Objective.To address the zero-count problem in low-dose, high-spatial-resolution photon counting detector CT (PCD-CT) without introducing statistical biases or degrading spatial resolution.Approach.The classical approach to generate the sinogram projection data for estimating the line integrals of the linear attenuation coefficients of the image object is to take a log transform of detector counts, which requires zero counts to be replaced by positive numbers. Both the log transform and the zero-count replacement introduce biases. After analyzing the statistical properties of the zero-count replaced pre-log and post-log data, a formula for the statistical sinogram bias was derived, based on which a new sinogram estimator was empirically constructed to cancel the statistical biases. Dose- and object-independent free parameters in the proposed estimator were learned from simulated data, and then the estimator was applied to experimental low-dose PCD-CT data of physical phantoms for validation and generalizability testing. Both bias and noise performances of the proposed method were evaluated and compared with those of previous zero-count correction methods, including zero-weighting, zero-replacement, and adaptive filtration-based methods. The impact of these correction methods on spatial resolution was also quantified using line-pair patterns.Main Results.For all objects and reduced-dose levels, the proposed method reduces the statistical CT number biases to be within ± 10 HU, which is significantly lower than the biases given by the classical zero-count correction methods. The Bland-Altman analysis demonstrated that the proposed correction led to negligible sinogram biases at all attenuation levels, whereas the other correction methods did not. Additionally, the proposed method was found to have no discernible impact on image noise and spatial resolution.Significance.The proposed zero-count correction scheme allows the CT numbers of low-dose, high-spatial-resolution PCD-CT images to match those of standard-dose and standard-resolution PCD-CT images.