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Image missing recovery method based on truncated Schatten p-norm

A technology for image deletion and restoration methods, which is applied in image enhancement, image data processing, instrumentation, etc., and can solve problems such as no truncated Schattenp-norm technical solutions

Active Publication Date: 2020-04-17
GUANGDONG UNIV OF PETROCHEMICAL TECH
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Problems solved by technology

[0013] Therefore, using the truncated Schatten p-norm for image restoration has a certain application prospect, but the existing technology does not apply it to image restoration, nor does it propose a technical solution for the application of truncated Schatten p-norm in image restoration

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  • Image missing recovery method based on truncated Schatten p-norm
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  • Image missing recovery method based on truncated Schatten p-norm

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Embodiment Construction

[0083] refer to figure 1 , the concrete implementation process of TSPN-MC of the present invention is as follows:

[0084] Step 1, for the matrix X∈R to be restored m×n , and its matrix filling optimization model is

[0085]

[0086] where rank(·) represents the rank of the matrix, is the location coordinate set of known data, [P Ω (X)] ij is a sampling operator whose expression is

[0087] Step 2, use the truncated Schatten p-norm instead of the rank function to constrain the low rank of the matrix, and its model is

[0088]

[0089] where σ( ) is a singular value, A∈R r×m , B ∈ R r×n , AA=I r×r ,BB=I r×r , 0<p≤1.

[0090] Step 3, using the idea of ​​function expansion, transform the above non-convex optimization model into a convex optimization model:

[0091]

[0092] where ω i =p(1-σ i (B A))(σ i (X k )) p-1 .

[0093] First, make Then its derivative with respect to σ(X) is

[0094]

[0095] thereby,

[0096] Then, the first-order Tayl...

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Abstract

The invention discloses an image missing recovery method based on truncated Schatten p-norm, and mainly relates to the problems of matrix filling and low-rank sparse decomposition. The characteristicsand advantages of the truncation norm and the Schatten p-norm are combined, and the value of p (0 < p < = 1) is adjusted, so that the flexibility of the model and the effectiveness of the model in practical problem application are enhanced. When the model is solved, the non-convex optimization model is converted into the convex optimization model by utilizing function expansion. And then, solvingthe optimization model by applying a two-step iterative algorithm based on an alternating direction multiplier method (ADMM). The invention also provides a convergence proof of the algorithm. Compared with an existing recovery method, the method has higher recovery accuracy.

Description

technical field [0001] The invention belongs to the technical field of matrix restoration, in particular to an image loss restoration method based on truncated Schatten p-norm. Background technique [0002] In practical problems, the signal is often missing or polluted by noise, and at the same time, the signal to be restored usually appears in the form of a matrix, and is of low rank or approximately low rank. Based on this, people put forward the theory of low rank matrix recovery (Lowrankmatrix recovery), which realizes the recovery of signal loss through matrix recovery. [0003] Matrix completion is a special case of matrix restoration, and its purpose is how to complete an incomplete matrix based on existing information. It has good applications in image restoration, video denoising and recommendation systems. Taking the typical NetflixPrize problem as an example, based on the user's evaluation of some movies, infer how much they like other movies, and then recommend...

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06T5/00
CPCG06T5/77Y02T10/40
Inventor 曹飞龙张清华
Owner GUANGDONG UNIV OF PETROCHEMICAL TECH
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