Abstract: The performance of the deconvolution algorithm plays a crucial role in data processing of radio interferometers. The multi-scale multi-frequency synthesis (MSMFS) CLEAN is a widely used deconvolution algorithm for radio interferometric imaging, which combines the advantages of both wide-band synthesis imaging and multi-scale imaging and can substantially improve performance. However, how best to effectively determine the optimal scale is an important problem when implementing the MSMFS CLEAN algorithm. In this study, we proposed a Gaussian fitting method for multiple sources based on the gradient descent algorithm, with consideration of the influence of the point spread function (PSF). After fitting, we analyzed the fitting components using statistical analysis to derive reasonable scale information through the model parameters. A series of simulation validations demonstrated that the scales extracted by our proposed algorithm are accurate and reasonable. The proposed method can be applied to the deconvolution algorithm and provide modeling analysis for Gaussian sources, offering data support for source extraction algorithms.