A tractable approach for 1-bit compressed sensing on manifolds

Compressed Sensing 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 guaranteed 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. In this talk I introduce the one-bit problem and proposes a tractable strategy to solve one-bit CS problems for data lying on manifolds. This is based on joint work with Johannes Maly and Mark Iwen.