Here is what I did with Lyra.
Step 1 is to rotate the image, e.g., in Gimp or Photoshop, until the trails are all horizontal.
While doing this, identify the length of the tracks in pixels, in this case 20. Create an all-white 20x1 image. (I used ImageMagick, but a photo editor can also do it.) This image is the point spread function. Then run ImageJ. Then load both the 20x1 image and the rotated sky image. I made sure the sky image was the active image in ImageJ (click on it), and ran Plugins | DecompositionLab. Set the algorithm to Richardson-Lucy. In the Background module, set Subtract Background and Use minimal intensity to darken the sky. Run and here it is:
It's far from perfect but much better. Here's a before-and-after zoom. Note how nicely the double star was picked up.