Algorithm 1 Generalized Matching Pursuit: ${\mathbf{a}}_k=S({\mathbf{y}}_k;\Psi =\{\Phi ,z,N_0\})$

1:set the sparse vector ${\mathbf{a}}_k$ to zero, 2:initialize ${\overline{\mathbf{a}}}_{k,i}=\langle {\mathbf{y}}_k,{\Phi }_i\rangle$ for all i 3:while$\left|\right|{\mathbf{a}}_k{\left|\right|}_0<N_0$do: 4: select the best match: $i^{\ast }={error}_i\left[z_i\left({\overline{\mathbf{a}}}_{k,i}\right)\right]$ 5: update the sparse coefficient: ${\mathbf{a}}_{k,i^{\ast }}={\mathbf{a}}_{k,i^{\ast }}+{\overline{\mathbf{a}}}_{k,i^{\ast }}$, 6: update residual: $\forall i,{\overline{\mathbf{a}}}_{k,i}\leftarrow {\overline{\mathbf{a}}}_{k,i}-{\mathbf{a}}_{k,i^{\ast }}\langle {\Phi }_{i^{\ast }},{\Phi }_i\rangle$.