Old school signal processing, not based on machine learning but instead on a translation-invariant Haar wavelet decomposition, profitably exploiting correlations across channels. The manuscript includes an accessible and brief "Theory" section and a longer appendix. All it needs to run is a test function between two data points.
In their benchmarks and use cases, the new method outperforms existing denoising methods. In both time series and on fluorescent microscopy images.
Were polyphonic filters common in the 1960s? I've discussed this with @ezra and we think the answer is no, but I wanted to ask around here too. I am aware of only one example of a customized band pass filter from c. 1966, which could be played with a keyboard, allowing for polyphony, i.e., (I think) playing the input through several separate passbands simultaneously, where the width of each passband would be (up to?) a terce or octave. #SoundSynthesis#SignalProcessing#ExperimentalMusic
The Voyager 1 and 2 spacecraft sent back hundreds of color pictures as they flew by Jupiter and Saturn. But they could only transmit 14 kilobytes per second! So they used a highly efficient error-correcting code: the Golay code.
This is a 24-bit code. The first 12 bits convey the message, and the rest are computed from those. Up to 3 of the 24 bits can be wrong and you can still figure out what was intended! Up to 7 can be wrong and you can still know there was an error!
This image by @gregeganSF shows how it works. This shape, an icosahedron, has 12 vertices. There are also 12 pentagons inside this shape. Your first 12 bits say which pentagons to light up. 0 means "leave it dark" and 1 means "light it up". Your second 12 bits say which vertices to light up.
The second 12 bits are computed from the first 12 using this trick:
If you light up a single pentagon, then you only light up the vertices that don't contain that pentagon! What if you light up a bunch of pentagons? Then you use addition mod 2. You work out which vertices get lit up for each pentagon you light up. You think of those results as 12-bit strings. Then you add them up mod 2.
The last part may sound complicated, but it's a common trick, called a "linear code". What's special about the Golay code is its connection to the icosahedron. This gives it remarkable features, which I explain here:
@johncarlosbaez@gregeganSF
The latest NASA missions use the same coding scheme as 5G physical layer: LDPC (low-density parity-check) code.
Among capacity-approaching codes
LDPC approaches the Shannon limit more closely than any other class of codes.
LDPC was invented by Robert Gallager in 1961 and mostly forgotten (“a bit of 21st-century coding that happened to fall in the 20th century”). LDPC uses sparse Tanner graph.