Quasiparticle Interference Kernel Extraction with Variational Autoencoders via Latent Alignment

Quasiparticle interference (QPI) imaging is a powerful tool for probing electronic structures in quantum materials, but extracting the single-scatterer QPI pattern (i.e., the kernel) from a multi-scatterer image remains a fundamentally ill-posed inverse problem, because many different kernels can combine to produce almost the same observed image, and noise or overlaps further obscure the true signal. Existing solutions to this extraction problem rely on manually zooming into small local regions with isolated single-scatterers. This is infeasible for real cases where scattering conditions are too complex. In this work, we propose the first AI-based framework for QPI kernel extraction, which models the space of physically valid kernels and uses this knowledge to guide the inverse mapping. We introduce a two-step learning strategy that decouples kernel representation learning from observation-to-kernel inference. In the first step, we train a variational autoencoder to learn a compact latent space of scattering kernels. In the second step, we align the latent representation of QPI observations with those of the pre-learned kernels using a dedicated encoder. This design enables the model to infer kernels robustly under complex, entangled scattering conditions. We construct a diverse and physically realistic QPI dataset comprising 100 unique kernels and evaluate our method against a direct one-step baseline. Experimental results demonstrate that our approach achieves significantly higher extraction accuracy, improved generalization to unseen kernels. To further validate its effectiveness, we also apply the method to real QPI data from Ag and FeSe samples, where it reliably extracts meaningful kernels under complex scattering conditions.