On a Mathematical Theory of Coded Exposure

Abstract

This paper proposes a mathematical model and formalism to study coded exposure (flutter shutter) cameras. The model includes the Poisson photon (shot) noise as well as any additive (readout) noise of finite variance. This is an improvement compared to our previous work that only considered the Poisson noise. In addition, closed formulae for the Mean Square Error and Signal to Noise Ratio of the coded exposure method are given. These formulae take into account for the whole imaging chain, i.e., the Poisson photon (shot) noise, any readout noise of finite variance as well as the deconvolution and are valid for any exposure code. In addition, we give an explicit formula that gives an absolute upper bound for the gain of any coded exposure cameras in function of the temporal sampling of the exposure code. The gain is to be understood in terms of Mean Square Error (or equivalently in terms of Signal to Noise Ratio), with respect to a snapshot.

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 2014
Accession Number
ADA610254

Entities

People

  • Stanley Osher
  • Yohann Tendero

Organizations

  • University of California, Los Angeles

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Acquisition
  • Additives (Chemicals)
  • Cameras
  • Computational Science
  • Fourier Series
  • Images
  • Mathematical Analysis
  • Mathematical Models
  • Models
  • Numbers
  • Periodic Functions
  • Probability
  • Random Variables
  • Sampling
  • Stochastic Processes
  • Time Intervals
  • Two Dimensional

Fields of Study

  • Physics

Readers

  • Acoustics.
  • Calculus or Mathematical Analysis
  • Image Processing and Computer Vision.