Wind Damaged Garden Palms

Can anyone help me out. I have some large 6ft Garden palms with long spines. Due to the really high winds of late, most of the have become damaged and bent. Can anyone advise what I need to do. Should i cut them back below the damaged folds or do I have to dig them out completley. Please help.

 

I think some more info on the 'palms' are needed Wllmscot as sometimes palms are really Cordylines and are treated differently to true palms. A pic would help.

 

Wllmscot, sorry for delay in reply, have been out this afternoon.
If it is a Cordyline then you can leave it as it is and just remove some of the lower leaves, or if you think it really looks in a bad way and still want a Cordyline (or 2) cut it down to near ground level and it will throw out 1, 2 or even 3 suckers to replace the mother plant.
Only dig it out as a last resort, they aren't that expensive to replace if you are not prepared to wait for the suckers to grow.
I hope this has been of some help.