Joint sparsity pattern recovery with 1-bit compressive sensing in sensor networks

Vipul Gupta, Bhavya Kailkhura, Thakshila Wimalajeewa, Sijia Liu, Pramod K. Varshney

Abstract: We study the problem of joint sparsity pattern recovery with 1-bit compressive measurements in a sensor network. Sensors are assumed to observe sparse signals having the same but unknown sparsity pattern. Each sensor quantizes its measurement vector element-wise to 1-bit and transmits the quantized observations to a fusion center. We develop a computationally tractable support recovery algorithm which minimizes a cost function defined in terms of the likelihood function and the ℓ1,∞ norm. We observe that even with noisy 1-bit measurements, joint sparsity pattern can be recovered accurately with multiple sensors each collecting only a small number of measurements.