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Random Projections of Smooth Manifolds
Many types of data and information can be described by concise models that suggest each data vector (or signal) actually has â few degrees of freedomâ relative to its size N. This is the motivation for a variety of ...
Representation and Compression of Multi-Dimensional Piecewise Functions Using Surflets
We study the representation, approximation, and compression of functions in M dimensions that consist of constant or smooth regions separated by smooth (M-1)-dimensional discontinuities. Examples include images containing ...
Wavelet-domain Approximation and Compression of Piecewise Smooth Images
The wavelet transform provides a sparse representation for smooth images, enabling efficient approximation and compression using techniques such as zerotrees. Unfortunately, this sparsity does not extend to <i>piecewise ...
Random Projections of Signal Manifolds
Random projections have recently found a surprising niche in signal processing. The key revelation is that the relevant structure in a signal can be preserved when that signal is projected onto a small number of random ...