Compression is, as every schoolchild knows, bad. Even so, there are more reasons than the obvious why it can be a questionable idea to involve a lot of mathematics in the storage of images
With the very best equipment – such as Sony's HDCAM-SR tape format or SR Memory flash system – the recorded noise due to compression can be considerably less than the noise in the camera. In these systems, compression artifacts can be as trivial as errors in the least significant bit or two in any one pixel. This is technology to which any desktop computer has access, too; certain varieties of SR use compression based on the MPEG-4 standard, as does Panasonic's AVC Ultra spec, announced at NAB last year. Even more than this, it's actually possible to compress image data with absolutely no loss of quality whatsoever. Techniques such as Huffman coding, an entropy encoding algorithm developed in 1952 by computer scientist David A. Huffman, can reduce the space required to store information by 1.5 or perhaps 2 times, and yet recover the original data precisely. A complete description of the information-theory witchcraft required to achieve this is beyond the scope of this article, but it has certainly been implemented as a video codec called HuffYUV which operates exactly as advertised.
Lossless is possible
The work required to perform Huffman encoding on the huge data sets of video footage makes it impractical for use in most cameras, and many cameras will require more reduction in bitrate than it can provide. Certain varieties of h.264 – not the varieties commonly used in cameras – use arithmetic coding as part of its suite of technologies, another lossless compression technique. Arithmetic coding also takes a lot of work to encode (though not much to decode), and in any case it is not used as the sole mechanism of compression in h.264.
The thing is, even if lossless compression techniques were widely applied in cameras, which they aren't, and even if there were absolutely no concerns over image quality with lossy codecs, which there are, the deeper problem would remain: the problem of compatibility.