Title of article :
Cramer-Rao bounds for parametric shape estimation in inverse problems
Author/Authors :
P.، Moulin, نويسنده , , Ye، Jong Chul نويسنده , , Y.، Bresler, نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2003
Pages :
14
From page :
71
To page :
84
Abstract :
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 Cramer-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. We provide a general formula for computing Cramer-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.
Keywords :
heat transfer , natural convection , Analytical and numerical techniques
Journal title :
IEEE TRANSACTIONS ON IMAGE PROCESSING
Serial Year :
2003
Journal title :
IEEE TRANSACTIONS ON IMAGE PROCESSING
Record number :
100503
Link To Document :
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