Algorithm 1 Algorithm for direct Patlak reconstruction using the kernel method
Input: Maximum iteration number MaxIt, sub-iteration number SubIt, starting time frame FraSta and ending time frame FraEnd
1:	Initialize α0, SllbIt = 1N
2:	for n = 1 to MaxIt do
3:	xn (A ⊗ K)αn–I, SubIt
4:	αn,0 = αn–I, SubIt
5:	for k = FraSta to FraEnd do
6:	${\mathit{x}}_k^{n+1}=\frac{{\mathit{x}}_k^n}{({\mathit{N}}_k\mathit{P}\mathit{K})\prime {\mathbf{1}}_M}[({\mathit{N}}_k\mathit{P}\mathit{K})\prime \frac{\mathit{y}}{({\mathit{N}}_k\mathit{P}\mathit{K}){\mathit{x}}_k^n+\mathit{s}+\mathit{r}}]$
7:	end for
8:	for q = 1 to SubIt do
9:	${\mathit{\alpha }}^{n,q}=\frac{{\mathit{\alpha }}^{n,q-1}}{[\mathit{A}\otimes (\mathit{P}\mathit{K})]\prime \mathit{N}{\mathbf{1}}_{MT}}([\mathit{A}\otimes (\mathit{P}\mathit{K})]\prime \mathit{N}{\mathbf{1}}_{MT}\frac{{\mathit{x}}^{n+1}}{(\mathit{A}\otimes {\mathit{I}}_N){\mathit{\alpha }}^{n,q-1}})$, where 1MT is a MT × 1 all-one vector.
10:	end for
11:	end for
12:	return θ̂ = (I2 ⊗ K)α̂MaxIt,SubIt