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. Author manuscript; available in PMC: 2016 Oct 31.
Published in final edited form as: IEEE Trans Ultrason Ferroelectr Freq Control. 2015 Mar;62(3):475–493. doi: 10.1109/TUFFC.2014.006788

Algorithm 1 Gradient descent-based sequential waveform inversion.

Input: {gm}, {sm}, c(0)
Output: ĉ
1: k ← 0 {k is the number of algorithm iteration.}
2: while stopping criterion is not satisfied do
3: kk + 1
4: J0
5: for m := 0 to M − 1 do
6:    pmaHcsm {m is the index of the emitter.}
7:    qmaHcτm {τm is calculated via Eqn. (12).}
8:   JJ + Jm {Jm is calculated via Eqn. (10).}
9: end for
10: JJ + βJR
11:  Determine step size λ via a line search
12: c(k)c(k−1) − λJ
13: end while
14: ĉ = c(k)