Correct the image's borders illumination

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I'm developing an algorithm to stich images of vines. These images were taken at night with artificial illumination, because of this, the image's center is very well illuminated but their borders are almost black. To correct this I have tried the following:

1 - Convert the image to LAB.

2 - Get the channel L.

3 - Increase that channel's pixel values, following this rule: The incrementation value is the highest in the border's pixels, and it decreases as it reaches the image's center. For example, for an image's line:

                             Left border               Center                      Right border
Position of the pixel        0      1      2       3      4        5        6        7       8
Incrementation value         1      0.8   0.5     0.2    0.0      0.2       0.5     0.8     0.1

I think this method is not very good because it's "creating" information. How can I do this in a better way?