# Table 2 MFB-CoSaMP algorithm

Input:Measurement matrix Φ, noisy measurements y, and sparsity level K.
Output: CFO EMV $$\overset \smile {\boldsymbol {\Psi }}$$
Initial: $${\overset \smile {\boldsymbol {\Psi }}^{\left (0 \right)}} \leftarrow {\mathbf {0}}$$, vy, k←0.
Repeat:
a). k=k+1.
b). Form the metric-vector proxy: u=Φ H v.
c). Identify the circle-cluster location according to u
W 1={i:|u i |= max{|u 1|,|u 2|,,|u P |}};
W 1 ← the 2K indexes nearest to W 1 in index set { 1,2, ,P} including W 1.
d). Merge the support set:
$${\mathrm {T}} \leftarrow {\text {supp}}\left ({{\overset \smile {\boldsymbol {\Psi }}^{\left ({k - 1} \right)}}} \right) \bigcup {{\mathbf {W}}_{1}}.$$
e). Least square estimation: b| T←(Φ T) y.
f). $$\phantom {\dot {i}\!}{\mathbf {b}}\left | {{~}_{{{{\mathrm {T}}}^{c}}}} \right. \leftarrow {\mathbf {0}}$$.
g). Identify circle-cluster location according to b
W 2={i:|b i |= max{|b 1|,|b 2|,,|b P |}};
W 2 ←the K indexes nearest to W 2 in index set { 1,2, , P} including W 2.
h). $${\mathbf {b}}\left | {{~}_{{\mathbf {W}}_{2}^{c}}} \right. \leftarrow {\mathbf {0}}.$$
i). Prune to obtain the next approximation:
$${\overset \smile {\boldsymbol {\Psi }}^{\left (k \right)}} \leftarrow {\mathbf {b}}.$$
j). Update current samples $${\mathbf {v }} \leftarrow {\mathbf {y}} - {\boldsymbol {\Phi }}{\overset \smile {\boldsymbol {\Psi }}^{\left (k \right)}}.$$
Until: k=K
$$\overset \smile {\boldsymbol {\Psi }} \leftarrow {\overset \smile {\boldsymbol {\Psi }}^{\left (K \right)}}$$.