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Related Experiment Video

Updated: May 11, 2026

Lensless Fluorescent Microscopy on a Chip
11:23

Lensless Fluorescent Microscopy on a Chip

Published on: August 17, 2011

Near-optimal compressed sensing guarantees for total variation minimization.

Deanna Needell1, Rachel Ward

  • 1Department of Mathematics, Claremont McKenna College, Claremont, CA 91711, USA. dneedell@cmc.edu

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|May 28, 2013
PubMed
Summary

This study reconstructs multidimensional signals from limited data using total variation minimization. It guarantees accurate signal recovery even with significantly fewer measurements than signal dimensions.

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Last Updated: May 11, 2026

Lensless Fluorescent Microscopy on a Chip
11:23

Lensless Fluorescent Microscopy on a Chip

Published on: August 17, 2011

Area of Science:

  • Applied Mathematics
  • Signal Processing
  • Image Reconstruction

Background:

  • Signal reconstruction from underdetermined measurements is ill-posed without assumptions.
  • Total variation minimization offers good approximations for signals like natural images.

Purpose of the Study:

  • Extend existing reconstruction guarantees for 2D images to arbitrary dimensions (d ≥ 2).
  • Analyze reconstruction performance for isotropic total variation problems.

Main Methods:

  • Utilizing total variation minimization for signal reconstruction.
  • Developing theoretical guarantees for reconstruction accuracy.

Main Results:

  • Demonstrated reconstruction of multidimensional signals from O(s^d log(N(d))) linear measurements.
  • Achieved reconstruction accuracy related to the best s-term approximation of the signal's gradient.

Conclusions:

  • Reconstruction guarantees are optimal up to polynomial factors in spatial dimension d.
  • Total variation minimization is effective for high-dimensional signal recovery from limited data.