Convert black to white in scanned PDF

I have scanned many pages on a scanner with scan type set to 300 dpi black and white text and output format set to PDF. Unfortunately, a great deal of the pages were from a book and there is a shadow on the scanned pages. I wonder if there is any possibility to make the black area (which I marked with blue stripes below) automatically, with a function in Adobe PDF or any other software, white. In the red circle below, there is some text that spans from the black to the white background. This text I would like to be all black and appear on white background.

I don't think that this can be done easily. As you have scanned in black&white mode there is no way to distinguish between black shadow pixels and black text pixels.

@Robert I'm afraid so. However, this should be possible, especially when remembering that we deal with a large black connected area. Text pixels are not connected with that many other black pixels. Therefore, I hoped (and still hope) that there are some simple tool that does this.

And what about the white text pixels inside the large black connected area. They can be distinguished, since they are inside the large black connected area. They are surrounded by the large black connected area.

Then where is the problem? Extract the image from the PDF file and use an image editor for editing the extracted JPG file.

@Robert I hope that there are some existing tools that perform the action directly on the PDF. I have scanned around 1 000 pages with this problem and I am afraid it would take an enormous amount of time to fix all the pages with a simple image editor.