Fast and exact method for computing a stack of images at various focuses from a four-dimensional light field

Ziv Mhabary, Ofer Levi, Eran Small, Adrian Stern

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


This paper presents an efficient method for computing a stack of images digitally focused at various lengths from a four-dimensional light field (LF). The main contribution of this work is a fast and algebraically exact method that does not require interpolation in the frequency or spatial domains as alternative methods do. The proposed imaging operator combines two-dimensional (2-D) fast Fourier transform with 2-D fractional Fourier transform and has computational complexity of O(N log N), where N is the number of pixels in the LF tesseract of dimension N=nx×ny×nu×nv. The whole method consists of unitary vector-based operations; therefore, parallel implementation is easy and can contribute additional speed up. While current state of the art methods suffer from inherent tradeoff between the reconstruction quality and computational complexity, the proposed method benefits of both low-computational complexity and high-reconstruction quality. We also offer a solution for refocusing at distances that are not included in the reconstructed images stack. For such a case, we provide a modified version of our method, which is also algebraically exact and has lower computational complexity than other exact methods.

Original languageEnglish
Article number043002
JournalJournal of Electronic Imaging
Issue number4
StatePublished - 1 Jul 2016


  • Fourier transforms
  • computational imaging
  • digital refocusing
  • integral imaging
  • light field
  • plenoptic camera

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics
  • Computer Science Applications
  • Electrical and Electronic Engineering


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