Teletext is encoded as a non-return-to-zero signal with two levels representing one and zero. This is a fancy way of saying that a line of teletext data is a sequence of black and white "pixels" in the TV signal. Of course, since the signal is analogue there are no individual pixels, the signal is continuous. But you can imagine that there are pixels in the idealized "perfect" signal.
The problem of decoding teletext from a VHS recording is that VHS bandwidth is lower than teletext bandwidth. This means that the signal is effectively low pass filtered, which in terms of an image is equivalent to gaussian blurring.
There are methods for reversing gaussian blur, but they are designed to work with general image data. In the case of teletext we only have black or white levels, so these methods are not optimal. We can exploit the limitations on the input in order to get a better result. We can also exploit information about the protocol to further improve efficiency and accuracy.
When the black and white signal is blurred, the individual pixels are blurred in to each other. This makes the signal unreadable using normal methods, because instead of a clean sequence like "1010" you something close to "0.5 0.5 0.5 0.5". But all is not lost, because a sequence like "1111" or "0000" will be the same after blurring. So if you see a signal like "0.5 0.7 1.0 1.0" you can guess that the original was probably "0 1 1 1" or "0 0 1 1".
There are 45 bytes in each teletext line, so the space of possible guesses is 2^(45*8) which is a very big number, which makes trying every guess completely impractical. However there are ways to reduce this number:
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Nearly all bytes have a parity bit which means there are only 128 possible combinations instead of 256.
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Some bytes are hamming encoded. These have even fewer possible combinations.
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The first three bytes in the signal are always the same. We can use this to find the start of the signal in the sample data (it moves a bit in each line, but the width is always the same.)
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The protocol itself defines rules about which bytes are allowed in which positions, reducing the problem space further.
A known signal is recorded to a tape using a Raspberry Pi with rpi-teletext. This signal is played back into the computer, which builds a table of convolved -> original sequences.
The convolved training data can be compared to recorded tapes in order to determine what the data originally was. The line is first resampled to 1 sample per "bit". Then it is divided into "bytes". Each one is compared against the training tables, including a few bits before and after. The closest match is the most likely original signal.
This algorithm can be performed in parallel using CUDA. This allows deconvolution to run in near realtime with a GTX 780.
See TRAINING.md for more.
The algorithm outputs lots of teletext packets, but they will still not be perfect (even though they may be valid, they aren't necessarily correct.)
Since the teletext pages are broadcast on a loop, any recording of more than a few minutes will have multiple copies of every packet. This means, if two packets are received that only differ at a couple of bytes, they can be assumed to be the same.
The stream is first "paginated", ie split in to subpages.
All versions of the same subpage are compared, and for each byte, the most frequent decoding is used so for example if you had these inputs:
HELLO HELLP MELLO
Then the result "HELLO" would be decoded, since those are the most frequent bytes in this position. For this to work well, you need a lot of copies of every packet.