One-Bit MUSIC

One-Bit ExpanderSketch for One-Bit Compressed Sensing

Is it possible to obliviously construct a set of hyperplanes H such that you can approximate a unit vector x when you are given the side on which the vector lies with respect to every h ∈ H? In the sparse recovery literature, where x is approximately k-sparse, this problem is called onebit compressed sensing and has received a fair amount of attention the last decade. In this paper we obtain th...

One Bit of Advi

One Bit of Advice

The results in this paper show that coNP is contained in NP with 1 bit of advice (denoted NP/1) if and only if the Polynomial Hierarchy (PH) collapses to D, the second level of the Boolean Hierarchy (BH). Previous work showed that BH ⊆ D =⇒ coNP ⊆ NP/poly. The stronger assumption that PH ⊆ D in the new result allows the length of the advice function to be reduced to a single bit and also makes ...

Blind One-Bit Compressive Sampling

The problem of 1-bit compressive sampling is addressed in this paper. We introduce an optimization model for reconstruction of sparse signals from 1-bit measurements. The model targets a solution that has the least l0-norm among all signals satisfying consistency constraints stemming from the 1-bit measurements. An algorithm for solving the model is developed. Convergence analysis of the algori...

One Bit of Advi eHarry