Binary Reweighted l1-Norm Minimization for One-Bit Compressed Sensing

Abstract

The compressed sensing (CS) can acquire and reconstruct a sparse signal from relatively fewer measurements than the classical Nyquist sampling. Practical ADCs not only sample but also quantize each measurement to a finite number of bits; moreover, there is an inverse relationship between the achievable sampling rate and the bit depth. The quantized CS has been studied recently and it has been demonstrated that accurate and stable signal acquisition is still possible even when each measurement is quantized to just a single bit. Many algorithms have been proposed for 1-bit CS however, most of them require that the prior knowledge of the sparsity level (number of the nonzero elements) should be known. In this paper, we explored the reweighted l1-norm minimization method in recovering signals from 1-bit measurements. It is a nonconvex penalty and gives different weights according to the order of the absolute value of each element. Simulation results show that our method has much better performance than the state-of-art method (BIHT) when the sparsity level is unknown. Even when the sparsity level is known, our method can get a comparable performance with the BIHT method. Besides,we validate our methods in an ECG signal recovery problem.