I want to make a big tile mural (6 ft. x 3 ft.) from a photo that is 2' x 1.5', 300 dpi. Can I get a higher resolution in the end result if I take a picture of the stock photo with my Canon DSLR, using Camera Raw? Or should I try enlarging the stock photo with a software program like Perfect Resize? The mural will be installed on a wall in a showroom, at eye level or slightly higher. So the viewing range is pretty close, 3-4 ft, I'd say. (as you can tell, I'm not a professional photographer) Thanks!
You can take a photo that's arbitrarily detailed with respect to the dots that exist in your subject (at 300dpi), but you can't find new dots where there are none in the print now.
Perfect resize (and other resizing algorithms) will attempt to deduce what the "dots between the dots" should look like base on interpolation algorithms. Like most photo processing techniques, you may find that one variation looks better to you than another, but the algorithm will have the advantage of not introducing any new visual defects in its product. In this respect, the algorithm will certainly be more accurate, if not actually visually appealing.
If you have a circle made by putting a black spot in the center spot on each side of a 3 by 3 grid, what do you get if you take a photo of it that uses 300 spots? You get a square on the center of each side using a bunch of pixels to make each square.
You can't increase the amount of information in an image if there is no information to capture. Your highest quality is going to be to use the original image and apply a resize that tries to guess at the additional information that needs to be created, but it won't have any meaningful additional detail and will still look "low res".
That said, if the viewing distance is sufficient, you can go lower than 300 DPI comfortably. At 150 DPI, you'd have 4' by 3' which would still be ok when seen across a room, but would fall apart pretty quickly if someone got up close.
Use software. You also need to figure out what aspect ratio you want to use.... if you double the size of the pictures height from 1.5' to 3', and double the length 2 to 4' your mural is going to be too short and will not use up the full 6'.
If you triple the height from 1.5' to 4.5', and triple the length 2' to 6' you're going to have to crop off parts (top and/or bottom) of the picture. Be aware that if you are not careful you might end up with a distorted picture due to stretching.