Logan's graphical analysis (LGA) is a widely-used approach for quantification of biochemical and physiological processes from Positron emission tomography (PET) image data. A well-noted problem associated with the LGA method is the bias in the estimated parameters. We recently systematically evaluated the bias associated with the linear model approximation and developed an alternative to minimize the bias due to model error. In this study, we examined the noise structure in the equations defining linear quantification methods, including LGA. The noise structure conflicts with the conditions given by the Gauss-Markov theorem for the least squares (LS) solution to generate the best linear unbiased estimator. By carefully taking care of the data error structure, we propose to use structured total least squares (STLS) to obtain the solution using a one-dimensional optimization problem. Simulations of PET data for [11C] benzothiazole-aniline (Pittsburgh Compound-B [PIB]) show that the proposed method significantly reduces the bias. We conclude that the bias associated with noise is primarily due to the unusual structure of he correlated noise and it can be reduced with the proposed STLS method.