Figure 7:

Example of the low rank model for relaxation-weighted images. The “sparsity” of this model is in the singular values of the Casorati matrix of the images, as X = VSU^T. A reduced structure given by the principal components of the SVD, using only the first and most significant components of U = [u₁,.., u_Nt], V = [v₁,..,v_Nt], and S = diag(s1,…,s_Nt), reconstructs $\tilde{\mathit{X}}$ which yields a signal $\tilde{\mathit{x}}\mathit{ }$ with very small difference $\tilde{\mathit{x}}-\mathit{x}$.