Greedy algorithms for compressed sensing have received considerable attention because of their low computational complexity

high speed

and good recovery performance in image reconstruction.As a typical reconstruction method in greedy algorithms

the compressed sampling matching pursuit (CoSaMP) algorithm exhibits good robustness and can guarantee the reconstruction of signals from arbitrary observation noise background.However

the CoSaMP algorithm requires a large number of observations in the atom selection process

which affects reconstruction time.The principle of atom selection can also lead to the inaccurate estimation of a support set to reduce reconstruction precision.Therefore

a stagewise iterative matching pursuit (StIMP) algorithm based on generalized inversion was proposed to improve the reconstruction accuracy and performance of the CoSaMP algorithm. The observation matrix was processed via generalized inversion before iteration to ensure the accuracy and rapidity of atom selection with iteration

which could reduce mutual interference among atoms.The iterative process was divided into two stages.The first stage used the orthogonal matching pursuit (OMP) algorithm to iterate several times given that most of the atoms selected via the OMP algorithm were accurate.The number of iteration times during the first stage should not be too small to improve the accuracy of the support set.The number of iteration times during the first stage was set to /2 in consideration of the reconstruction time.The assumption of signal sparsity was an even number in this study.If is an odd number

then it should take the floor value (/2).The CoSaMP algorithm was used to continue the iteration in the second stage.The initial input of the CoSaMP algorithm was the residual atoms obtained from the OMP iteration in the first stage

which could reduce the dependence of the CoSaMP algorithm on sparsity.The atom selection criteria of the CoSaMP algorithm were changed simultaneously

and 3/2 atoms were selected instead of 2

and /2 atoms were removed each time to ensure that the support set would contain atoms.A threshold was set to control the stopping of the algorithm and to reconstruct sparse signals rapidly and accurately. For 1D Gauss random signals

the signal reconstructed by the proposed StIMP algorithm is close to the original signal

and the error range is (-5e

5e).The changing trend of the success rate with signal sparsity shows that the StIMP algorithm is more robust and has a higher success rate for reconstruction than the OMP

CoSaMP

regularized OMP (ROMP)

and Fourier ring (FR)-CoSaMP algorithms.For 2D image signals

the images reconstructed using the OMP and ROMP algorithms exhibit problems in the subjective quality aspect

such as large noise particles

high fuzziness

and poor comfort

whereas the CoSaMP

FR-CoSaMP

and StIMP algorithms can achieve better image reconstruction and have higher resolution

better contrast

and sense of hierarchy.However

the CoSaMP and FR-CoSaMP algorithms are less relaxed than the StIMP algorithm

and the images reconstructed using the StIMP algorithm are smoother and closer to the original image.In the objective quality aspect

the average peak signal-to-noise ratios (PSNRs) of the StIMP algorithm are higher than those of the other reconstruction algorithms at each sampling rate.For example

when the sampling rate is 0.7

the average PSNR of the StIMP algorithm is higher than those of the OMP

CoSaMP

ROMP

and FR-CoSaMP algorithms (2.14 dB

1.20 dB

3.67 dB

and 0.90 dB

respectively).The reconstruction time of the StIMP algorithm is only 7.85 s

whereas those of the OMP

CoSaMP

and FR-CoSaMP algorithms are 11.79 s

32.86 s

and 11.09 s

respectively. An improved reconstruction algorithm

which exhibited high reconstruction speed and exerted considerable effect on 1D Gauss random signal and 2D image signal

was proposed.Compared with the original algorithm

StIMP demonstrates high efficiency and practicability.This algorithm has important practical significance in processing medical and remote sensing images.The StIMP algorithm is also improved based on OMP and CoSaMP;therefore

it should be conducted within the premise of known signal sparsity.Further study should refer to the principle of the sparse adaptive matching pursuit algorithm to improve the StIMP algorithm

such that it can be adaptive in a case with unknown signal sparsity.