How can I remove white stripes from an old photo without losing detail?

Question

I have this old photo:

I want to remove these vertical white stripes from it.

I have managed to remove it by using the darken blend mode with motion blur, but as you can see down below, I have lost a lot of details that I couldn't retrieve by sharpening the image. I want to preserve as much detail as I can.

Answer 1

By doing a quick edit using Fourier Transform as described in this Imagemagick tutorial I managed to considerable reduce the annoying effect when viewed at 100%.

A more thorough edit using this method might provide better results, but the repeating pattern appears so often that some areas of the picture are basically left without any detail.

Answer 2

At a pixel level, you want to blur the lighter pixels horizontally, without blurring the picture as a whole too much. I took two times two similar steps in Adobe Photoshop to create the picture below.

The first two steps:

1. I selected the white colors using the "Select color range" tool, selecting an almost white pixel and using a large range to select similar colors.
2. Next, I used the custom filter (Menu: Filter, Other, Custom Filter) with all zero's except on the center row, I used the weights: 1, 2, 3, 2, 1. And a scale factor of 9 (the sum of the weights).

The effect of this is that the most white vertical stripes are averaged (blurred). Every pixel becomes a weighted average of its neighbors on the left and right.

In the second iteration, I did the same for the picture as a whole:

3. Deselect the previous selection (ctrl-d)
4. Repeat the same filter as before on the picture as a whole.

The result is this: