Efficient accurate Gaussian fitting is an important topic in many applications, take localization based super-resolution microscopy and image scanning microscopy for example, which requires localizing plenty of Gaussian patterns for accurately reconstructing a super-resolution image. Existing Gaussian fitting methods usually require inputting a good initial value for all parameters for efficient and robust fitting, which apparently is not suitable for the task of large scale Gaussian fitting with a computer. It would be even more challenge to estimate an appropriate initial value for all parameters and guarantee the robustness of the fitting algorithm for low signal-to-noise ratio measured data with strong background. In this paper, we propose a two-step fitting algorithm for robust and accurate 2D Gaussian fitting without inputting any initial parameter value. Our simulation shows that the performance of the fitting algorithm can be improved significantly with the proposed parameter initial value estimation algorithm.
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