To broaden the frequency band for the gravitational wave observation, Laser Interferometer Space Antenna (LISA) has been studying and developing as the first space-based GW detector, aiming to detect the GW signals from various astrophysical sources and cosmological sources in the most sensitive band from 0.1 mHz to 1 Hz. Stochastic gravitational wave background (SGWB) is one of the main science objectives of LISA. The detection and characterization of SGWBs can enrich our knowledge about our Universe, especially the processes in its early history at very high energy scales. The signal reconstruction for SGWBs from realistic data is challenging because of the various possible components contributing to the SGWB, and some SGWBs are statistically similar to the instrumental noises. Therefore, it is necessary to develop robust data analysis techniques and computational tools to resolve the noises and the SGWB components from the LISA data. In this talk, we will present a possible pipeline to generate the simulated data, including noise and SGWB signals, and another data analysis pipeline to reconstruct the SGWB signal and the noise without information of SGWB overall shape. It is crucial to understand the LISA noise and model it in SGWB data analysis since any wrong reconstruction in the noise could be misleading as the SGWB signal. With the better noise model, we could mitigate the uncertainties of the noise, and therefore we will have a better signal reconstruction.