High-speed spinning targets dection and imaging is essential to some special applicaions

such as targets classificationand recognition

missile defense

the protection of spacecraft

etc. A higher pulse repetition frequency（ PRF） is required for the radar system to obtain focused images for high-speed spinning targets. However

the observations of targets are always undersampled or nonuniformly-sampled when the radar PRF cannot satisfy the sampling requirement

which influences target identification.To solve the problem

this paper establishes an imaging model of azimuth undersampled echoes

according to the compressed sensing（ CS） theory and the sparsity nature of ISAR echoes. Then the compressive sampling matching pursuit（ CoSaMP） algorithm is used for signal reconstruction to improve the stability of traditional imaging algorithm using OMP.The overall procedures of the proposed algorithm are as follows.（ 1） After range compression and rough translational motion compensation of the echoes

a range bin containing the target component is determined due to the usage of narrowband radar.（ 2）The spinning period and residual translational motion parameters are estimated using the time-frequency spectrum of the echoes.（ 3） The noise level is estimated using the range bins containing only noise. The observation matrix is constructed according to the estimated target motion parameters. The narrowband imaging of spinning targets is transformed into an optimization problem based on CS.（ 4） The target signal is reconstructed using the CoSaMP algorithm

which is then transformed into the target space. Then the two-dimensional images are obtained.The first experiment is provided to show the effectiveness of the proposed algorithm. Compared with imaging algorithm based on OMP

the algorithm improves the reconstruction accuracy and stability due to the usage of backtracking strategy. The imaging quality is highly decided by two factors

the PRF and the signal-to-noise ratio（ SNR）. In the second experiment

the influences of these two factors on the imaging performance using different imaging algorithms are investigated. Two indicators

including the number of false selections and normalized mean-square error

are introduced to evaluate the influences of RRF and SNR on the imaging performance. The results about these two indicators show that compared to the OMP and the SP algorithms

the proposed algorithm can reconstruct the target signal more effective and stable

especially under the conditions of low SNR and PRF. The shadowing effect

which results from the scatterers of the target that will be unsighted to radar in some observation intervals during a spin cycle

is considered in the third experiment. It well demonstrates the ability of the proposed algorithm to alleviate the shadowing effect. The locations of all the scatterers can be correctly estimated from the seriously insufficient samples.When the radar PRF cannot satisfy the Nyquist sampling theorem

the CoSaMP algorithm is used for image formation of highspeed spinning targets based on the CS theory. The algorithm further improves the ability of information-access of low PRF radar on the high-speed spinning targets

which benefits the target recognition.