If I print the following noise texture image in which I've embedded some information with steganography, can I retrieve the information back or can I detect the information loss occurred due to degradation of quality in printing the steganographic image?
Steganography is basically hidden information. It can be as simple as a picture that is mirrored versus a non-mirrored picture. This would convey one bit of information, and may not be easily detectable to an adversary. It would survive even extremely crude reproductions.
If you however hide data in the least significant bit of the colorspace, it would likely not survive, as color reproduction is not that accurate. It also depends on data density; fewer bits with a lot of space used for error correction will give you higher chance of success.
In essence this is a question about the bandwidth of the reproduction. A digital reproduction (e.g. copy of the file) is identical to the original. When you print it, you somehow transform it from digital information, to colored dots on a page. With what accuracy does this process happen? Do you rescale it, so 10 digital pixels ends up being 2-3 colored dots? Is the same color space used? Digital images are commonly RGB, while printed images are commonly CMYK.
When you scan the image you take these dots, shine some light on them, and digitize the return. How accurate is your light source? Is it a cheap LED with a very narrow light color? How accurate is your digital sensor? What resolution can you achieve?
As for your picture, I doubt you'd be able to recover much. The resolution is poor, and there's white and black dots at the size of individual pixels. Paper exhibits bleeding, as ink is a liquid,and paper is a fiber. The problem of bleeding even led to development of ink traps in typefaces to make characters sharp. A print medium could probably not reproduce a single white pixel surrounded in black.
On the other hand,it's two colors. If you print it in large enough scale, you will be able to accurately recover all information present, given that you know it is in two colors only, and pixels are printed significantly larger than any bleed effects. What size this will be probably depends on printing technology and paper stock used.