The model by imposing the low-rank minimization has been proved to be effective for magnetic resonance imaging(MRI) completion. Recent studies have also shown that imposing tensor train(TT) and total variation(TV) con...The model by imposing the low-rank minimization has been proved to be effective for magnetic resonance imaging(MRI) completion. Recent studies have also shown that imposing tensor train(TT) and total variation(TV) constraint on tensor completion can produce impressive performance, and the lower TT-rank minimization constraint can be represented as the guarantee for global constraint, while the total variation as the guarantee for regional constraint. In our solution, a new approach is utilized to solve TT-TV model. In contrast with imposing the alternating linear scheme, nuclear norm regularization on TT-ranks is introduced in our method as it is an effective surrogate for rank optimization and our solution does not need to initialize and update tensor cores. By applying the alternating direction method of multipliers(ADMM), the optimization model is disassembled into some sub-problems, singular value thresholding can be used as the solution to the first sub-problem and soft thresholding can be used as the solution to the second sub-problem. The new optimization algorithm ensures the effectiveness of data recovery. In addition, a new method is introduced to reshape the MRI data to a higher-dimensional tensor, so as to enhance the performance of data completion. Furthermore, the method is compared with some other methods including tensor reconstruction methods and a matrix reconstruction method. It is concluded that the proposed method has a better recovery accuracy than others in MRI data according to the experiment results.展开更多
CANDECOMP/PARAFAC(CP) tensor factorization is an efficient technique for incomplete tensor-data processing through capturing the multilinear latent factors. Based on the incorporate a sparsity-inducing prior over mult...CANDECOMP/PARAFAC(CP) tensor factorization is an efficient technique for incomplete tensor-data processing through capturing the multilinear latent factors. Based on the incorporate a sparsity-inducing prior over multiple latent factors and appropriate hyper-priors over all hyper-parameters, a Bayesian-based hierarchical probabilistic CP factorization model could be formed. By this way, the rank of the incomplete tensor can be determined automatically. In this paper, we explored the tensor completion method in processing incomplete multidimensional electroencephalogram(EEG) and magnetic resonance imaging(MRI) clinical data. The empirical results indicated that the Bayesian CP tensor factorization of incomplete data method can effectively recover EEG signal with missing data and denoised the noisy MRI data.展开更多
基金This work was supported by Japan Science and Technology Agency:CREST(Grant No.JPMJCR1784)Japan Society for the Promotion of Science:Grants-in-Aid for Scientific Research(KAKENHI)(Grant No.18K04178)。
文摘The model by imposing the low-rank minimization has been proved to be effective for magnetic resonance imaging(MRI) completion. Recent studies have also shown that imposing tensor train(TT) and total variation(TV) constraint on tensor completion can produce impressive performance, and the lower TT-rank minimization constraint can be represented as the guarantee for global constraint, while the total variation as the guarantee for regional constraint. In our solution, a new approach is utilized to solve TT-TV model. In contrast with imposing the alternating linear scheme, nuclear norm regularization on TT-ranks is introduced in our method as it is an effective surrogate for rank optimization and our solution does not need to initialize and update tensor cores. By applying the alternating direction method of multipliers(ADMM), the optimization model is disassembled into some sub-problems, singular value thresholding can be used as the solution to the first sub-problem and soft thresholding can be used as the solution to the second sub-problem. The new optimization algorithm ensures the effectiveness of data recovery. In addition, a new method is introduced to reshape the MRI data to a higher-dimensional tensor, so as to enhance the performance of data completion. Furthermore, the method is compared with some other methods including tensor reconstruction methods and a matrix reconstruction method. It is concluded that the proposed method has a better recovery accuracy than others in MRI data according to the experiment results.
基金supported by the JSPS KAKENHI,Japan(Grant Nos.17K00326 and 18K04178)the National Natural Science Foundation of China(Grant Nos.61773129,61633010)the JST CREST,Japan(Grant No.JPMJCR1784)。
文摘CANDECOMP/PARAFAC(CP) tensor factorization is an efficient technique for incomplete tensor-data processing through capturing the multilinear latent factors. Based on the incorporate a sparsity-inducing prior over multiple latent factors and appropriate hyper-priors over all hyper-parameters, a Bayesian-based hierarchical probabilistic CP factorization model could be formed. By this way, the rank of the incomplete tensor can be determined automatically. In this paper, we explored the tensor completion method in processing incomplete multidimensional electroencephalogram(EEG) and magnetic resonance imaging(MRI) clinical data. The empirical results indicated that the Bayesian CP tensor factorization of incomplete data method can effectively recover EEG signal with missing data and denoised the noisy MRI data.
