The local low-dimensionality of natural images: International conference on learning representations (ICLR)

Olivier J. Hénaff, Johannes Ballé, Neil C. Rabinowitz, Eero Simoncelli

Research output: Contribution to conferencePaper

Abstract

We develop a new statistical model for photographic images, in which the local responses of a bank of linear filters are described as jointly Gaussian, with zero mean and a covariance that varies slowly over spatial position. We optimize sets of filters so as to minimize the nuclear norm of matrices of their local activations (i.e., the sum of the singular values), thus encouraging a flexible form of sparsity that is not tied to any particular dictionary or coordinate system. Filters optimized according to this objective are oriented and band-pass, and their responses exhibit substantial local correlation. We show that images can be reconstructed nearly perfectly from estimates of the local filter response covariance alone, and with minimal degradation (either visual or MSE) from low-rank approximations of these covariances. As such, this representation holds much promise for use in applications such as denoising, compression, and texture representation, and may form a useful substrate for hierarchical decompositions.

Original languageEnglish (US)
StatePublished - Jan 1 2015
Event3rd International Conference on Learning Representations, ICLR 2015 - San Diego, United States
Duration: May 7 2015May 9 2015

Conference

Conference3rd International Conference on Learning Representations, ICLR 2015
CountryUnited States
CitySan Diego
Period5/7/155/9/15

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ASJC Scopus subject areas

  • Education
  • Computer Science Applications
  • Linguistics and Language
  • Language and Linguistics

Cite this

Hénaff, O. J., Ballé, J., Rabinowitz, N. C., & Simoncelli, E. (2015). The local low-dimensionality of natural images: International conference on learning representations (ICLR). Paper presented at 3rd International Conference on Learning Representations, ICLR 2015, San Diego, United States.