I feel a bit like Jeff Goldblum's character "David" in "Independence Day"...
I got a lock on the pattern, so I can filter it out...
Okay, so figuring out image aberrations and trying to think of ways to remove them is a hobby of mine, believe it or not...
In this case I converted the image to 16 bits/channel and a linear color profile, did a high pass filter operation, reduced the image to 1 pixel high, then stretched it back to the original height. Then I could easily see the 8 pixel vertical pattern. The accuracy of the pattern wasn't quite even, so I used a technique from astroimage processing to average successive repetitions of the pattern, each moved right 8 pixels. In the end I got something the full size of the image that looked like this (this image is cropped and enhanced to show the pattern more clearly).

Once the above pattern derived, removing the pattern from the original image is a matter of placing that pattern over the image, inverting the brightness levels, and using Overlay mode mixing.
Since it's an 8 pixel-wide repeating pattern of light to dark transitions, I'm imagining it's possibly a miscalibration (or just plain bug) in the JPEG compression algorithm used by the camera software. Eugenio.NYC's advice to use the JPEG noise reduction was good.

-Noel