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In inverse synthetic aperture radar (ISAR) imaging, a target is usually regarded as consist of a few strong (specular) scatterers and the distribution of these strong scatterers is sparse in the imaging volume. In this paper, we propose to incorporate the sparse signal recovery method in 3D multiple-input multiple-output radar imaging algorithm. Sequential order one negative exponential (SOONE) function, which forms homotopy between ℓ1 and ℓ0 norms, is proposed to measure the sparsity. Gradient projection is used to solve a constrained nonconvex SOONE function minimization problem and recover the sparse signal. However, while the gradient projection method is computationally simple, it is not robust when a matrix in the algorithm is ill conditioned. We thus further propose using diagonal loading and singular value decomposition methods to improve the robustness of the algorithm. In order to handle targets with large flat surfaces, a combined amplitude and total-variation objective function is also proposed to regularize the shapes of the flat surfaces. Simulation results show that the proposed gradient projection of SOONE function method is better than orthogonal matching pursuit, CoSaMp, ℓ1-magic, Bayesian method with Laplace prior, smoothed ℓ0 method, and ℓ1-ℓs in high SNR cases for recovery of ±1 random spikes sparse signal. The quality of the simulated 3D images and real data ISAR images obtained using the new method is better than that of the conventional correlation method and minimum ℓ2 norm method, and competitive to the aforementioned sparse signal recovery algorithms.