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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.

Thank you for your help.

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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.

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    $\begingroup$ 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. $\endgroup$ – Royi Mar 18 at 7:10

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