Under sub-Gaussian designs, uniform recovery of ℓ₁-sparse signals from one-bit measurements requires Ω̃((k/m)^{1/3}) Euclidean error, matching known upper bounds up to logs for both dithered and undithered models.
Milman.Asymptotic Geometric Analysis, Part I, volume 202 ofMathematical Surveys and Monographs
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Near-Optimal Lower Bounds on One-Bit Compressed Sensing of Approximately Sparse Signals
Under sub-Gaussian designs, uniform recovery of ℓ₁-sparse signals from one-bit measurements requires Ω̃((k/m)^{1/3}) Euclidean error, matching known upper bounds up to logs for both dithered and undithered models.