (12)

[0054] if and only if .

[0055] Accordingly, the present invention proposes a fractional order primal dual denoising model, expressed as:

[0056] (13)

[0057] In the formula, represents a dual space. is a function in the dual space, that is, the topologi...

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Abstract

The invention discloses a method for fractional order original duality for image noise elimination and relates to a method for image noise elimination. A fractional order original dual noise elimination model and a fractional order original dual numerical algorithm are adopted in the method. The method is characterized in that the fractional order original dual noise elimination model refers to an original dual description of a fractional order ROF noise elimination model, and an expression is shown in a specification. The resolvent fractional order original dual numerical algorithm is adopted in numerical calculation of the model and the defects that certain traditional numerical algorithms are extremely high in requirement for the step size are overcome through self-adaption variable step size iteration of the algorithm. Experimental results show that the visual effect of an image can be effectively improved by the fractional order original dual noise elimination model and the raised fractional order original dual numerical algorithm can conduct effective rapid convergence.

Description

technical field [0001] The invention relates to a fractional primordial dual model for improving image visual effects, in particular to a fractional primal dual algorithm for image denoising. Background technique [0002] Image denoising is one of the important research topics in the field of digital image processing. Its main purpose is to improve the image quality and facilitate the follow-up work of image processing. At present, one of the research hotspots and difficulties in this field is that both image noise and edges are high-frequency information in the image. How to find a denoising method that can effectively eliminate noise while retaining details such as image edges. In order to solve this problem, in 1992 Rudin et al. proposed the famous full variation regularization model, also known as the ROF model. The model transforms the image denoising problem into a functional extremum problem by introducing an energy function. The adopted function space allows jumpin...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06T5/00
Inventor 田丹韩晓微
Owner SHENYANG UNIV
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