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#### OhMyMarkov

##### Member

- Mar 5, 2012

- 83

Hello everyone!

The soft-thresholding function often arrises when trying to find the MAP estimate with a Laplacian model of the parameter to be estimated. It is defined as:

\[

w(y) = \left\{

\begin{array}{l l}

y+T & \text{y < -T}\\

y-T, & \text{y > T}\\

0, & \text{otherwise}\\

\end{array} \right.

\]

Now, in a different context, could this be described as a soft thresholding function?

\[

w(y) = \left\{

\begin{array}{l l}

T-y & \quad \text{if $0 < y < T$}\\

0, & \quad \text{otherwise}\\

\end{array} \right.

\]

Thanks for the help!

The soft-thresholding function often arrises when trying to find the MAP estimate with a Laplacian model of the parameter to be estimated. It is defined as:

\[

w(y) = \left\{

\begin{array}{l l}

y+T & \text{y < -T}\\

y-T, & \text{y > T}\\

0, & \text{otherwise}\\

\end{array} \right.

\]

Now, in a different context, could this be described as a soft thresholding function?

\[

w(y) = \left\{

\begin{array}{l l}

T-y & \quad \text{if $0 < y < T$}\\

0, & \quad \text{otherwise}\\

\end{array} \right.

\]

Thanks for the help!

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