Bayesian Compressive Sensing Theroy And Application

Conventional approaches to sampling signals or images follow Shannon’ s celebrated theorem: the sampling rate must be at least twice the maximum frequency present in the signal(the so-called Nyquist rate). In fact, this principle underlies nearly all signal acquisition protocols used in consumer audio and visual electronics, medical imaging devices, radio receivers, and so on.(For some signals, such as images that are not naturally bandlimited, the sampling rate is dictated not by the Shannon theorem but by the desired temporal or spatial resolution.Compressed sensing also applied into DOA estimation.While in there is phase error in the receiver.At the same time the conventional sparse bayesian learning algorithm complexity is so high to implement in DOA estimation scenario.We address these two problem.In this thesis we consider the problem of DOA estimation with phase perturbation based on bayesian compressive sensing.In practical scenario the signal received from the transmitter might be corrupted by the noise or through multi-path. So there will some phase error in the receiver. We develop DOA estimation algorithm based Varitional-EM frame to accomodate this problem.We introduce a Gaussian prior to the unknown DOA amplitude.Meawhile we treat the director of the arrival as deterministic unknown parameter.In the E-step we estimate the posterior distribution of the amplitude the DOA.Then the DOA is estimated in the M-step through pure Newton gradient method, at the same time we do the phase compensation.Next we propose a fast method to address the DOA estimation based Laplace prior which will introduce more sparsity than Gaussian prior.when covariance is calculated through matrix inversion which is cost a lot time and its complexity is O(3).In the Estep we avoid the process of calculating inversion.A splitting method is proposed in this step which dramatic decrease the computation complexity and save time.