Objective: Measurement matrix optimization with given dictionary D, i.e., $${\boldsymbol {\Phi }} =\mathop {\arg \min }\limits _{\boldsymbol {\Phi }} \left \{ {\frac {1}{2}\eta + \left ({1 - \alpha } \right)\mu _{NC}^{t} + \alpha {\mu _{C}^{t}}} \right \}.$$ Initialization:Set n=0, and calculate the eigenvalue decomposition of D D H, i.e., D D H=U Λ U H. Then, we calculate the initial value of Φ according to $${{\boldsymbol {\Phi }}^{\left (0 \right)}} = \left [ {\begin {array}{cccc} {{{\mathbf {I}}_{M}}}&0 \end {array}} \right ]{{\boldsymbol {\Lambda }}^{- \frac {1}{2}}}{{\mathbf {U}}^{H}}.$$ Repeat: a). Update G (n) according to Φ (n): G (n)=(Φ (n) D)H Φ (n) D. b). Calculate h t (G (n)) according to the forthcoming Eq. (24), and form the matrix $${\boldsymbol {\Upsilon }=} {{\boldsymbol {\Lambda }}^{- \frac {1}{2}}}{{\mathbf {U}}^{H}}{\mathbf {D}}{h_{t}}\left ({{{\mathbf {G}}^{\left (n \right)}}} \right){\mathbf {U}}{{\mathbf {D}}^{H}}{{\boldsymbol {\Lambda }}^{- \frac {1}{2}}}.$$ c). Calculate the eigenvalue decomposition of Υ, and find its M top eigenvalues Δ M and the corresponding eigenvectors V M of Υ. d). Update measurement matrix according to $${{\boldsymbol {\Phi }}^{\left ({n+1} \right)}} = {\boldsymbol {\Delta }}_{M}^{\frac {1}{2}}{\mathbf {V}}_{M}^{H}{{\boldsymbol {\Lambda }}^{- \frac {1}{2}}}{{\mathbf {U}}^{H}}.$$ e). n=n+1. Until: Convergence criterion is satisfied.