Learning Binary Sampling Patterns for Single-Pixel Imaging using Bilevel Optimisation

Single-Pixel Imaging (SPI) enables the reconstruction of objects using a single detector through sequential illuminations with structured light patterns. The choice of illumination patterns is critical, particularly in highly undersampled regimes, where it directly determines reconstruction quality and acquisition speed. Instead of relying on handcrafted or fixed patterns, we propose to learn task-specific patterns directly from data. Practical SPI hardware only supports binary patterns, making binary pattern design a necessary consideration. We propose a bilevel optimisation method for learning task-specific binary illumination patterns optimised for applications such as single-pixel fluorescence microscopy. We address the non-differentiable nature of binary optimisation using the Straight-Through Estimator. In addition, we incorporate learned variational regularisation, improving reconstruction quality and robustness. We demonstrate our method on the CytoImageNet microscopy dataset. We show that our learned patterns achieve superior reconstruction performance compared to baseline methods and end-to-end deep learning, particularly in highly undersampled regimes and in scarce-data settings.