A tractable approach for one-bit Compressed Sensing on manifolds

Classical Compressed Sensing (CS) deals with reconstructing some unknown vector from few linear measurements in high dimension by additionally assuming sparsity, i.e., many entries are zero. Recent results guarantee recovery even when just signs of the measurements are available (one-bit CS). A natural generalization of classical CS replaces sparse vectors by vectors lying on manifolds having low intrinsic dimension. This paper studies the one-bit problem and proposes a tractable strategy to solve one-bit CS problems for data lying on manifolds. The paper describes ongoing work.