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This work focuses on the reconstruction of sparse signals from their 1-bitmeasurements. The context is the one of 1-bit compressive sensing where themeasurements amount to quantizing (dithered) random projections. Our maincontribution shows that, in addition to the measurement process, we canadditionally reconstruct the signal with a binarization of the sensing matrix.This binary representation of both the measurements and sensing matrix candramatically simplify the hardware architecture on embedded systems, enablingcheaper and more power efficient alternatives. Within this framework, given asensing matrix respecting the restricted isometry property (RIP), we prove thatfor any sparse signal the quantized projected back-projection (QPBP) algorithmachieves a reconstruction error decaying like O(m-1/2)when the number ofmeasurements m increases. Simulations highlight the practicality of thedeveloped scheme for different sensing scenarios, including random partialFourier sensing.

One Bit to Rule Them All : Binarizing the Reconstruction in 1-bit Compressive Sensing