Well, I've not tried it, but maybe others could say if it is good or bad idea, how about this...
Print out the image at its current size on best glossy paper you can get hold of. Don't try expand the image, like fit to paper, just leave it as it is in its original size. Set the printer's settings to maximum possible, in other words, depending on printer make and model, find highest quality setting, like Best rather than Fast, Print it out.
Stick the printed out image on wall, then set up a camera on tripod (or any other support you can use) at best possible distance from the printed out copy. Make sure it fills up the viewfinder screen. Don't use direct flash as it may reflect off the glossy paper. Use camera on lowest ISO setting possible (like 100) to avoid noise grain, but at the camera's maximum resolution and highest quality setting (For example: With a Nikon, it's set to Fine).
Take a photo. Hopefully you have a second photograph at the highest resolution of the original image at the lowest resolution.
Just don't try to resize the new photo to a smaller resolution or compress it too much to save desk space, otherwise, next time you open it and attempt to upscale it, you'll be back to having blocky pixels, leave the new copy at the highest resolution.
No idea if it's of any help, but I'm guessing it's better than nothing.