One-bit compressive sampling with time-varying thresholds for sparse parameter estimation

This paper considers the problem of estimating the parameters of a signal using time-varying thresholded noisy one-bit measurements. The problem is shown to be deterministically identifiable under reasonable conditions on the signal and thresholds. A spectral sensing application is considered, and two sparse methods are presented. In addition to the standard ℓ
₁
norm based approach, a “zero-norm” approximation via the logarithm function is used, and shown to yield sparser estimates in a numerical example.