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Have a gradient map of a gray scale image and want to recover the original gray scale image.

While trying to implement a paper on artifact removal from photos I got stuck upon a point where I have the resultant artifact free image gradient but want to recover the corresponding image. The methods I have tried till now are not giving any fruitful result. Need help on this topic.

Have a gradient map of a gray scale image and want to recover the original gray scale image.

While trying to implement Have a paper on artifact removal from photos I got stuck upon gradient map of a point where I have the resultant artifact free gray scale image gradient but and want to recover the corresponding image. The methods I have tried till now are not giving any fruitful result. Need help on this topic.original gray scale image.