Algorithm 1.

The generalized algorithm for direct reconstruction of parametric images

1:	Input parameters: Maximum iteration number for reconstruction MaxIter; Regularization parameter β
2:	Initialize the parametric images θ;
3:	Compute the dynamic image x:= {xm(θj )} by Eq.(3);
4:	for n = 1 to MaxIter do
5:	Frame-wise EM image reconstruction:
	${\widehat{x}}_{jm}^{\text{em}}:=\frac{x_m({\mathit{\theta }}_j)}{p_j}{\sum }_{i=1}^{n_i}{p}_{ij}\frac{y_{im}}{{\overline{y}}_{im}(\mathit{\theta })}$
	where $p_j={\sum }_{i=1}^{n_i}{p}_{ij}$ and ȳim(θ ) is calculated by Eq. (4);
6:	Frame-wise image smoothing if β > 0:
	${\widehat{x}}_{jm}^{\text{reg}}:=\frac{1}{2w_{jm}^{\text{reg}}}{\sum }_{l\in {\mathcal{N}}_j}{\gamma }_{jl}\left(x_m({\mathit{\theta }}_j)+x_m({\mathit{\theta }}_l)\right)$
	where the weight $w_{jm}^{\text{reg}}$ is calculated by Eq.(21);
7:	Pixel-wise penalized likelihood fitting
	$({\mathit{\theta }}_j,{\mathit{x}}_j):=\text{PLFit}\left({\mathit{\theta }}_j,{\widehat{\mathit{x}}}_j^{\text{em}},{\widehat{\mathit{x}}}_j^{\text{reg}},\frac{\beta }{p_j}{\mathit{w}}_j^{\text{reg}}\right)$
8:	end for
9:	return the parametric images θ