t_svd {rTensor}

Tensor Singular Value Decomposition

Description

TSVD for a 3-Tensor. Constructs 3-Tensors U, S, V such that tnsr = t_mult(t_mult(U,S),t(V)). U and V are orthgonal 3-Tensors with orthogonality defined in Kilmer et al. (2013), and S is a 3-Tensor consists of facewise diagonal matrices. For more details on the TSVD, consult Kilmer et al. (2013).

Usage

t_svd(tnsr)

Arguments

tnsr

3-Tensor to decompose via TSVD

Value

a list containing the following:

U

the left orthgonal 3-Tensor

V

the right orthgonal 3-Tensor

S

the middle 3-Tensor consisting of face-wise diagonal matrices

Note

Computation involves complex values, but if the inputs are real, then the outputs are also real. Some loss of precision occurs in the truncation of the imaginary components during the FFT and inverse FFT.

References

M. Kilmer, K. Braman, N. Hao, and R. Hoover, "Third-order tensors as operators on matrices: a theoretical and computational framework with applications in imaging". SIAM Journal on Matrix Analysis and Applications 2013.

See Also

t_mult, t_svd_reconstruct

Examples

tnsr <- rand_tensor()
tsvdD <- t_svd(tnsr)