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I would tend to doubt it, as that would defeat the very purpose of securely deleting a file.
 
With software? Not really. You'll have to go to professionals who'll charge you an arm and a leg to get it back.

Because when you 'securely delete' a file, it actually physically writes over the portion of the drive that your file was stored on with random data, making it all but impossible to recover unless you had powerful equipment which basically looks at the shadow of what was there previously.
 
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