Recent advances in unsupervised learning have highlighted the possibility of learning to reconstruct signals from noisy and incomplete linear measurements alone. These methods play a key role in medical and scientific imaging and sensing, where ground truth data is often scarce or difficult to obtain. However, in practice, measurements are not only noisy and incomplete but also quantized. Here we explore the extreme case of learning from binary observations and provide necessary and sufficient conditions on the number of measurements required for identifying a set of signals from incomplete binary data. Our results are complementary to existing bounds on signal recovery from binary measurements. Furthermore, we introduce a novel self-supervised learning approach, which we name SSBM, that only requires binary data for training. We demonstrate in a series of experiments with real datasets that SSBM performs on par with supervised learning and outperforms sparse reconstruction methods with a fixed wavelet basis by a large margin.

翻译：无监督学习的最新进展表明，仅从含噪且不完整的线性测量中学习重建信号成为可能。这些方法在医学和科学成像及传感领域发挥关键作用，而此类场景中真实数据往往稀缺或难以获取。然而实际中的测量不仅含噪且不完整，还存在量化问题。本文探索从二元观测中学习的极端情况，给出了从不完整二元数据中识别信号集所需测量数量的充要条件。我们的结论补充了现有二元测量信号恢复的界限。此外，我们提出了一种名为SSBM的新型自监督学习方法，该方法仅需二元数据即可训练。通过一系列真实数据集实验证明，SSBM在性能上与监督学习持平，且显著优于采用固定小波基的稀疏重建方法。