This paper explores sparse coding of natural images in the highly overcomplete regime. We show that as the overcompleteness ratio approaches l0x, new types of dictionary elements emerge beyond the classical Gabor function shape obtained from complete or only modestly overcomplete sparse coding. These more diverse dic tionaries allow images to be approximated with lower L1 norm (for a fixed SNR), and the coefficients exhibit steeper decay. We also evaluate the learned dictionaries in a denoising task, showing that higher degrees of overcompleteness yield modest gains in peformance.
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Bruno A. Olshausen
Highly overcomplete sparse coding
", Proc. SPIE 8651, Human Vision and Electronic Imaging XVIII, 86510S (March 14, 2013); doi:10.1117/12.2013504; http://dx.doi.org/10.1117/12.2013504