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CHAPTER6

Super Resolved Imaging

in Wigner-Based Phase

Space

Zeev Zalevsky
School of Engineering, Bar-Ilan University
Ramat-Gan, Israel

6.1 Introduction
Super resolution (SR) is a field integrating the sciences of optics with
the expertise of image processing and computer vision science. 1–7
Basically any imaging system, digital as well as a human eye, has a
limited capability to separate close spatial features. This limitation can
be related either to the diffraction or to the geometry of the imaging
1
sensing array. In the case of diffraction, given an imaging lens with
limited aperture size, not all the rays reflected from the object are
collected by the lens. According to Rayleigh criteria, 8–10 this limitation
is proportional to the product of the wavelength of the illumination
and the F number of the optics (the ratio of the focal length to the
diameter of the lens). Thus, the smaller the F number, the better the
spatial separation becomes. In the case of the geometry of the sensing
array, the smaller the pixels are, i.e., the denser the spatial sampling of
the space, the better the capability to reconstruct closer point sources
originated from the imaged object. 1
To overcome the limitation of a given imaging system, one may
convert the spatial degrees of freedom, which before could not pass
through the limited spectral bandwidth of the imaging system, into
other domains that the imaging system can transmit, and then after

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