OhMyMarkov
				
				
			 
			
	
	
	
		
	
	
			
		
		
			
			
				
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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!
			
				Last edited by a moderator: 
			
		
	
								
								
									
	
								
							
							 
 
		 
 
		