This is a VERY interesting question. I used to deal with this type of problem with live IR imagers (video systems). We actually had algorithms built into the cameras to deal with this problem prior to the user ever seeing or getting their hands on the image. Couple questions:
1) are you dealing with RAW images or are you dealing with already pre-processed grayscale (or RGB) images?
2) what is your ultimate goal with these images. Is the goal to simply get rid of the lines regardless of the quality in the rest of the image that results, or is the point to preserve the absolute best image quality. Are you to perform other processing afterwards?
I agree that those lines are most likely in ALL of your images. There are 2 reasons for those lines ever showing up in an image, one would be in a bright scene where OP AMPs for columns get saturated, thus causing whole columns of your image to get the brightest value camera can output. Another reason could be bad OP AMPs or ADCs (Analog to Digital Converters) themselves (Most likely not an ADC as normally there is essentially 1 ADC for th whole sensor, which would make the whole image bad, not your case). The saturation case is actually much more difficult to deal with (and I don't think this is your problem). Note: Too much saturation on a sensor can cause bad pixels and columns to arise in your sensor (which is why they say never to point your camera at the sun). The bad column problem can be dealt with. Above in another answer, someone had you averaging images. While this may be good to find out where the bad columns (or bad single pixels, or the noise matrix of your sensor) are (and you would have to average pointing the camera at black, white, essentially solid colors), it isn't the correct answer to get rid of them. By the way, what I am explaining with the black and white and averaging, and finding bad pixels, etc... is called calibrating your sensor.
OK, so saying you are able to get this calibration data, then you WILL be able to find out which columns are bad, even single pixels.
If you have this data, one way that you could erase the columns out is to:
for each bad column
for each pixel (x, y) on the bad column
pixel(x, y) = Average(pixel(x+1,y),pixel(x+1,y-1),pixel(x+1,y+1),
pixel(x-1,y),pixel(x-1,y-1),pixel(x-1,y+1))
What this essentially does is replace the bad pixel with a new pixel which is the average of the 6 remaining good pixels around it. The above is an over-simplified version of an algorithm. There are certainly cases where a singly bad pixel could be right next the bad column and shouldn't be used for averaging, or two or three bad columns right next to each other. One could imagine that you would calculate the values for a bad column, then consider that column good in order to move on to the next bad column, etc....
Now, the reason I asked about the RAW versus B/W or RGB. If you were processing a RAW, depending on the build of the sensor itself, it could be that only one sub-pixel (if you will) of the bayer filtered image sensor has the bad OP AMP. If you could detect this, then you wouldn't necessarily have to throw out the other good sub-pixel's data. Secondarily, if you are using an RGB sensor, to take a grayscale photo, and you shot it in RAW, then you may be able to calculate your own grayscale pixels. Many sensors when giving back a grayscale image when using an RGB sensor, will simply pass back the Green pixel as the overall pixel. This is due to the fact that it really serves as the luminescence of an image. This is why most image sensors implement 2 green sub-pixels for every r or g sub-pixel. If this is what they are doing (not ALL sensors do this) then you may have better luck getting rid of just the bad channel column, and performing your own grayscale conversion using.
gray = (0.299*r + 0.587*g + 0.114*b)
Apologies for the long winded answer, but I hope this is still informational to someone :-)