Algorithm 1 Estimating the local noise variance ${\left\{{\left({\widehat{\sigma }}_n^2\right)}_l\right\}}_{l=1}^L$

Input:$N\times M$ NSST coefficients ${\left\{Y_j^i\right\}}_{i=1,j=1}^{M,N}$ of the observed interferograms with N different baselines, the size of patch $m\times n$ and the maximum iteration number $N_{iter}$.

Initialization:${\left\{{({\widehat{\sigma }}_n^2)}_l\right\}}_{l=1}^L$ = 0.

1: Divide all coefficients into L patches whose size is $m\times n$ and calculate the kurtosis ${\left\{{\kappa }_l\left(y_i^j\right)\right\}}_{i=1,j=1,l=1}^{N,M,L}$ and variance ${\left\{{({\sigma }_{y_i^j}^2)}_l\right\}}_{i=1,j=1,l=1}^{N,M,L}$ of eath patch.

2: Repeat.

3: Let ${\left\{{\left({\sigma }_n^2\right)}_l\right\}}_{l=1}^L$ equals the solution of the last optimization, update ${\left\{{\widehat{\kappa }}_l\left(x\right)\right\}}_{l=1}^L$ by optimization function 1.

4: Let ${\left\{{\kappa }_l\left(x\right)\right\}}_{l=1}^L$ equals the solution of the step 3, update ${\left\{{({\widehat{\sigma }}_n^2)}_l\right\}}_{l=1}^L$ by optimization function 2.

5: Until ${\left\{{({\widehat{\sigma }}_n^2)}_l\right\}}_{l=1}^L$ and ${\left\{{\widehat{\kappa }}_l(x)\right\}}_{l=1}^L$ converges or $N_{iter}$ is reached.

6: Return ${\left\{{({\widehat{\sigma }}_n^2)}_l\right\}}_{l=1}^L$.