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是可能的。这些方法在医学和科学成像与传感领域发挥着关键作用，此类场景中真实数据往往稀缺或难以获取。然而在实际应用中，测量不仅存在噪声和不完整性，还会经历量化过程。本文探索了从二值观测中学习的极端情况，并给出了从不完整二值数据中识别信号集所需测量次数的充要条件。我们的结果与现有二值测量信号恢复的界互为补充。此外，我们提出了一种名为SSBM的新型自监督学习方法，该方法仅需二值数据即可训练。通过在真实数据集上的一系列实验证明，SSBM的性能与监督学习相当，并显著优于采用固定小波基的稀疏重建方法。