Is it possible to undo the steganographic process given the modified image to reconstruct the original one? I want to obtain the same bits of the original image.
Not under normal circumstances. They have been changed.
Your question does not state whether or not the message is known. Any information like that can assist in the detective work that would help make any progress along these lines.
There is another possibility of having more information: For instance, Playboy.com places digital watermarks inside their images. So given a raw watermark and the steganos message, it is theoretically possible to reconstruct what was changed.
Of course, visually it will not matter. That is the beauty of steganography. If there are billions of possible colors and your eyes can really only tell the difference between 50-100,000 of them, then using those low-order bits is visually undetectable.
Where it gets complicated is if you use Steganos to put a message inside an image that already had another, the first one gets lost.
If you ask whether there is a scientific/engineering proven way/formula/algorithm to revert back to the original - then no, there is no such one (at least I am not aware of).
From practical standpoint, all de-stegano software today work first by trying to identify the patterns/signatures in the 'encrypted' file for known stegano software packages. if it succeeds, then it tries to reverse the changes back to original based on the known algorithm used by the known software. So if the file was processed by a custom software with a custom algorithm ( I can come with an algorithm to change say every 7th byte only, XORing every 3 bits, then change algorithm at exactly half the file size), it would not be reverted back.
Of course it does not mean it is so secure, just that there is no general algo/software to 'undo' changes done by any stegano-software. The statistical/manual process can still be applied comparing the file with a file standard looking for anomalies, then reiterating the process until the original is found to some degree of certainty.