Electronic – Linear image sensor output signal processing

The typical clock frequency mentioned in the datasheet is 8 MHz. I haven't used an ATMega but I expect the onboard ADC has a maximum rate of < 1Msps.
You could probably drop the frequency but then your scanning would be slow. The datasheet doesn't mention minimums/maximums, so I'd be wary of doing anything other than what it does mention (not a lot) without confirming with Rohm. Maybe there is a separate app note that covers this stuff.

Anyway, you would be best off with a flash ADC with parallel interface, and a uC fast enough to read it comfortably (say at least 20 MIPS, maybe with a parallel port peripheral/DMA)
The datasheet gives no info in the analogue output quality, but I wouldn't expect it to be great so an 8/10 bit ADC will probably be suitable.
Then it looks like a simple case of pulse the SP input, wait 65 cycles and read just after the negative edge for 144 cycles. You may need an inverter with a slight delay (low pass RC would probably do to trim) on the ADC clock if it samples on the rising edge and you are driving both ADC/Module from same output pin.

If the pattern of the column is the same whenever they appear, the problem is called fixed-pattern noise. This is just something you need to deal with, especially when dealing with a raw sensor. The sensor vendor should be able to help with characterizing it.

To deal with it, you can either go through a manual calibration procedure that allows you to derive offset and gain correction factors for each column, which you then store in nonvolatile memory, or you can develop an adaptive algorithm that can recognize and compensate for FPN in live images on the fly.

To characterize the FPN, you'll need to take a series of flat-field images (same amount of light on each pixel) at various light levels (including completely dark) and various exposure times. For each combination of light level and exposure, take the average value of the pixels in each column, and average these values over many frames (to eliminate thermal noise).

From this set of data for each sensor column, you will be able to determine what gain and offset values to apply to that column to eliminate the fixed pattern. You will also be able to determine whether the correction values need to be different for different exposure times, or a common set of values will work well enough for all exposure settings.

You'll also want to do this across a number of individual sensors, to make sure that the statistical variations among sensors don't invalidate the solution you come up with.