  The robust estimation of the tiny distortions (shears) of galaxy shapes
caused by weak gravitational lensing in the presence of much larger shape
distortions due to the point-spread function (PSF) has been widely
investigated. One major problem is that most galaxy shape measurement methods
are subject to bias due to pixel noise in the images ("noise bias"). Noise bias
is usually characterized using uncorrelated noise fields; however, real images
typically have low-level noise correlations due to galaxies below the detection
threshold, and some types of image processing can induce further noise
correlations. We investigate the effective detection significance and its
impact on noise bias in the presence of correlated noise for one method of
galaxy shape estimation. For a fixed noise variance, the biases in galaxy shape
estimates can differ substantially for uncorrelated versus correlated noise.
However, use of an estimate of detection significance that accounts for the
noise correlations can almost entirely remove these differences, leading to
consistent values of noise bias as a function of detection significance for
correlated and uncorrelated noise. We confirm the robustness of this finding to
properties of the galaxy, the PSF, and the noise field, and quantify the impact
of anisotropy in the noise correlations. Our results highlight the importance
of understanding the pixel noise model and its impact on detection
significances when correcting for noise bias on weak lensing.
