The inverse synthetic aperture radar(ISAR) imaging can be converted into a sparse reconstruction problem and solved by the l_1-norm minimization algorithm. The basis matrix in sparse ISAR imaging is usually characterized by the unknown rotation rate of a moving target, thus the rotation rate and the sparse signal should be jointly estimated. Especially due to the imperfect coarse motion compensation, we consider the phase error correction problem in the context of the sparse signal reconstruction. To address this issue, we propose an iterative reweighted method,which jointly estimates the rotation rate, corrects the phase error and reconstructs a high resolution ISAR image. The proposed method gives a gradual and interweaved iterative process to refine the unknown parameters to achieve the best sparse representation for the ISAR signals. Particularly, in ISAR image reconstruction,the l_1-norm minimization algorithm is sensitive to user parameters.Setting these user parameters are not trivial and the reconstruction performance depends significantly on their choices. Then, we consider an expansion-compression variance-component(ExCoV) based method, which is automatic and demands no prior knowledge about signal-sparsity or measurement-noise levels. Both numerical and electromagnetic data experiments are implemented to show the effectiveness of the proposed method. It is shown that the proposed method can estimate the rotation rate and correct the phase errors simultaneously, and its superior performance is proved in terms of high resolution ISAR image. The basis synthetic matrix in sparse ISAR imaging is most characterized by the unknown rotation rate of a moving target, thus the rotation Especially due to the imperfect coarse motion compensation, we consider the phase error correction problem in the context of the sparse signal reconstruction. To address this issue, we propose an iterative reweighted method, which jointly estimates the rotation rate, corrects the phase error and reconstructs a high resolution ISAR image. The proposed method gives a gradual and interweaved iterative process to refine the unknown parameters to achieve the best sparse representation for the ISAR signals. Particularly, in ISAR image reconstruction, the l_1-norm minimization algorithm is sensitive to user parameters.Setting these user parameters are not t rivial and the reconstruction performance depends significantly on their choices. Both, we consider an expansion-compression variance-component (ExCoV) based method, which is automatic and demands no prior knowledge about signal-sparsity or measurement-noise levels. Both numerical and electromagnetic data experiments are implemented to show the effectiveness of the proposed method. It is shown that the proposed method can estimate the rotation rate and correct the phase errors simultaneously, and its superior performance is proved in terms of high resolution ISAR image.