Visual data completion method based on local low-rank tensor estimation

Abstract

The invention relates to a visual data completion method based on local low-rank tensor estimation. The method comprises the following steps of 1) acquiring original visual data to be completed, mapping the original visual data to a three-dimensional tensor space with a size of n1*n2*n3 so as to form an original tensor possessing a deletion value; 2) according to the original tensor, initializing a target tensor so that the target tensor satisfies the following formula which is defined in the description, wherein X[omega] is non-deletion value data in the target tensor, T[omega] is non-deletion value data in the original tensor, X[omega-bar] is deletion value data in the target tensor, and the target tensor is decomposed into ng child tensors Mij in an overlapped mode; 3) solving each child tensor Mij respectively so that a trace norm is weighted and minimized, and finally acquiring an optimal solution of the target tensor; and 4) converting the optimal solution of the target tensor into a corresponding format of visual data and acquiring a final completion result. Compared to the prior art, the method possesses advantages that a completion effect is good; and estimation is accurate and so on.

Description

technical field [0001] The invention relates to a visual data completion method, in particular to a visual data completion method based on local low-rank tensor estimation. Background technique [0002] The missing data imputation method based on tensor decomposition has been extensively studied abroad, and a series of algorithms have been proposed. In 2005, Tomasi et al. adopted the idea of ​​iterative least squares method and proposed a specific missing tensor interpolation algorithm based on tensor CP decomposition model, called PARAFAC-ALS algorithm. However, the PARAFAC-ALS algorithm adopts the idea of ​​iteration and continuous approximation, and the convergence speed is slow. When the proportion of missing data is large, it may even not converge at all, resulting in wrong interpolation results. In order to solve this problem, Tomasi et al. also proposed the PARAFAC-LM algorithm, which uses the idea of ​​nonlinear least squares and the CP decomposition model to effect...

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Problems solved by technology

In order to solve the problem of high computational complexity of the tensor nuclear norm minimization problem, Liu Yuanyuan also proposed a new CP decomposition model calculation method, and applied it to the imputation problem of missing t

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