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

arXiv: https://arxiv.org/abs/2508.19068 · HTML: https://mlsanity.com/paper/2508.19068/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 52 references that are in the map.
- First posted on arXiv 26 Aug 2025.

## Builds on (most cited first, 20 of 20)

- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [BinaryConnect: Training Deep Neural Networks with binary weights during propagations](https://mlsanity.com/paper/1511.00363/) (2015)
- [Understanding Straight-Through Estimator in Training Activation Quantized Neural Nets](https://mlsanity.com/paper/1903.05662/) (2019)
- [Truncated Back-propagation for Bilevel Optimization](https://mlsanity.com/paper/1810.10667/) (2018)
- [JFB: Jacobian-Free Backpropagation for Implicit Networks](https://mlsanity.com/paper/2103.12803/) (2021)
- [Total Deep Variation for Linear Inverse Problems](https://mlsanity.com/paper/2001.05005/) (2020)
- [Learning Weakly Convex Regularizers for Convergent Image-Reconstruction Algorithms](https://mlsanity.com/paper/2308.10542/) (2023)
- [Learning the Sampling Pattern for MRI](https://mlsanity.com/paper/1906.08754/) (2019)
- [Learning-Based Compressive MRI](https://mlsanity.com/paper/1805.01266/) (2018)
- [Learning a Compressed Sensing Measurement Matrix via Gradient Unrolling](https://mlsanity.com/paper/1806.10175/) (2018)
- [Deep Equilibrium Learning of Explicit Regularizers for Imaging Inverse Problems](https://mlsanity.com/paper/2303.05386/) (2023)
- [Learning Provably Robust Estimators for Inverse Problems via Jittering](https://mlsanity.com/paper/2307.12822/) (2023)
- [CytoImageNet: A large-scale pretraining dataset for bioimage transfer learning](https://mlsanity.com/paper/2111.11646/) (2021)
- [Learning-based Compressive Subsampling](https://mlsanity.com/paper/1510.06188/) (2015)
- [Custom Gradient Estimators are Straight-Through Estimators in Disguise](https://mlsanity.com/paper/2405.05171/) (2024)
- [Super sub-Nyquist single-pixel imaging by means of cake-cutting Hadamard basis sort](https://mlsanity.com/paper/1903.11175/) (2019)
- [Giga-voxel multidimensional fluorescence imaging combining single-pixel detection and data fusion](https://mlsanity.com/paper/2107.12337/) (2021)
- [A detail-enhanced sampling strategy in Hadamard single-pixel imaging](https://mlsanity.com/paper/2209.04449/) (2022)

## Built on by (most cited first, 1 of 1)

- [Learning Regularization Functionals for Inverse Problems: A Comparative Study](https://mlsanity.com/paper/2510.01755/) (2025)

## Abstract (arXiv)

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.