TABLE I.

R-SBL GAMP Algorithm

Initialization

S ← |Φ|2 (component wise magnitude squared)

Initialize ${\dot{\mathit{\tau }}}_x^0>0$

s0, ẋ0 ← 0

for n = 1, 2, …․, Nmax

Initialize ${\mathit{\tau }}_x^1\leftarrow {\dot{\mathit{\tau }}}_x^{n-1},{\mathit{x}}^1\leftarrow {\dot{\mathit{x}}}^{n-1}$

E-Step approximation

for k = 1, 2, …․, Kmax

$1/{\mathit{\tau }}_p^k\leftarrow \mathit{S}{\mathit{\tau }}_x^k$

${\mathit{p}}^k\leftarrow {\mathit{s}}^{k-1}+{\mathit{\tau }}_p^k\mathbf{\Phi }{\mathit{x}}^k$

${\mathit{\tau }}_s^k\leftarrow \frac{{\sigma }^{-2}{\mathit{\tau }}_p^k}{{\sigma }^{-2}+{\mathit{\tau }}_p^k}$

${\mathit{s}}^k\leftarrow (1-{\theta }_s){\mathit{s}}^{k-1}+{\theta }_s({\mathit{p}}^k/{\mathit{\tau }}_p^k-\mathit{y})/({\sigma }^2+1/{\mathit{\tau }}_p^k)$

$1/{\mathit{\tau }}_r^k\leftarrow {\mathit{S}}^{\top }{\mathit{\tau }}_s^k$

${\mathit{r}}^k\leftarrow {\mathit{x}}^k-{\mathit{\tau }}_r^k{\mathbf{\Phi }}^{\top }{\mathit{s}}^k$

if MaxSum then

${\mathit{\tau }}_x^{k+1}\leftarrow {\mathit{\nu }}^k$

x̂k+1 ← ηku(rk)

else

${\mathit{\tau }}_x^{k+1}\leftarrow {\mathit{\nu }}^{k}g(\frac{{\mathit{\eta }}^k}{{\mathit{\nu }}^k})$

${\hat{\mathit{x}}}^{k+1}\leftarrow {\mathit{\eta }}^k+\sqrt{{\mathit{\nu }}^k}h(\frac{{\mathit{\eta }}^k}{{\mathit{\nu }}^k})$

end if

if ‖x̂k+1 − x̂k‖2/x̂k+1‖2 < εgamp, break

end for %end of k loop

if MaxSum

${\dot{\mathit{x}}}^i\leftarrow {\mathit{\eta }}^{k+1}+\sqrt{{\mathit{\nu }}^{k+1}}h(\frac{{\mathit{\eta }}^{k+1}}{{\mathit{\nu }}^{k+1}}),{\dot{\mathit{\tau }}}_x^i\leftarrow {\mathit{\nu }}^{k+1}g(\frac{{\mathit{\eta }}^{k+1}}{{\mathit{\nu }}^{k+1}})$

else

${\dot{\mathit{x}}}^n\leftarrow {\hat{\mathit{x}}}^{k+1},{\dot{\mathit{\tau }}}_x^n\leftarrow {\mathit{\tau }}_x^{k+1}$

end if

M-Step

${\mathit{\gamma }}^{n+1}\leftarrow {|{\dot{\mathit{x}}}^n|}^2+{\dot{\mathit{\tau }}}_x^n$

if ‖ẋn − ẋn−1‖2/‖ẋn‖2 < εem, break

end for %end of i loop