Cramér-Rao bounds for parametric shape estimation in inverse problems

Research output: Contribution to journalArticlepeer-review


We address the problem of computing fundamental performance bounds for estimation of object boundaries from noisy measurements in inverse problems, when the boundaries are parameterized by a finite number of unknown variables. Our model applies to multiple unknown objects, each with its own unknown gray level, or color, and boundary parameterization, on an arbitrary known background. While such fundamental bounds on the performance of shape estimation algorithms can in principle be derived from the Cramér-Rao lower bounds, very few results have been reported due to the difficulty of computing the derivatives of a functional with respect to shape deformation. In this paper, we provide a general formula for computing Cramér-Rao lower bounds in inverse problems where the observations are related to the object by a general linear transform, followed by a possibly nonlinear and noisy measurement system. As an illustration, we derive explicit formulas for computed tomography, Fourier imaging, and deconvolution problems. The bounds reveal that highly accurate parametric reconstructions are possible in these examples, using severely limited and noisy data.

Original languageEnglish (US)
Pages (from-to)71-84
Number of pages14
JournalIEEE Transactions on Image Processing
Issue number1
StatePublished - Jan 2003


  • Cramér-Rao bounds
  • Deconvolution
  • Domain derivative
  • Fourier imaging
  • Global confidence region
  • Linear inverse problems
  • Parametric shape estimation
  • Performance analysis
  • Radon transform
  • Tomography

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Computer Graphics and Computer-Aided Design
  • Computer Vision and Pattern Recognition
  • Software
  • Electrical and Electronic Engineering
  • Theoretical Computer Science


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