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A sparse model, reconstruction method and dictionary training method for multidimensional signals

A dictionary training and sparse reconstruction technology, applied in the fields of sparse reconstruction and dictionary training of sparse representation, can solve the problems of sparse representation model describing tensors, algorithm complexity and storage space contradiction, and reduce algorithm complexity and storage space. , the effect of reducing the complexity of the algorithm

Active Publication Date: 2021-11-30
BEIJING UNIV OF TECH
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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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  • A sparse model, reconstruction method and dictionary training method for multidimensional signals
  • A sparse model, reconstruction method and dictionary training method for multidimensional signals
  • A sparse model, reconstruction method and dictionary training method for multidimensional signals

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Embodiment Construction

[0024] The sparse model of this multi-dimensional signal is formula (1)

[0025]

[0026] 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 .

[0027] Preferably, given a sparse dictionary The corresponding sparse model is formula (2)

[0028]

[0029] Among them, λ is used to balance fidelity and sparsity.

[0030] Preferably, the conversion to l by relaxation 1 Constrained convex programming problem, the corresponding sparse model is formula (3)

[0031]

[0032] 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)

[0033]

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Abstract

The invention discloses a sparse model of a multi-dimensional signal, which can ensure that no Kronecker product is used, thereby ensuring obvious improvements in algorithm complexity and storage space. The sparse model of this multi-dimensional signal is the formula where the tensor X is expressed as the tensor product of an N-dimensional sparse tensor and a series of sparse dictionaries, I n ≤M n ,D n Defined as a dictionary in the nth direction, K is the degree of sparsity, which is used to describe the number of non-zero elements in the sparse coefficient. Reconstruction methods and dictionary training methods are also provided.

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...

Claims

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Application Information

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Patent Type & Authority Patents(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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