Algorithm 2.

(PET Image Recovering) Given the coefficient matrix $\mathbf{E}\in {\mathbb{R}}_{+}^{d\times p}$, coincident counts $\mathbf{y}=(y_1,\dots ,y_d)\in {\mathbf{Z}}_{+}^d$, and roughness parameter μ > 0, find the intensity vector $\mathbf{\lambda }=({\lambda }_1,\dots ,{\lambda }_p)\in {\mathbb{R}}_{+}^p$ that maximizes the objective function (3.6).

Scale E to have unit l1 column norms.

Compute | | = Σk:{j,k}∈ 1 and aj − 2μ| | for all 1 ≤ j ≤ p.

Initialize: λ0j ← 1, j = 1, …, p.

repeat

znij ← (yieijλnj)/(Σkeikλnk) for all 1 ≤ i ≤ d, 1 ≤ j ≤ p

for j = 1 to p do

bnj ← μ(| | λnj + Σk∈ λnk) − 1

cnj ← Σi znij

${\lambda }_{n+1,j}\leftarrow (-b_{nj}-\sqrt{b_{nj}^2-4a_j{c}_{nj}})/(2a_j)$

end for

until convergence occurs