Losslessly double JPEG resolution without SmartScale

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How can I convert a 256x256 JPEG to a 512x512 JPEG without losing any quality? (I can use jpegtran, but that uses SmartScale, which isn't widely supported.)

It must be converted to JPEG specifically. If it cannot be a literally lossless conversion, can it get very close? Virtually lossless? Thanks.

EDIT: If it's not possible with any existing tool, please tell me if and how it might be possible in theory.

EDIT 2: The reason I'm asking is because I want to losslessly combine 512x512 image tiles from the internet in order to re-assemble a panoramic image. The problem is that some of these tiles (along the top and bottom rows of the image) are 256x256 resolution, and require stretching before being combined with the other tiles. So in short, most of the tiles are 512x512 and thus wouldn't require reencoding, but some 256x256 tiles would.

If the 256x256 JPEGs became 512x512 JPEGs, I could combine all the tiles with jpegtran without reencoding, and they would form a simple equirectangular image.

I don't want to encode these panoramas to a different format like PNG, if I can help it, but I know I may need to. So I'm wondering if these few half-sized tiles can be scaled up essentially losslessly.

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