Table 1. Pseudocode for the Iterative Soft Thresholding Processing of Ultrafast 2D NMR Data.

Input:
G(t)- Gradient waveform (N×1); FID (N×1); k/ν1-axis grid (n×1); ν2 – the direct domain frequency vector (1×m), ε , MaxIter – maximal number of iterations
Output:
S(k/ν1, ν2) – 2D spectrum matrix (n-by-m):
Preliminary calculations:
k(t) – wavenumber as a function of acquisition
t2(k) – n vectors containing the t2 points at each wavenumber k
${\underset{¯}{\underset{¯}{A}}}_k=\text{exp}\left(i\cdot 2\pi \cdot {\left(t_2\left(k\right)\right)}^T{v}_2\right)$ - n complex matrices
Initialization:
Residual vectors	r0(k)=FID(k,t2)
Correlation vectors	${\text{c}}_0\left(k\right)={\underset{¯}{\underset{¯}{A}}}_k^{†}{r}_0\left(k\right)$
Global threshold value	λ0=μ·max{|c0(k)|}
Solution	S0=0 of size n×m
while (p<MaxIter) and $\left({\Vert {\text{r}}_{\text{p}}\Vert }_2\ge \epsilon {\Vert \text{FID}\Vert }_2\right):$
Update solution	Sp+1(k) = Sp(k)+δλp (cp (k))
Calculate residual	$r_{p+1}\left(k\right)=FID\left(k\right)-\underset{¯}{\underset{¯}{A_k}}{S}_{p+1}\left(k\right)$
Calculate correlation	$c_{p+1}\left(k\right)=\underset{¯}{\underset{¯}{A_k^{†}}}{r}_{p+1}\left(k\right)$
Update threshold value	λp+1=μ·max{|cp+1(k)|}
end while
Post-processing: Inverse FT for S(k/ν1, ν2) along the direct domain; Exponential, Gaussian or                               Lorentzian Filtering; FT for S(k/ν1, ν2) along the direct domain.