This paper proposes a novel bistatic inverse synthetic aperture radar (ISAR) imaging algorithm for the target with complex motion under low signal to noise ratio (SNR) condition. Note the bistatic ISAR system generally suffers from a lower SNR than the monostatic one because of its non-mirror reflection geometry. A de-noising method, therefore, is proposed to improve SNR of range profiles, which accumulates the aligned range profiles non-coherently to obtain a window for noise suppression. Additionally, since the complex motion of target induces nonstationary Doppler, which is destructive to ISAR imaging, an optimal coherent processing interval (CPI) selection algorithm is further proposed to find out the interval where the Doppler is relatively stationary, so as to produce well-focused ISAR images. It utilizes the reassigned time-frequency (TF) method to obtain the high resolution instantaneous Doppler spectrum, and the minimum entropy criterion to select the optimal CPI, respectively. Note the selected CPI often contains too limited pulses to produce ISAR images with high resolution. A sparse aperture ISAR imaging method within the Bayesian framework is further proposed, which introduces the Laplacian scale mixture (LSM) model as the sparse prior, so as to reconstruct well-focused ISAR images with high resolution and low side lobes from the limited data. Compared with the traditional sparse Bayesian learning method, the proposed LSM based ISAR imaging performs superiorly on resolution improvement and noise reduction. Experimental results based on both simulated and measured data validate the effectiveness of the proposed algorithms.