Resolution helps in this situation but not much: the Nokia Lumia 1020 has 41 megapixels and the photos are far from good. Only the use of special equipment and good illumination make an image ready to place on a billboard. This raster images are taken with professional cameras that capture every detail of the scene.
You may find plugins that convert images to high resolution minimizing the loss of detail, but the results are blurry and smudgy even when the result is high-res.
Take into consideration that when you look at a billboard you are
looking from a far distance, and it is hard to detect irregularities
for the human eye. It will always look good, unless you have superhuman
Also, in Photoshop or any other photo retouching program you may use sharpen filters that "cheat" the human eye, making you believe that what you are seeing is a very sharp image. For example, this site has a tool that
suggests how much 'sharpen' you must apply to an image based on the distance of the viewer.