Overlapping object perception aims to decouple the randomly overlapping foreground-background features, extracting foreground features while suppressing background features, which holds significant application value in fields such as security screening and medical auxiliary diagnosis. Despite some research efforts to tackle the challenge of overlapping object perception, most solutions are confined to the spatial domain. Through frequency domain analysis, we observe that the degradation of contours and textures due to the overlapping phenomenon can be intuitively reflected in the magnitude spectrum. Based on this observation, we propose a general Frequency-Optimized Anti-Overlapping Framework (FOAM) to assist the model in extracting more texture and contour information, thereby enhancing the ability for anti-overlapping object perception. Specifically, we design the Frequency Spatial Transformer Block (FSTB), which can simultaneously extract features from both the frequency and spatial domains, helping the network capture more texture features from the foreground. In addition, we introduce the Hierarchical De-Corrupting (HDC) mechanism, which aligns adjacent features in the separately constructed base branch and corruption branch using a specially designed consistent loss during the training phase. This mechanism suppresses the response to irrelevant background features of FSTBs, thereby improving the perception of foreground contour. We conduct extensive experiments to validate the effectiveness and generalization of the proposed FOAM, which further improves the accuracy of state-of-the-art models on four datasets, specifically for the three overlapping object perception tasks: Prohibited Item Detection, Prohibited Item Segmentation, and Pneumonia Detection. The code will be open source once the paper is accepted.