1-Bit Compressed Sensing Based On Rademacher Complexities

Compressed Sensing(CS)is a new research direction in signal processing field,and combining the compression and sample of signals.Compressed Sensing has a high application value and it can overcome the insufficient that traditional sample need to satisfy the Nyquist sampling principle.This principle needs a large number of measurements which need high hardware conditions.The main research problem is the quantification of measurements.Considering whether the measurements have extreme qualification,yielded a hot research direction of Compressed Sensing – 1-bit Compressed Sensing.The theory quantify the measurements to the quantity only consider its signs,then design reconstruction algorithm to recover signals.Due to the quantitative value will only take a bit of storage,the branch theory of compressed sensing thus named.This method greatly simplify the hardware structure,and reduce the sampling values of the storage space.Because of its simple structure and remarkable reconstruction effect,1-bit CS has attracted more and more people's attention in recent years.1-bit Compressed Sensing theory about the sample and reconstruction of signals has some mature research results.But the choices of measurements have a lot of limitations,only consider the use of Guass matrix.This paper take use of Rademacher random matrix to sample and reconstruct signals.The theory based on the knowledge of Rademacher complexities,combining the special structure of signals in 1-bit CS and take use of the empirical risk minimization method in statistics,analysis the feasibility of reconstruction algorithm in the global and local scope,and the recover effect is remarkable.