# Understanding Soft Thresholding Operator

I want to understand what is soft thresholding operator? Why we use this operator? I came across this term while I was reading the paper - A New Algorithm Based on Linearized Bregman Iteration with Generalized Inverse for Compressed Sensing (at page no 4.).

Any reference that can explain this will also help me.

The soft-thresholding function finds the minimizer of an objective function that involves data fitting in an $$\ell_2$$ sense as well as minimization of the $$\ell_1$$ norm (i.e. absolute value). The Lecture Notes - Penalty and Shrinkage Functions for Sparse Signal Processing gives a good discussion of how the soft threshold function is derived.
• Please use the names of the resources you link to and not something like this. One day the link won't be available, but the name is always searchable.