Table 2.

Considered noise estimation techniques.

Technique/Reference	Noise estimate
Spectral expectation (Veraart et al., 2016b)	$\begin{array}{cc}{\tilde{\sigma }}_{\text{EXP}1}^2\left(R\right)=& \frac{\sqrt{N}\left({\eta }_{\mathbf{Y}R+1}^2-{\eta }_{\mathbf{Y}M}^2\right)}{4\sqrt{M-R}}\\ {\tilde{\sigma }}_{\text{EXP}2}^2\left(R\right)=& \frac{\sqrt{N-R}\left({\eta }_{\mathbf{Y}R+1}^2-{\eta }_{\mathbf{Y}M}^2\right)}{4\sqrt{M-R}},\\ {\hat{R}}_{\text{EXP}\left\{\mathrm{1,2}\right\}}=& \inf \left\{R|\overline{)\sum _{r=R+1}^M{\eta }_{\mathbf{Y}r}^2\ge \left(M-R\right){\tilde{\sigma }}_{\text{EXP}\left\{1,2\right\}}^2\left(R\right)}\right\}\text{(19)}\\ {\hat{\sigma }}_{\text{EXP}\left\{\mathrm{1,2}\right\}}^2=& {\tilde{\sigma }}^2\left({\hat{R}}_{\text{EXP}\left\{\mathrm{1,2}\right\}}\right)\end{array}$
Spectral median (Gavish and Donoho, 2014)	${\hat{\sigma }}_{\text{MED}}^2=\frac{{\eta }_{\mathbf{Y}M/2}^2}{{\theta }_{M/2}^2}$ (20)