Lavender?

Lavender?

My yard has some well established lavender. The plants are large and did well the end of last summer and fall, when I first bought my house.
Now they look a bit sad. There are many dead stalks sticking up and some of the leaf areas are all dead. Other parts of the plant look ok, with new green leaves growing.
I’m not sure what to do next: remove the dead looking parts or just let the plant work itself out?
I live in Zone 5 and the lavender was covered in snow for most of the winter.
Here’s a picture of what I saw last August and what I hope to have again.

http://www.thevillagetc.com/blog/wp-content/uploads/2010/02/lavender.jpg

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