Algorithm 1.

Basic outline of algorithm focusing on the line search and acceleration.

μ0 ← deblur and FDK recon

n ← 0, t0 ← 1, z0 ← μ0

while n < N do

pn ← − Δψ|μn, αi ← 0, i ← 0

while i < I do

$c\leftarrow \frac{d^2\psi }{d{\alpha }^2}{|}_{{\alpha }_i}$

if c < 0 then

c ← cub

end if

${\alpha }_{i+1}\leftarrow {\alpha }_i-c^{-1}\frac{d\psi }{d\alpha }{|}_{{\alpha }_i}$, i ← i + 1

end while

$t_{n+1}\leftarrow (1+\sqrt{1+4t_n^2})/2$, μn+1 ← [zn + αIp]+

$z_{n+1}\leftarrow {\mu }_{n+1}+\frac{t_{n-1}}{t_{n+1}}({\mu }_{n+1}-{\mu }_n)$, n ← n + 1

end while