Multi-scale learning with point spread function and spectral energy distribution constraints for faint source detection in lobster-eye X-ray telescopes

Context. Detecting faint and cross-shaped sources in long-exposure images from lobster-eye X-ray telescopes is particularly challenging due to the low signal-to-noise ratio (S/N), complex noise, and unique point spread function (PSF) of these instruments. Conventional deep learning networks struggle in such conditions as they fail to effectively incorporate astrophysical priors such as photon arrival time, energy, and PSF morphology. Furthermore, the significant flux-scale differences between faint and bright sources complicate feature extraction in the standard feature pyramid network (FPN). Aims. The goal is to propose a PSF-guided multi-scale detection framework that integrates prior physical features and is specifically designed for the Wide-field X-ray Telescope (WXT) on board the Einstein Probe (EP). Methods. Our approach began by constructing three-channel inputs, combining conventional grayscale images with photon energy and arrival time data. We then introduced a PSF-guided morphological convolution module (PSFConv) and a multi-kernel multi-scale FPN (MKMS-FPN) to enhance the extraction of morphological features and improve multi-scale target perception. Additionally, we integrated high-level convolutional features with prior physical statistics within a multibranch binary classifier of our detection network to boost both detection sensitivity and interpretability. Results. Using simulated long-exposure WXT data and in-orbit EP observations, our framework achieves 90% precision with recall rates of 0.85 and 0.95 for sources with flux >2 mCrab (i.e. 3.21 × 10−11 erg cm−2 s−1, unabsorbed, 0.5-4 keV) and flux >3 mCrab, respectively. At moderate precision levels, the framework further doubles the number of detectable sources with flux < 1 mCrab compared to conventional CNNs and the SExtractor pipeline. Conclusions. The integration of physical priors with deep convolutional features demonstrates a robust detection performance across diverse flux regimes. The proposed framework offers a practical reference for data processing in future lobster-eye X-ray missions, promising enhanced sensitivity for detecting faint sources in challenging astrophysical observations.