Robust 1-Bit Compressive Sensing via Binary Stable Embeddings of Sparse Vectors

The Compressive Sensing (CS) framework aims to ease the burden on analog-to-digital converters (ADCs) by reducing the sampling rate required to acquire and stably recover sparse signals. 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. In this paper, we investigate an alternative CS approach that shifts the emphasis from the sampling rate to the number of bits per measurement. In particular, we explore the extreme case of 1-bit CS measurements, which capture just their sign. Our results come in two flavors. First, we consider ideal reconstruction from noiseless 1-bit measurements and provide a lower bound on the best achievable reconstruction error. We also demonstrate that a large class of measurement mappings achieve this optimal bound. Second, we consider reconstruction robustness to measurement errors and noise and introduce the Binary -...

• Type: Journal
• Year: 2011
• Where: CORR
• Authors: Laurent Jacques, Jason N. Laska, Petros Boufounos, Richard G. Baraniuk
• Keywords: 1-bit Measurements, CORR 2011, Education, Measurements, Sampling Rate