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Abstract:
We apply a general technique for learning overcomplete bases
(Lewicki and Sejnowski, 1997) to the problem of finding efficient
image codes. The bases learned by the algorithm are localized,
oriented, and bandpass, consistent with earlier results obtained
using different methods (Olshausen and Field, 1996; Bell and
Sejnowski 1997). We show that higher degrees of overcompleteness
produce bases which have much greater likelihood and results in a
Gabor-like basis with greater sampling density in position,
orientation, and scale. This framework also allows different bases
to be compared objectively by calculating their probability given
the observed data. Compared to the complete and overcomplete
Fourier and wavelet bases, the learned bases have much greater
probability and thus have the potential to yield better coding
efficiency. We demonstrate the improvement in the representation of
the learned bases by showing superior noise reduction
properties.
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