Living in POST SANDY HURRICANE construction zone for almost 2 years now, we feel your pain. Put up a sturdy fence as high as you are permitted as close to the edge of your property as you are allowed and then fill in the space with the largest trees/shrubs that are aesthetically pleasing as well as native/low maintenance to your area as possible.
See if there is a swap meet/flea market near by or a wholesale nursery or Craigslist person who is reliable, and get a deal on a bunch of natural shrubbery and RECLAIM THE WOODS! We are so thankful that after a year, so much of the native vines that were drowned came back and also thankful that as gardeners, we didn't give up on so many trees and shrubs for a long time (i.e. until they were TOTALLY DEAD). So many came back and stronger than ever.
Turn up the volume on some great Jazz and plant, plant, plant (or Robert Plant!).
Regards,
Karen & Joseph
for Decorative Philosophy
PS Excuse the bad puns, it's been a long strange day!
K

A fence won't do much to block noise -- at least one you would be allowed to build.

Noise reduction needs two things: density (like concrete/cinder blocks filled with sand) and "soft coverings" like plants. Decorative Philosophy has touched on both (I personally would choose R. Plant...but then again I'm a fan ;-). If you can add DENSITY such as you find with concrete or cinder block together with foliage (something native = easy to keep alive) you can get the most bang for your buck.

I'm not aware of what "noise reduction foil" can do for you. It needs to be wrapped around a baffle (looks like sound absorbing fibreglass is used) which itself adds to the noise abatement. I'm not sure where you would find it available for "landscaping". I've found information regarding "factory installation" as a way to reduce machine noise...but I've yet to find anything that offers an outdoor solution.

plants don't abate sound and typical fences don't either. a berm is best.