SOME RECENT PREPRINTS
Title (No specific order)
The subspace segmentation problem, nonlinear approximations and applications
Akram Aldroubi
preprint
The subspace segmentation problem is fundamental in many applications. The goal is to cluster data drawn from an unknown union of subspaces. In this review article we state the problem and describe its connection to other areas of mathematics and
engineering. We then review the mathematical and algorithmic methods created to solve this problem and some of its particular cases. We also describe the problem of motion tracking in videos, its connection to the subspace segmentation problem, and compare the various techniques for solving it.
Key Words: Subspace clustering data clustering manifold learning data mining motion segmentation dictionary learning compressed sensing sampling and reconstruction nonlinear models dimensionality reduction.
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Dynamical Sampling: Time-Space Trade-off
Akram Aldroubi, Jacqueline Davis, and Ilya Krishtal
To appear in Foundation of Computational Mathematics
We consider the problem of spatiotemporal sampling in which an initial state of an evolution process is to be recovered from a set of samples at different time levels. We are particularly interested in lossless trade-off between spatial and temporal samples. We show that for a special class of signals it is possible to recover the initial state using a reduced number of measuring devices activated more frequently. We present several algorithms for this kind of recovery and describe their robustness to noise.
Key Words:Distributed sampling, reconstruction, Wiener denoising, frames.
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