TY - JOUR
T1 - Sparse signal recovery from one-bit quantized data
T2 - An iterative reweighted algorithm
AU - Fang, Jun
AU - Shen, Yanning
AU - Li, Hongbin
AU - Ren, Zhi
PY - 2014/9
Y1 - 2014/9
N2 - This paper considers the problem of reconstructing sparse signals from one-bit quantized measurements. We employ a log-sum penalty function, also referred to as the Gaussian entropy, to encourage sparsity in the algorithm development. In addition, in the proposed method, the logistic function is introduced to quantify the consistency between the measured one-bit quantized data and the reconstructed signal. Since the logistic function has the tendency to increase the magnitudes of the solution, an explicit unit-norm constraint is no longer necessary to be included in our optimization formulation. An algorithm is developed by iteratively minimizing a convex surrogate function that bounds the original objective function. This leads to an iterative reweighted process that alternates between estimating the sparse signal and refining the weights of the surrogate function. Numerical results are provided to illustrate the effectiveness of the proposed algorithm.
AB - This paper considers the problem of reconstructing sparse signals from one-bit quantized measurements. We employ a log-sum penalty function, also referred to as the Gaussian entropy, to encourage sparsity in the algorithm development. In addition, in the proposed method, the logistic function is introduced to quantify the consistency between the measured one-bit quantized data and the reconstructed signal. Since the logistic function has the tendency to increase the magnitudes of the solution, an explicit unit-norm constraint is no longer necessary to be included in our optimization formulation. An algorithm is developed by iteratively minimizing a convex surrogate function that bounds the original objective function. This leads to an iterative reweighted process that alternates between estimating the sparse signal and refining the weights of the surrogate function. Numerical results are provided to illustrate the effectiveness of the proposed algorithm.
KW - Compressed sensing
KW - Iterative reweighted algorithm
KW - One-bit quantization
KW - Surrogate function
UR - http://www.scopus.com/inward/record.url?scp=84898626738&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84898626738&partnerID=8YFLogxK
U2 - 10.1016/j.sigpro.2014.03.026
DO - 10.1016/j.sigpro.2014.03.026
M3 - Article
AN - SCOPUS:84898626738
SN - 0165-1684
VL - 102
SP - 201
EP - 206
JO - Signal Processing
JF - Signal Processing
ER -