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For inverse synthetic aperture radar (ISAR) imaging of targets with micromotion parts, the removal of micro-Doppler (m-D) effects is the key procedure. However, under the condition of a sparse aperture, the echo pulse is limited or incomplete, giving rise to the difficulty of eliminating m-D effects. Thus, a novel m-D effects removal algorithm is proposed, which can effectively eliminate m-D effects, as well as the interference introduced by noise and sparse aperture in the ISAR image of the main body. The proposed algorithm mainly includes two processing steps. First, combined with the cut-off point determined by the normalized singular value difference spectrum, the rough estimation of the main body is achieved by singular value decomposition (SVD). Then, the variational mode extraction (VME) is extended to complex variational mode extraction (CVME). The constrained variational problem constructed by bandwidth and spectral overlap constraints is solved by the alternating direction method of multipliers (ADMM), and the precise estimation of the main body is obtained. Experimental results based on both simulated and measured data demonstrate that the proposed algorithm can acquire the high-resolution ISAR image of the main body under noisy and sparse conditions. [ABSTRACT FROM AUTHOR]