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For DCMRI, the CS-MRI usually exploits image signal sparsity and low-rank property to reconstruct dynamic images from the undersampled k-space data. In this paper, a novel CS algorithm is investigated to improve dynamic cardiac MR image reconstruction quality under the condition of minimizing the k-space recording.<\/jats:p>\n              <\/jats:sec><jats:sec>\n                <jats:title>Methods<\/jats:title>\n                <jats:p>The sparse representation of 3D cardiac magnetic resonance data is implemented by synergistically integrating 3D total generalized variation (3D-TGV) algorithm and high order singular value decomposition (HOSVD) based Tensor Decomposition, termed <jats:italic>k-t<\/jats:italic> TGV-TD method. In the proposed method, the low rank structure of the 3D dynamic cardiac MR data is performed with the HOSVD method, and the localized image sparsity is achieved by the 3D-TGV method. Moreover, the Fast Composite Splitting Algorithm (FCSA) method, combining the variable splitting with operator splitting techniques, is employed to solve the low-rank and sparse problem. Two different cardiac MR datasets (cardiac perfusion and cine MR datasets) are used to evaluate the performance of the proposed method.<\/jats:p>\n              <\/jats:sec><jats:sec>\n                <jats:title>Results<\/jats:title>\n                <jats:p>Compared with the state-of-art methods, such as <jats:italic>k-t<\/jats:italic> SLR, 3D-TGV, HOSVD based tensor decomposition and low-rank plus sparse method, the proposed <jats:italic>k-t<\/jats:italic> TGV-TD method can offer improved reconstruction accuracy in terms of higher peak SNR (PSNR) and structural similarity index (SSIM). The proposed <jats:italic>k-t<\/jats:italic> TGV-TD method can achieve significantly better and stable reconstruction results than state-of-the-art methods in terms of both PSNR and SSIM, especially for cardiac perfusion MR dataset.<\/jats:p>\n              <\/jats:sec><jats:sec>\n                <jats:title>Conclusions<\/jats:title>\n                <jats:p>This work proved that the <jats:italic>k-t<\/jats:italic> TGV-TD method was an effective sparse representation way for DCMRI, which was capable of significantly improving the reconstruction accuracy with different acceleration factors.<\/jats:p>\n              <\/jats:sec>","DOI":"10.1186\/s12880-022-00826-1","type":"journal-article","created":{"date-parts":[[2022,5,27]],"date-time":"2022-05-27T11:04:08Z","timestamp":1653649448000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Compressed sensing based dynamic MR image reconstruction by using 3D-total generalized variation and tensor decomposition: k-t TGV-TD"],"prefix":"10.1186","volume":"22","author":[{"given":"Jucheng","family":"Zhang","sequence":"first","affiliation":[]},{"given":"Lulu","family":"Han","sequence":"additional","affiliation":[]},{"given":"Jianzhong","family":"Sun","sequence":"additional","affiliation":[]},{"given":"Zhikang","family":"Wang","sequence":"additional","affiliation":[]},{"given":"Wenlong","family":"Xu","sequence":"additional","affiliation":[]},{"given":"Yonghua","family":"Chu","sequence":"additional","affiliation":[]},{"given":"Ling","family":"Xia","sequence":"additional","affiliation":[]},{"given":"Mingfeng","family":"Jiang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,5,27]]},"reference":[{"key":"826_CR1","volume-title":"MRI in practice (5th edn)","author":"C Westbrook","year":"2018","unstructured":"Westbrook C, Talbot J. 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