The Second-Order Born Approximation in Diffuse Optical Tomography

Algorithm 1

Numerical algorithm (continuous version).

(I) Compute the solution Φ(𝑥) and the Robin function 𝑅(𝑥) and its first and second derivatives.

(II) Find 𝛿𝑥^† by solving ℛ¹(𝛿𝑥^†)=Φ(𝑥+𝛿𝑥)−Φ(𝑥) as in (1.6).

(III) Find 𝛿𝑥^Δ=𝛿𝑥^𝐵−𝛿𝑥^† by solving ℛ¹(𝛿𝑥^Δ)=−ℛ²(𝛿𝑥^†) as in (2.2).

(IV) Compute 𝛿𝑥^𝐵 by adding 𝛿𝑥^† and 𝛿𝑥^Δ.