Noise induced by the fluctuation of laser phase, frequency, intensity, etc., can deteriorate the point spread function (PSF) in distributed optical fiber sensing and testing systems, which is the core concern for measurement performance, such as measurement spatial resolution, length range, accuracy and dynamic range. In this paper, we review the development of noise compensation methods for improving the PSF in optical fiber frequency sweeping interferometry (OFFSI) systems and provide a reference to select appropriate compensation methods in different applications (e.g., fiber optics component characterization, optical fiber network diagnosis). A discussion of noise impacts on PSF is made, including laser source phase noise, laser source intensity noise and ambient noise. The most serious noise is the laser source phase noise involved in frequency tunable lasers, including deterministic frequency tuning nonlinearity and stochastic laser phase noise. Also, a comprehensive and detailed classification of the compensation strategies for different noise is provided according to the dominant noise in the laser source. Recent progress on each kind of compensation method is analyzed based on the principles, performance, advantages and limitations, and a comparison of compensation methods is presented. Finally, an overview of trends and future developments is given.