Generalized Approximate Message Passing For Noisy 1-Bit Compressed Sensing With Side-Information

We consider the problem of sparse signal reconstruction from noisy 1-bit compressed measurements when the receiver has access to side information. We assume that compressed measurements are corrupted by additive white Gaussian noise before quantization and sign-flip error after quantization. A generalized approximate message passing-based algorithm for signal reconstruction from noisy 1-bit compressed measurements is proposed and then, it is extended to the case when side information is available. We show that 1-bit compressed measurements based signal reconstruction is quite sensitive to noise and the reconstruction performance can be greatly improved by exploiting available side information at the receiver.