We investigated the off-line metrology for line edge roughness (LER) determination by using the discrete power spectral density (PSD). The study specifically addresses low-dose scanning electron microscopy (SEM) images in order to reduce the acquisition time and the risk of resist shrinkage. The first attempts are based on optimized elliptic filtering of noisy experimental SEM images, where we use threshold-based peak detection to determine the edge displacements. The effect of transversal and longitudinal filterings cannot be ignored, even when considering an optimized filter strength. We subsequently developed a method to detect the edge displacements without the use of a filter and thus avoiding biasing. This makes it possible to study how much image noise is acceptable and still determine the LER. The idea is to generate random images of line edges using the model of Palasantzas and the algorithm of Thorsos. We study the simulated PSDs as a function of the number of line edges and report on the convergence of the parameters (LER, correlation length, and roughness exponent) by fitting the Palasantzas model extended with a white noise term. This study demonstrates that a very noisy image with 12 line edges and about 2 electrons per pixel on average (charge density ) already produces an estimation for LER with a relative error (one-sigma) of about 10%. Furthermore, increasing the dose beyond 20 electrons per pixel does not significantly improve the LER determination.