Recovering signals with variable sparsity levels from the noisy 1-bit compressive measurements

In this paper, we consider the 1-bit compressive sensing reconstruction problem in a scenario that the sparsity level of the signal is unknown and time variant, and the binary measurements are contaminated with the noise. We introduce a new reconstruction algorithm which we refer to as Noise-Adaptive Restricted Step Shrinkage (NARSS). NARSS is superior in terms of performance, complexity and speed of convergence to the algorithms already introduced in the literature for 1-bit compressive sensing reconstruction from the noisy binary measurements.