Light field reconstruction using sparsity in the continuous Fourier domain

Lixin Shi, Haitham Hassanieh, Abe Davis, Dina Katabi, Fredo Durand

Research output: Contribution to journalArticlepeer-review

Abstract

Sparsity in the Fourier domain is an important property that enables the dense reconstruction of signals, such as 4D light fields, from a small set of samples. The sparsity of natural spectra is often derived from continuous arguments, but reconstruction algorithms typically work in the discrete Fourier domain. These algorithms usually assume that sparsity derived from continuous principles will hold under discrete sampling. This article makes the critical observation that sparsity is much greater in the continuous Fourier spectrum than in the discrete spectrum. This difference is caused by a windowing effect. When we sample a signal over a finite window, we convolve its spectrum by an infinite sinc, which destroys much of the sparsity that was in the continuous domain. Based on this observation, we propose an approach to reconstruction that optimizes for sparsity in the continuous Fourier spectrum. We describe the theory behind our approach and discuss how it can be used to reduce sampling requirements and improve reconstruction quality. Finally, we demonstrate the power of our approach by showing how it can be applied to the task of recovering non-Lambertian light fields from a small number of 1D viewpoint trajectories.

Original languageEnglish (US)
Article numbera12
JournalACM Transactions on Graphics
Volume34
Issue number1
DOIs
StatePublished - Dec 29 2014
Externally publishedYes

Keywords

  • Computational photography
  • Continuous spectrum
  • Fourier transform
  • Light fields
  • Sparse fft

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design

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