Title :
On a Link Between Kernel Mean Maps and Fraunhofer Diffraction, with an Application to Super-Resolution Beyond the Diffraction Limit
Author :
Harmeling, Stefan ; Hirsch, Michele ; Scholkopf, Bernhard
Author_Institution :
Max Planck Inst. for Intell. Syst., Tubingen, Germany
Abstract :
We establish a link between Fourier optics and a recent construction from the machine learning community termed the kernel mean map. Using the Fraunhofer approximation, it identifies the kernel with the squared Fourier transform of the aperture. This allows us to use results about the invertibility of the kernel mean map to provide a statement about the invertibility of Fraunhofer diffraction, showing that imaging processes with arbitrarily small apertures can in principle be invertible, i.e., do not lose information, provided the objects to be imaged satisfy a generic condition. A real world experiment shows that we can super-resolve beyond the Rayleigh limit.
Keywords :
Fourier transform optics; Fourier transforms; Fraunhofer diffraction; Rayleigh scattering; image resolution; learning (artificial intelligence); Fourier optics; Fraunhofer approximation; Fraunhofer diffraction invertibility; Rayleigh limit; aperture; diffraction limit; imaging process; kernel mean maps; machine learning; squared Fourier transform; superresolution; Apertures; Diffraction; Fourier transforms; Kernel; Optical diffraction; Optical imaging;
Conference_Titel :
Computer Vision and Pattern Recognition (CVPR), 2013 IEEE Conference on
Conference_Location :
Portland, OR
DOI :
10.1109/CVPR.2013.144