Algorithm 1 Processing flow for the proposed data reduction invariant LASSO technique

Input: M × N matrix $Y$ at the output of the MWC scheme, M × L X sampling-related matrix $T=W^H$ and N × M matrix $V_Y$, obtained from the SVD of the $Y$ matrix using Equation (3). Initialization:   Compute $Y_r=Y{V}_Y$ according to Equation (2).   Take an initial solution for the L × M matrix ${\widehat{Z}}_r$ belonging to $Fix\left\{Y_r\right\}$.   Find the optimal λ value using the cross-validation method [30]. Fori←1 to L, do   Obtain the matrices $T^{(-i)}$ and ${\widehat{Z}}_{(-i)}$ by removing the ith column from the matrix $T$ and the ith row from the matrix ${\widehat{Z}}_r$, respectively.   In addition, obtain the ith column of matrix $T$ and denote it by $b=T^{(i)}$.   Calculate $R_{part(i)}=Y_r-T^{(-i)}{\widehat{Z}}_{(-i)}$ according to Equation (20).   Calculate $a=R_{part(i)}^H{T}^{(i)}$ according to Equation (22).   Calculate $\tilde{z}=a^H/{\Vert a\Vert }_2^{}$ according to Equation (32) and then $\mu =\frac{\mathrm{Re}\left[\tilde{z}a\right]-\lambda }{{\Vert b\tilde{z}\Vert }_2^2}$ according to Equation (24).   Calculate ${\widehat{Z}}_{(i)}=\mu \tilde{z}$ according to Equation (22).   Update the estimated solution ${\widehat{Z}}_r$ by replacing its ith row with ${\widehat{Z}}_{(i)}$. End for Output: Calculate the final estimated solution, i.e., the L × N matrix $\widehat{Z}={\widehat{Z}}_r{V}_Y^H$.