Joint Reconstruction of Multi-channel, Spectral CT Data via Constrained Total Nuclear Variation Minimization

. Author manuscript; available in PMC: 2016 Mar 7.

Published in final edited form as: Phys Med Biol. 2015 Feb 6;60(5):1741–1762. doi: 10.1088/0031-9155/60/5/1741

Algorithm 2 Data-constrained VTV Update Equations

Initialize:

θ = 1, σ τ {‖ (\begin{matrix} A \\ D \end{matrix}) ‖}_{2}^{2} = 1, (u, \bar{u}, q, Z) \to 0

repeat

Z^(k+1) = П_𝒮/𝒩(Z^(k) + σDū^(k))

q^(k+1) = prox_{σεF_q} (q^(k)+σ(Aū^(k)−g))

u^{(k +1)} = u^(k) + τ (Div Z^{(k +1)} − A^T q^{(k +1)})

ū^(k+1) = u^(k+1) + θ (u^(k+1) − u^(k+1))

until

▹ stop when convergence criteria met