Hi. My name is***** a camera repair technician with over 20 years in the business and I'll be glad to help you with your question today.
Yes. It is possible to recover deleted videos as long as the space they occupied on the hard drive has not been recorded over.
There are many excellent video recovery programs on the market today. My favorite is UndeletePlus by TouchStone software available at the site below. It's not free, but it is easy to use and very thorough.I have found it invaluable on many occasions