Efficient and Robust Signal Approximations
CARNEGIE-MELLON UNIV PITTSBURGH PA SCHOOL OF COMPUTER SCIENCE
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Representation of natural signals such as sounds and images is critically important in a broad range of fields such as multimedia, data communication and storage, biomedical imaging, robotics, and computational neuroscience. Often it is crucial that the representation be efficient, i.e., the signals of interest are encoded economically. It is also desirable that the representation be robust to various types of noise. In this thesis, we advocate several ways to expand current signal encoding approaches via the framework of adaptive representations. In recent decades, the multiresolution paradigm has provided powerful mathematical and algorithmic tools to signal encoding. In spite of widely proven effectiveness, such methods ignore statistical structure of the class of signals they should represent. On the other hand, high computational costs artificially confine standard linear adaptive statistical models to relatively small block-based encoding scenarios. We show that a good tradeoff between computational complexity and coding efficiency can be achieved via a hybrid encoding scheme Multiresolution ICA.
- Numerical Mathematics
- Statistics and Probability