I am looking for (lossy or lossless) compression algorithms dedicated to complex signals. The latter could be composite data (like the left and right for stereo audio), a Fourier transformation or an intermediate step of a complex processing, an Hilbert pair of generic signals, or complex measurements like some NMR (Nuclear magnetic resonance ) or mass spectrometry data.
A little background: I have been working on real signal and image coding, and mildly on video and geological mesh compression. I have practiced adaptive lossless and lossy compression (RLS, LPC, ADPCM), Huffman and arithmetic coding, transforms (DCT, wavelets), etc. Using standard compression tools separately on each of the real and the imaginary parts is not the main aspect of the question. I am interested in compression-related ideas specific to complex data, for instance:
- sampling of the complex plane,
- joint quantization of module and phase,
- optimal quantization of 2D complex values: Loyd-Max is "optimal" for 1D data. I remember that 2D optimal quantization is generally more complicated. Are there 2D binnings dedicated to complex, or for instance Gauss integers?
- entropy coding methods, arranging along complex "features" (angle, magnitude),
- entropy calculation for complex data,
- use of specific statistical tools (e.g. from Statistical Signal Processing of Complex-Valued Data: The Theory of Improper and Noncircular Signals)
- integer transformations for Gauss integers.
I have not found much tools. My scarce references are:
- An experimental audio codec based on warped linear prediction of complex valued signals, 1997
- Compression of Complex-Valued SAR Images, 1999 (Download)
- Lossless Signal Processing with Complex Mersenne Transforms, 2003
I would be interested in more authoritative references. A compression file format dedicated to complex data would be a plus.