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I have reduced size of images and put them in a Word document. Can I get the original size and dpi back (I did not save the original!)

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Depends. If you just resized the image in Word, it probably only changed the display scaling and didn't actually resize the image.

If you did actually resize the image, though, this is an operation which inherently discards data. Once that information is gone, there's no way to get it back, because there's no where to get it back from.

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Can I get the original size and dpi back (I did not save the original!)

As mattdm mentioned if you only changed the scale of the image then nothing has been lost, yet.

When you export the image be certain to use an uncompressed format or you will be recompressing the data and losing some information.

If the original is gone you can upscale the image using various techniques, this does not "recover" the original, it recreates it by guessing.

Try Let'sEnhance.io (Online Tool), A Sharper Scaling (Download), Waifu2x (Online Tool or Download Source Code), etc.

Here are a couple of examples of the results you might expect:

Star Rails

Woman's Eye

There are also forensic techniques that you can use. These range from using your Operating System's "Undelete" command to using a program designed to scan your computer and look for deleted photos. See: "DIY Computer Forensics: How to Recover a Deleted File", one of many articles available on the subject. That will try to find your original photo and any partial or corrupted copies too.

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