Wavelet Detail Coefficient for Edge Detection

Hey guys, just have a quick question about the detail coefficients from a wavelet transform.

I have very noisy signal data, and using a Stationary Wavelet Transform with a Haar mother-wavelet to denoise the signal so I can essentially go ahead and edge detect (there are steps in the signal like this ).

From my understanding, the detail coefficients give the location of where these peaks/edges occur. What is the best way (computationally) to filter out the unnecessary noise in the detail coefficients and search for the peaks/edges? Any help would be greatly appreciated. Thank you!!