Manifold-based Compressed Sensing Parameter Estimation Algorithms And Its Applications To Signal Processing

In the field of modern signal processing,as the requirement of information amount increases rapidly,the essential band of signal carrying the information becomes wider and wider therewith.The increasingly growth of essential bandwidth necessarily brings up a huge challenge for signal discretization and representation.The novel theory and technique of compressed sensing or compressed sampling enables the sampling system to work at a signal's intrinsic information rate instead of its Nyquist rate,which is determined by the signal's bandwidth.A CS system only acquires the signal's low dimensional projection y = ?x?Rm,m ? n,rather than its Nyquist sampling x?Rn.Furthermore,if m = O(K log(n/k)),the random projection operator ? of size m×n holds the restricted isometric property(RIP)for a k-sparse signal x with high probability.Therefore,a compressed measurement vector y =?x is enough to retain all the information of x with which can we recover the original signal.Standard compressed sensing(CS)problem always requires the sensing matrix to be defi-nitely known as a priori.However,this condition may not be met in various practical applications,especially the scenes which involve the free propagation of waveforms(e.g.in the systems of wire-less communication,radar and sonar).Recent studies find that the perturbation in sensing matrix(which is also dubbed as basis mismatch or ofF-the-grid issue)may seriously worsen the results obtained by standard CS algorithms.In this paper we focus on the ofF-the-grid recovery algorithm within the framework of manifold-based compressed sensing.Under the assumption of knowing this manifold-based sparse model,we propose a post-processing-based named dynamic parame-terized e1 regularization(DPL1),which starts with an on-the-grid result obtained by a standard CS algorithm,e.g.Basis Pursuit(BP)or Orthogonal Matching Pursuit(OMP),and finally optimizes it into a precise solution.Moreover,we study and implement the other two kind of state-of-the-art ofF-the-grid algo-rithms,Band-Exclusion based Orthogonal Matching Pursuit(BOMP)and Semidefinite Program based Atomic Norm Minimization(SDP-ANM),which act as the contrasts against our algorithm DPL1.In addition,we also optimize these two algorithms for a better performance in estimation accuracy and computational complexity respectively.Finally,we apply the algorithm DPL1 to the following three typical practical applications which suffer the off-the-grid issue seriously,i.e.,the spectral compressed sensing,the off-the-grid time delay estimation and the single-snapshot direction of arrival(DOA)estimation.Encourag-ingly,the numerical results indicate that our algorithm outperforms most of the state-of-the-art algorithms in this field,especially in the aspects of accuracy and resolution,sample complexity(or sparsity tolerance),and computation complexity.