QuoteOriginally posted by: blackscholesIn the wavelet domain, isn't the signal made sparse so you can theoretically speed up your computation by dropping out the zeros.Unless the original signal was created by a noise-free wavelet-based process (with a small number of modes and the same kernel as your chosen transform), there will be no "zeros" and no lossless data reduction. In general, all components will have non-zero energy and removing any of the components will mean losing some information. Whether that lost information is "essential" is another issue.First, you need to model the signal process and any noise processes. Then you can pick the best wavelet kernel that creates the greatest discrimination between signal and noise. Then you can develop a proper threshold for deleting wavelet components that have a very low (but always non-zero) probability of containing useful information.You might also think in transmitter-receiver terms with a given low frequency rate of information encoded on a high frequency time-varying signal (e.g., a person striking X piano keys per second producing Y kHz audio signal) that's imperfectly measured by a microphone and run through a wavelet-based process to decide which key they hit and when they hit it.