k-t-TMNN

This is the code of the paper 'Dynamic Cardiac MRI Reconstruction Using Combined Tensor Nuclear Norm and Casorati Matrix Nuclear Norm Regularizations'.

Dynamic Cardiac MRI Reconstruction Using Combined Tensor Nuclear Norm and Casorati Matrix Nuclear Norm Regularizations.
Zhang, Yinghao, and Yue Hu. 
2022 IEEE 19th International Symposium on Biomedical Imaging (ISBI). IEEE, 2022.

• For the k-t TMNN algorithm, run the Main_dmri_TMnn.m to test it. The file uses the fast algorithm in frequency domain. The file also contains the fast algorithms for only tensor nuclear norm (TNN) and only Casorati matrix nuclear norm (MNN).

• For the comparation of the classical algorithm in spatiotemporal domain and the fast algorithm in frequency domain, run the Main_dmri_TMnn_vs_fast.m

• The data used in this code can be found in yhao-z/dMRI-Data: dMRI data that I always use (github.com)

• The files in the path algs :

mnnAlg.m and mnnAlg_fast.m denotes the classical algorithm using Casorati matrix nuclear norm based on ADMM and the fast algorithm of that.

so is the tnnAlg.m and tnnAlg_fast.m , where tnn denotes tensor nuclear norm.

tmnnAlg.m and tmnnAlg_fast.m is the same relationship.

prox_nuclear.m and prox_tnn.m implement the singular value thresholding on Casorati and the tensor singular value thresholding.

calc_tnn.m calculate the tensor nuclear norm of a tensor, e.g.,

• the mnnAlg.m and the tnnAlg.m is not used in the Main codes, but it has been tested.