Nonlinear encoding in multilayer LNL systems optimized for the representation of natural images

by Christoph Zetzsche, Ulrich Nuding

Abstract:

We consider the coding properties of multilayer LNL (linear-nonlinear-linear) systems. Such systems consist of interleaved layers of linear transforms (or filter banks), nonlinear mappings, linear transforms, and so forth. They can be used as models of visual processing in higher cortical areas (V2, V4), and are also interesting with respect to image processing and coding. The linear filter operations in the different layers are optimized for the exploitation of the statistical redundancies of natural images. We explain why even simple nonlinear operations-like ON/OFF rectification-can convert higher-order statistical dependencies remaining between the linear filter coefficients of the first layer to a lower order. The resulting nonlinear coefficients can then be linearly recombined by the second-level filtering stage, using the same principles as in the first stage. The complete nonlinear scheme is invertible, i.e., information is preserved, if nonlinearities like ON/OFF rectification or gain control are employed. In order to obtain insights into the coding efficiency of these systems we investigate the feature selectivity of the resulting nonlinear output units and the use of LNL systems in image compression.

Reference:

Nonlinear encoding in multilayer LNL systems optimized for the representation of natural images (Christoph Zetzsche, Ulrich Nuding), In Human Vision and Electronic Imaging XII (Bernice E. Rogowitz, Thrasyvoulos N. Pappas, Scott J. Daly, eds.), SPIE-Intl Soc Optical Eng, 2007.

Bibtex Entry:

@InProceedings{Zetzsche2007, author = {Christoph Zetzsche and Ulrich Nuding}, title = {Nonlinear encoding in multilayer {LNL} systems optimized for the representation of natural images}, booktitle = {Human Vision and Electronic Imaging {XII}}, year = {2007}, editor = {Bernice E. Rogowitz and Thrasyvoulos N. Pappas and Scott J. Daly}, month = {feb}, publisher = {{SPIE}-Intl Soc Optical Eng}, abstract = {We consider the coding properties of multilayer LNL (linear-nonlinear-linear) systems. Such systems consist of interleaved layers of linear transforms (or filter banks), nonlinear mappings, linear transforms, and so forth. They can be used as models of visual processing in higher cortical areas (V2, V4), and are also interesting with respect to image processing and coding. The linear filter operations in the different layers are optimized for the exploitation of the statistical redundancies of natural images. We explain why even simple nonlinear operations-like ON/OFF rectification-can convert higher-order statistical dependencies remaining between the linear filter coefficients of the first layer to a lower order. The resulting nonlinear coefficients can then be linearly recombined by the second-level filtering stage, using the same principles as in the first stage. The complete nonlinear scheme is invertible, i.e., information is preserved, if nonlinearities like ON/OFF rectification or gain control are employed. In order to obtain insights into the coding efficiency of these systems we investigate the feature selectivity of the resulting nonlinear output units and the use of LNL systems in image compression.}, doi = {10.1117/12.710650}, url = {10.1117/12.710650">http://dx.doi.org/10.1117/12.710650}, }