A dithered one-bit compressed sensing estimator over ReLU generative priors achieves O~(kn log d / epsilon^2) uniform recovery and a benign optimization landscape under a weight distribution condition.
Robust one-bit compressed sensing with partial circulant matrices
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abstract
We present optimal sample complexity estimates for one-bit compressed sensing problems in a realistic scenario: the procedure uses a structured matrix (a randomly sub-sampled circulant matrix) and is robust to analog pre-quantization noise as well as to adversarial bit corruptions in the quantization process. Our results imply that quantization is not a statistically expensive procedure in the presence of nontrivial analog noise: recovery requires the same sample size one would have needed had the measurement matrix been Gaussian and the noisy analog measurements been given as data.
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Robust One-Bit Recovery via ReLU Generative Networks: Near-Optimal Statistical Rate and Global Landscape Analysis
A dithered one-bit compressed sensing estimator over ReLU generative priors achieves O~(kn log d / epsilon^2) uniform recovery and a benign optimization landscape under a weight distribution condition.