Abstract
The modified adaptive orthogonal matching pursuit algorithm has a lower convergence speed. To overcome this problem, an improved method with faster convergence speed is proposed. In respect of atomic selection, the proposed method computes the correlation between the measurement matrix and residual and then selects the atoms most related to residual to construct the candidate atomic set. The number of selected atoms is the integral multiple of initial step size. In respect of sparsity estimation, the proposed method introduces the exponential function to sparsity estimation. It uses a larger step size to estimate sparsity at the beginning of iteration to accelerate the algorithm convergence speed and a smaller step size to improve the reconstruction accuracy. Simulations show that the proposed method has better performance in terms of convergence speed and reconstruction accuracy for one-dimension signal and two-dimension signal.
Highlights
Compressed sensing (CS) [1] has become a popular research topic in recent years
The reconstructed signal obtained by l2-norm optimization is not sparse, and the reconstruction accuracy is large. erefore, many researchers pay more attention to the use of the optimization algorithms based on l1-norm or l0-norm to reconstruct sparse signal in compressed sensing. e sparse signal reconstruction methods based on l1-norm include the basis pursuit (BP) method [6], iterative thresholding (IT) method [7], and homotopy method [8]
We proposed a generalized sparsity adaptive matching pursuit algorithm with variable step size. is algorithm uses the idea of generalized atom selection to choose more atoms at the beginning of the iteration, and the signal estimation solution is more accurate by backtracking
Summary
Compressed sensing (CS) [1] has become a popular research topic in recent years. Compared with traditional compression methods, the CS can be sampled at a rate far below the Nyquist sampling theorem, and the signal can be reconstructed with high probability. Signal reconstruction is one of the most important parts of compressed sensing. A good reconstruction algorithm can improve the accuracy and time of signal recovery. In the design of the reconstruction algorithm, the signal reconstruction based on the l2-norm optimization is firstly adopted. The reconstructed signal obtained by l2-norm optimization is not sparse, and the reconstruction accuracy is large. Erefore, many researchers pay more attention to the use of the optimization algorithms based on l1-norm or l0-norm to reconstruct sparse signal in compressed sensing. E sparse signal reconstruction methods based on l1-norm include the basis pursuit (BP) method [6], iterative thresholding (IT) method [7], and homotopy method [8]. Some researchers proposed the sparse signal recovery method with minimization of l1-norm minus l2-norm [9]
Sign-in/Register to view highlights & summary 
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call