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We describe a new, noise-adaptive, quasi-linear image reconstruction algorithm for positron emission tomography that seeks to equalize the signal-to-noise ratio (SNR) across an image by applying spatially varying smoothing. It is based on the fact that for linear reconstruction algorithms such as filtered back-projection (FBP), operating on uncorrelated Poisson distributed data, it is possible to directly compute the corresponding noise variance image, and thus the SNR, at all points, for any smoothing kernel (or filter function). Increased smoothing generally results in higher SNR. Therefore, by varying the amount of smoothing locally, one can tune the image to achieve a target SNR at most points. The resulting image appears to share some of the advantages of maximum likelihood reconstruction (e.g., improved hot spot contrast versus noise trade-off) while retaining the quantitative advantages of FBP (biased only by the known smoothing kernel). Examples for clinical time-of-flight (TOF) and non-TOF reconstructions are shown.