Algorithm 2.

3D fluorescence imaging reconstruction

Require: $I_{f,\mathcal{l}}$, ${\mathbf{r}}_{\mathcal{l}}$, $f_{1,\mathcal{l}},\cdots ,f_{M,\mathcal{l}}\mathcal{l}=1,\dots ,N_{\text{img}}$
1:	initialize $o_1^{\left(1,0\right)},\cdots ,o_M^{\left(1,0\right)}$, $p_c^{\left(1,0\right)}$, ${\tilde{h}}_f^{\left(1,0\right)}$; normalize $I_{f,\mathcal{l}}$
2:	for $k=1:K_f$ do
3:	Sequential gradient descent
4:	for $\mathcal{l}=1:N_{\text{img}}$ do
5:	if $j<N_{\text{img}}$ then
6:	for $m=1:M$ do
7:	$o_m^{\left(k,j\right)}=o_m^{\left(k,j-1\right)}-{\nabla }_{o_m}{e}_{f,\mathcal{l}}(o_1^{\left(k,j-1\right)},\cdots ,o_M^{\left(k,j-1\right)},$
	$p_c^{\left(k,j-1\right)},{\tilde{h}}_f^{\left(k,j-1\right)})/\max {\left(|f_{1,\mathcal{l}}^{\left(k,j-1\right)}|,\cdots ,|f_{M,\mathcal{l}}^{\left(k,j-1\right)}|\right)}^4$
8:	end for
9:	$p_c^{\left(k,j\right)}=p_c^{\left(k,j-1\right)}\left(\mathbf{r}\right)-{\nabla }_{p_c}{e}_{f,\mathcal{l}}(o_1^{\left(k,j-1\right)},\cdots ,o_M^{\left(k,j-1\right)},$
	$p_c^{\left(k,j-1\right)},{\tilde{h}}_f^{\left(k,j-1\right)})/\max {\left(|t_1^{\left(k,j-1\right)}|,\cdots ,|t_M^{\left(k,j-1\right)}|\right)}^2$
10:	${\tilde{h}}_f^{\left(k,j\right)}={\tilde{h}}_f^{\left(k,j-1\right)}-{\nabla }_{{\tilde{h}}_f}{e}_{f,\mathcal{l}}(o_1^{\left(k,j-1\right)},\cdots ,o_M^{\left(k,j-1\right)},$
	$p_c^{\left(k,j-1\right)},{\tilde{h}}_f^{\left(k,j-1\right)})/\max \left(|\mathcal{F}\{o^{\left(k,j-1\right)}\cdot {|f_{\mathcal{l}}^{\left(k,j-1\right)}|}^2\}|\right)$
11:	else
12:	Do the same update but save to $o_1^{\left(k+1,0\right)},\cdots ,o_M^{\left(k+1,0\right)},p_c^{\left(k+1,0\right)},{\tilde{h}}_f^{\left(k+1,0\right)}$
13:	end if
14:	end for
15:	end for