What you're basically describing is compressive sensing. The basic idea is that if you can find a domain in which your data is maximally sparse, then you can tr

What you're basically describing is compressive sensing. The basic idea is that if you can find a domain in which your data is maximally sparse, then you can transmit the same information with many fewer bits. Unless you're extremely lucky with your basis functions, it is not strictly speaking a lossless compression algorithm.