With fluid antenna system (FAS) gradually establishing itself as a possible enabling technology for next generation wireless communications, channel estimation for FAS has become a pressing issue. Existing methodologies however face limitations in noise suppression. To overcome this, in this paper, we propose a maximum likelihood (ML)-based channel estimation approach tailored for FAS systems, designed to mitigate noise interference and enhance estimation accuracy. By capitalizing on the inherent sparsity of wireless channels, we integrate an ML-based iterative tomographic algorithm to systematically reduce noise perturbations during the channel estimation process. Furthermore, the proposed approach leverages spatial correlation within the FAS channel to optimize estimation accuracy and spectral efficiency. Simulation results confirm the efficacy of the proposed method, demonstrating superior channel estimation accuracy and robustness compared to existing benchmark techniques.