ABSTRACT
In general, only the acquired 1-bit information is insufficient to exactly reconstruct a sparse signal. For instance, if sign(Ax∗) = y, where y ∈ {1,−1}m, then any sufficiently small perturbation x∗+u also satisfies this equation, making the exact recovery of x∗ impossible by whatever decoding algorithms. Although the sign measurements may not be enough for reconstructing a signal, they might be adequate to recover part of the information (e.g., support or sign) of the target signal. Thus 1-bit CS still has some applications in signal and imaging processing (see [28, 29, 31, 125, 152, 32, 72]).
