JSON isn't an image
A .json file stores text data — settings, coordinates, lists — not pixels. There's no image inside to extract, and a picture can't be saved as a JSON data file.
Looking to turn a BMP into JSON? Here's the honest answer — and the conversions that actually work.
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BMP is an uncompressed raster format that stores pixel data with no quality loss, producing large files. It is common on Windows.
BMP opens in most image viewers and editors on Windows and Mac.
No — JSON is a data format, not an image, so there's nothing to convert. You can convert your BMP to PNG, JPG or TIFF instead.
JSON is a text-based data format used for app settings and, with a matching image, sprite-sheet coordinates. It isn't a picture.
A sprite sheet is a .png + .plist pair. Use a texture packer (TexturePacker, Cocos2d) to pack or unpack them together; a single-file converter can't.