In this paper, we present a framework for perceptual error minimization and sinusoidal frequency estimation based on a new perceptual distortion measure, and we state its optimal solution. Using this framework, we relate a number of well-known practical methods for perceptual sinusoidal parameter estimation such as the prefiltering method, the weighted matching pursuit, and the perceptual matching pursuit. In particular, we derive and compare the sinusoidal estimation criteria used in these methods. We show that for the sinusoidal estimation problem, the prefiltering method and the weighted matching pursuit are equivalent to the perceptual matching pursuit under certain conditions.