TY - JOUR

T1 - Stopping rules for a nonnegatively constrained iterative method for ill-posed Poisson imaging problems

AU - Bardsley, Johnathan M.

N1 - Funding Information:
★ Received December 18, 2007. Accepted September 8, 2008. Communicated by Per Christian Hansen. ★★ This work was partially supported by the NSF under grant DMS-0504325.

PY - 2008/12

Y1 - 2008/12

N2 - Image data is often collected by a charge coupled device (CCD) camera. CCD camera noise is known to be well-modeled by a Poisson distribution. If this is taken into account, the negative-log of the Poisson likelihood is the resulting data-fidelity function. We derive, via a Taylor series argument, a weighted least squares approximation of the negative-log of the Poisson likelihood function. The image deblurring algorithm of interest is then applied to the problem of minimizing this weighted least squares function subject to a nonnegativity constraint. Our objective in this paper is the development of stopping rules for this algorithm. We present three stopping rules and then test them on data generated using two different true images and an accurate CCD camera noise model. The results indicate that each of the three stopping rules is effective.

AB - Image data is often collected by a charge coupled device (CCD) camera. CCD camera noise is known to be well-modeled by a Poisson distribution. If this is taken into account, the negative-log of the Poisson likelihood is the resulting data-fidelity function. We derive, via a Taylor series argument, a weighted least squares approximation of the negative-log of the Poisson likelihood function. The image deblurring algorithm of interest is then applied to the problem of minimizing this weighted least squares function subject to a nonnegativity constraint. Our objective in this paper is the development of stopping rules for this algorithm. We present three stopping rules and then test them on data generated using two different true images and an accurate CCD camera noise model. The results indicate that each of the three stopping rules is effective.

KW - Image reconstruction

KW - Iterative methods

KW - Regularization

KW - Statistical methods

UR - http://www.scopus.com/inward/record.url?scp=57649140529&partnerID=8YFLogxK

U2 - 10.1007/s10543-008-0196-6

DO - 10.1007/s10543-008-0196-6

M3 - Article

AN - SCOPUS:57649140529

SN - 0006-3835

VL - 48

SP - 651

EP - 664

JO - BIT Numerical Mathematics

JF - BIT Numerical Mathematics

IS - 4

ER -