1609.07937
Weak-lensing shear estimates with general adaptive moments, and studies of bias by pixellation, PSF distortions, and noise
Simon, Schneider
In WL, weighted quadrupole moments of the brightness profile in galaxy images are a common way to estimate gravitational shear. Employ general adapt moments (GLAM) to study causes of shear bias on a fundamental level and for a practical definition of an image ellipticity. For GLAM, the ellipticity is identical to that of isophotes of elliptical images, and this ellipticity is always an unbiased estimator of reduced shear. The theoretical framework reiterates that moment-based techniques are similar to a model-based approach in the sense that they fit an elliptical profile to the image to obtain weighted moments. As a result, moment-based estimates of ellipticities are prone to undercutting bias. The estimation is fundamentally limited mainly by pixellation which destroys information on the original, pre-seeing image. Give an optimized estimator for the pre-seeing GLAM ellipticity and its bias for noise-free images. To deal with images where pixel noise is prominent, consider a likelihood model of GLAM parameters in the pre-seeing frame. Similar to the noise-free case, this likelihood is biased in the presence of undercutting. The bias does not vary with the overall noise level but it depends in detail on the correlation of pixel noise as well as the noise homogeneity over the image, which could be relevant for the calibration strategies of other methodologies. Give an analytic expression for the undercutting bias and suggest means to reduce it. Moreover, within a Bayesian framework of the GLAM ellipticity, noise-dependent bias emerges after marginalization of the likelihood over image size or centroid position, even in the absence of undercutting. Therefore, a Bayesian approach to shape measurements does not necessarily mitigate noise bias although the tests show that it can be reduced.
Weak-lensing shear estimates with general adaptive moments, and studies of bias by pixellation, PSF distortions, and noise
Simon, Schneider
In WL, weighted quadrupole moments of the brightness profile in galaxy images are a common way to estimate gravitational shear. Employ general adapt moments (GLAM) to study causes of shear bias on a fundamental level and for a practical definition of an image ellipticity. For GLAM, the ellipticity is identical to that of isophotes of elliptical images, and this ellipticity is always an unbiased estimator of reduced shear. The theoretical framework reiterates that moment-based techniques are similar to a model-based approach in the sense that they fit an elliptical profile to the image to obtain weighted moments. As a result, moment-based estimates of ellipticities are prone to undercutting bias. The estimation is fundamentally limited mainly by pixellation which destroys information on the original, pre-seeing image. Give an optimized estimator for the pre-seeing GLAM ellipticity and its bias for noise-free images. To deal with images where pixel noise is prominent, consider a likelihood model of GLAM parameters in the pre-seeing frame. Similar to the noise-free case, this likelihood is biased in the presence of undercutting. The bias does not vary with the overall noise level but it depends in detail on the correlation of pixel noise as well as the noise homogeneity over the image, which could be relevant for the calibration strategies of other methodologies. Give an analytic expression for the undercutting bias and suggest means to reduce it. Moreover, within a Bayesian framework of the GLAM ellipticity, noise-dependent bias emerges after marginalization of the likelihood over image size or centroid position, even in the absence of undercutting. Therefore, a Bayesian approach to shape measurements does not necessarily mitigate noise bias although the tests show that it can be reduced.
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