Algorithm 4.

Frequency marching algorithm

Input: Normalized bispectrum B̃[k1, k2] = eiΨ[k1,k2], ỹ[0] and ỹ[1] ≠ 0

Output: ŷ: estimation of ỹ Set ŷ[0] = ỹ[0] and eiψ̂[1] = ỹ[1] For k = 2, …, N do: Average the phase measurements: $$u=\text{phase}\left({\displaystyle \sum _{\ell =1}^{\lfloor \frac{k}{2}\rfloor }}{e}^{i\left(\widehat{\psi }[\ell ]+\widehat{\psi }[k-\ell ]-\mathrm{\Psi }[\ell ,k]\right)}\right)$$ Estimate ψ̂[k] through: $$e^{i\widehat{\psi }[k]}=\{\begin{array}{ll}u,\hfill & u\ne 0,\hfill \\ 1,\hfill & u=0,\hfill \end{array}$$

Return: ŷ ← eiψ̂