I'm willing to print a black and white picture with quite big dimension (more or less, 3x2 feet), but the image has pretty low resolution and appears quite blury. I was wondering which kind of post processing operation could help me sharpening the image, with softwares as GIMP or photoshop.
Contrary to all those Sci-Fi and police shows on TV it is not possible to create detail where there is non in an image. So if your image is low resolution, blowing it up will only add to the pain. If there is any detail in the image and the image has sufficient bit depth and has not been compressed by creating a jpeg, then you may have a chance.
Use PhotoZoom Pro 5 for the enlargement and you won't lose details. Then sharpen with Photoshop's Smart Sharpen tool to remove as much blur as possible in your image. Play around with the settings to see what lens blur or motion blur, or gaussian blur will do to help bring back details in your image.
If your image is real bad you may be better off sharpening it a bit first to remove the blur but not actually adding sharpness. Then increase the sharpness after the enlargement.
Three techniques worth looking at, both using open source tools. 1. Using gimp try oversampling, scaling up, using the Lanczos algorithm. 2. Intentionally reduce resolution but provide texture using a halftone filter. This is what magazines used for printing. 3. Use Inkscape bitmap importing using potrace. This gives a vector representation that can be manipulated and gives a lithographic or engraved look. This is very effective for scans of photos from old books or newspapers.
Aside from using resizing and sharpening techniques, you can add some background noise, texture, or "grain". This can be done digitally or by selecting an output medium such as matte paper or canvas. This will increase the apparent sharpness of the image by triggering the brain's built-in pattern-seeking mechanisms.