Study On Compressed Sensing Reconstruction Algorithms For Sparse Time-Varing Signals

Compressed sensing (CS) is a low-rate sampling theory developed from signal sparse representation and function approximation theory. Targeting sparse signals, CS performs low-rate measurements through random projections which project the sparse signals into a low-dimensional space and reconstruct the sparse signals by sparse optimization methods. The sparsity of the signals is the precondition to implement the low-rate sampling.Conventional CS theory studies the signals with time-invariant sparsity. However, in the applications of communication, radar and satellite navigation, the sparsity of the signals is often time-varying. Then it will be practically important to study the CS of signals with time-varying sparsity. In this dissertation, we study compressed sensing reconstruction algorithm for sparse time-varing signals in the background of pulsed radar application. According to time-varing characteristic of the pulsed radar echoes, we build up the sparse time-varing signals model and develope the sparse time-varing signals reconstruction algorithm by applying the iteratively reweighted method. Then we take the quadrature compressive sampling system as an example to sample the radar echoes and implement the dynamical reconstruction of the radar echoes with our proposed algorithms. The reconstruction performance is discussed through the extensive simulation experiments. The main works of this paper are as follows:1. Brief introduction of CS theory and sparse representation. The sparse representation, compressive measurement and signal reconstruction are firstly introduced. Then the signal reconstruction algorithms are classified with special attention on iteratively reweighted reconstruction algorithms. Finally, the reconstruction performances are compared through computer simulations.2. Development of the reconstruction algorithms for signals with time-varying sparsity. Two algorithms, Reciprocal Weighted l1Minimization (RWL1) and Multiple-Reciprocal Weighted l1Minimization (M-RWL1), are developed. The core of the two algorithms is to inject a priori information of the sparse signals into the reconstruction process, which tracks the variations of the signal sparsity. Simulations demonstrate the effectiveness of the developed algorithms. M-RWL1algorithm has performance superior to RWL1because of multiple inner-iteration strategy.3. Study of pulse-Doppler echoes reconstruction. With compressive data derived from quadrature compressive sampling, we take RWL1and M-RWL1algorithms to reconstruct the pulsed radar echoes. Simulations show that the two algorithms can effectively reconstruct the time-varying pulsed radar echoes.