Sparse model of multi-directional signal, reconstruction method of sparse model and dictionary training method of reconstruction method

A sparse model and dictionary training technology, applied in the field of sparse reconstruction of sparse representation and dictionary training, which can solve the problems of algorithm complexity and storage space contradiction, and describe the sparse representation model of tensors, so as to reduce the algorithm complexity and storage space. , the effect of reducing the complexity of the algorithm

Active Publication Date: 2016-11-09
BEIJING UNIV OF TECH
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AI Technical Summary

Problems solved by technology

However, these tensor-based methods decompose or approximate the tensor signal itself. At present, there is no unified framework to describe the tensor sparse representation model, and there are contradictions in algorithm complexity and storage space.

Method used

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  • Sparse model of multi-directional signal, reconstruction method of sparse model and dictionary training method of reconstruction method
  • Sparse model of multi-directional signal, reconstruction method of sparse model and dictionary training method of reconstruction method
  • Sparse model of multi-directional signal, reconstruction method of sparse model and dictionary training method of reconstruction method

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Embodiment Construction

[0023] The sparse model of this multi-dimensional signal is formula (1)

[0024]

[0025] where the tensor Represented as an N-dimensional sparse tensor with a series of sparse dictionaries The tensor product of I n ≤M n ,D n Defined as a dictionary in the nth direction, K is the degree of sparsity, used to describe the sparse coefficient The number of non-zero elements in .

[0026] Preferably, given a sparse dictionary The corresponding sparse model is formula (2)

[0027]

[0028] Among them, λ is used to balance fidelity and sparsity.

[0029] Preferably, the conversion to l by relaxation 1 Constrained convex programming problem, the corresponding sparse model is formula (3)

[0030]

[0031] Also provided is a method for reconstructing a sparse model of a multidimensional signal, which is an iterative shrinkage threshold method TISTA based on tensors (such as figure 1 shown), formulas (10), (11) are obtained for formulas (3) and (2)

[0032]

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Abstract

The invention discloses a sparse model of a multi-directional model, wherein the sparse model can ensure remarkable improvement on algorithm complexity and storage space without Kronecker product. The sparse model of the multi-directional model is represented by a formula x=B*1D1*2*D2...NDN, wherein ||B||<=K. In the formula, tension x represents a tension product between an N-directional sparse tension B which belongs to R<M1*M2*...*MN and a series of sparse dictionary Dn which belongs to R<In*Mn>, wherein In<=Mn, Dn is defined as the dictionary in an n-th direction, K is sparsity and is used for representing the number of non-zero elements in a sparse coefficient B. The invention furthermore provides a reconstruction method of the sparse model and a dictionary training method of the reconstruction method.

Description

technical field [0001] The invention belongs to the technical field of sparse reconstruction of sparse representation and dictionary training, and in particular relates to a sparse model of multidimensional signals, a reconstruction method and a dictionary training method. Background technique [0002] As an effective method for image and video modeling in recent years, sparse representation has been successfully applied in computer vision fields such as image denoising, super-resolution reconstruction, and face recognition. Traditional sparse representations usually convert multidimensional signals into one-dimensional signals that can be represented by a linear combination of several primitives in a dictionary. High-order signals (images, videos, etc.) first need to be converted into one-dimensional signals, and processed by some methods of vector processing. Research on traditional sparse representation models includes model building, sparse reconstruction, and dictionar...

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06T5/00G06T7/00
CPCG06T5/002G06T7/00G06T2207/20081
Inventor 齐娜施云惠尹宝才丁文鹏
Owner BEIJING UNIV OF TECH
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