Walking Dead isn't filmed on a low budget; they chose to film it that way. They almost wanted to keep it like to book and do it all in B+W.In the case of the Walking Dead, it is almost certainly film grain. I believe it is filmed on a lower budget and uses 16mm film. American viewers are irritated with the video quality as well.
Cinematographer, David Boyd in an interview said "16mm is the perfect choice. Regardless if we did it in HD or 35mm film, we'd add grain in the end to make it have this look. It calls up the language of what we're used to seeing in a horror film. George Romero's stuff was all grainy. It's like looking at a documentary, and you instantly get into the 16mm documentary world. And if you take those same cameras and put them into The Walking Dead, it begins to be a believable, real experience. We were looking at a day exterior the other day, and it actually becomes scary -- the moment when you realize it's possible to do something this frightful in broad daylight."