Algorithm 1.

Gauss-Newton for Distorted Born Iterative Method

i ← 0

{\hat{ε}}_{0}^{b}

← initial background profile

repeat

for m = 1 to N do

FDTD: E^b (r_n|r_m) for n = 1, …, N; E^b(r_k|r_m) and Ḡ^b(r_k|r_m) for k = 1, …, K

E^s(r_n|r_m) ← E^meas (r_n|r_m) − E^b (r_n|r_m) for n = 1, …, N

Ḡ^b(r_m|r_k) ← Ḡ^b(r_k|r_m)^T for k = 1, …, K

end for

construct A_i, y_i

x̂_i ← CGLS(A_i,y_i)

{\hat{ε}}_{i + 1}^{b} \leftarrow {\hat{ε}}_{i}^{b} + F ({\hat{x}}_{i})

i ← i + 1

until ||y_i₋₁|| − ||y_i|| < δ ||y₀||