Algorithm 2.

Non-convex optimization on phase manifold

Input: The normalized bispectrum B̃[k1, k2] and a weight matrix W ∈ ℝN×N

Output: ŷ: an estimation of ỹ

Compute: Using RTR [62], [63], approximately solve: $$\widehat{y}=arg\underset{z\in {ℂ}^N}{max}\mathfrak{R}\{z^{\ast }M(z)z\}\text{subject}\text{to}\mid z[k]\mid =1,\forall k,(\text{if}x\text{is}\text{real})z[k]=\overline{z[-k]},\forall k,$$

where $M(z):=(W\circ W)\circ \stackrel{\sim }{B}\circ \overline{T(z)}$.