S(z,γ)S(z,\gamma)S(z,γ) is the soft-thresholding operator with value
S(z,γ)=sign(z)(∣z∣−γ)+={ z−r,ifz>0andγ<∣z∣,z+r,ifz<0andγ<∣z∣,0,ifγ≥∣z∣.S(z,\gamma)={\rm{sign}}(z)(|z|-\gamma)_+ = \left\{ \begin{array}{rcl} z-r, \quad if &z>0 &and& \gamma<|z|, & \\ z+r, \quad if &z<0 &and&\gamma<|z|, & \\ 0, \quad if &\gamma \geq |z|. & \end{array} \right. S(z,γ)=sign(z<