Learning to reconstruct signals from binary measurements alone
Abstract: 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.
Certifications: Featured Certification
License: Creative Commons Attribution 4.0 International (CC BY 4.0)
Submission Length: Long submission (more than 12 pages of main content)
Previous TMLR Submission Url: https://openreview.net/forum?id=N7Qp5Lww1N
Changes Since Last Submission: The revised manuscript takes into account all the comments from the reviewers. In summary, the changes in this version are: - We have improved the proofs of Theorems 1, 7, and 10, by correcting typos, restructuring some parts, and fixing errors in the derivation of the constants of the theorems. - We have included a new theoretical result (Proposition 8) which lower bounds the error of the optimal reconstruction function learned from binary measurement data alone. - We have included a new example showing that for a certain family of forward operators (those with highly quantized entries), the model identification error might not improve when considering more measurements. - We have included new experiments illustrating the impact of the trade-off parameter $\alpha$ as a function of the undersampling ratio $m/n$. - We have included new experiments with noisy measurement data, which demonstrate the robustness of the proposed algorithm to the presence of noise. - We have included more experiments illustrating the proposed algorithm and other competing methods for the setting where there are more measurements than pixels, i.e., $m>n$. - We have included a formal definition of the model identification error (Definition 3.1). Please see the responses to the reviewer's comments for a detailed description of the changes in the revised manuscript. All changes from the previously submitted version are highlighted in red.
Assigned Action Editor: ~Florent_Krzakala1
Submission Number: 1400