Micro-Doppler Effect Removal in ISAR Imaging by Promoting Joint Sparsity in Time-Frequency Domain

2018 Sensors  
For micromotion scatterers with small rotating radii, the micro-Doppler (m-D) effect interferes with cross-range compression in inverse synthetic aperture radar (ISAR) imaging and leads to a blurred main body image. In this paper, a novel method is proposed to remove the m-D effect by promoting the joint sparsity in the time-frequency domain. Firstly, to obtain the time-frequency representations of the limited measurements, the short-time Fourier transform (STFT) was modelled by an
more » ... ed equation. Then, a new objective function was used to measure the joint sparsity of the STFT entries so that the joint sparse recovery problem could be formulated as a constrained minimization problem. Similar to the smoothed l 0 (SL0) algorithm, a steepest descend approach was used to minimize the new objective function, where the projection step was tailored to make it suitable for m-D effect removal. Finally, we utilized the recovered STFT entries to obtain the main body echoes, based on which cross-range compression could be realized without m-D interference. After all contaminated range cells were processed by the proposed method, a clear main body image could be achieved. Experiments using both the point-scattering model and electromagnetic (EM) computation validated the performance of the proposed method. Sensors 2018, 18, 951 2 of 17 the sparse representation (SR)-based algorithms where the sinusoids are eliminated. Nevertheless, the aforementioned methods [5-7] cannot remove the m-D effect generated by a micromotion scatterer with a small rotating radius, since the m-D signal has the same straight line shape as the main body signal in the spectrogram when the rotating radius is smaller than half of the range resolution. Recently, some methods based on the time-frequency analysis have been developed to address the problem of the removal of the m-D effect under a small rotating radius. L. Stanković et al. 's method [8], based on L-statistics, performs the short-time Fourier transform (STFT) to the echoes in the contaminated range cell. It is assumed in L. Stanković et al. [8] that the m-D interference occupies a small portion of time instants at each frequency bin. Using the L-statistics, a fixed fraction of the most significant STFT entries were eliminated to achieve m-D effect removal. Subsequently, the remaining entries were utilized to recover the main body signal. However, a large amount of STFT entries corresponding to the main body might be removed together with the m-D interference, which leads to a high sidelobe level in the imaging result [9] . A method based on histogram analysis is proposed in R. Zhang et al. [9], where the STFT entries with a high frequency of occurrence were regarded as the main body components and were preserved to reconstruct the ISAR image. On the other hand, the STFT entries with a low frequency of occurrence were considered to correspond to the m-D interference and suppressed. When the m-D effect is severe, the method in R. Zhang et al. [9] cannot remove the m-D signal in the time-frequency domain completely because the m-D components might be mistaken for the main body signal. Consequently, there are some spurious points in the imaging result due to the residual m-D signal. In real world situations, the data samples of the echoes might be randomly missing at given time instants [10] where strong electromagnetic interference or sensor failure prevents effective observation. As a result, the effective pulses are limited. The L-statistics-based method is combined with the short-time compressed sensing (STCS) [11] approach in Q. K. Hou et al. [12] to reduce the m-D effect with limited pulses. The STCS was employed to recover the STFT entries where the number of the frequency bins was equal to the number of full pulses. Nevertheless, the window width in the STCS could have been much shorter than the signal duration to obtain the local frequency characteristics. Thus, the measurements in the window were much fewer than the frequency bins in the time-frequency domain. The frequency resolution of the recovered STFT entries was reduced due to the extremely limited measurements. As a result, the L-statistics-based method in Q.K. Hou et al. [12] cannot obtain the accurate support of the main body signal in the frequency dimension and some spurious points exist near the main body scatterers in the imaging result. The main body scatterer has a constant Doppler frequency [13] . Thus, the support of the main body signal is a slow time invariant in the time-frequency domain which indicates the joint sparsity [14, 15] of the main body signal. In contrast, the Doppler frequency of the micromotion scatterer varies with the slow time [13] . Based on the distinct patterns in the time-frequency domain, this paper proposes a joint sparsity-based ISAR imaging method to remove the m-D effect generated by the micromotion scatterers with small rotating radii. Firstly, the echoes in the contaminated range cell were modelled by an underdetermined equation where the relation of the echoes and the corresponding STFT entries is built on the STFT matrix. Generally, the l 2 /l 0 -norm [16] of the STFT entry vector could be used to measure the joint sparsity in the time-frequency domain because it is equal to the number of frequency bins having nonzero STFT entries. Nonetheless, minimizing the l 2 /l 0 -norm leads to a combinatorial optimization problem [17] that is difficult to solve. In M. Bevacqua et al. [18], the l 1
doi:10.3390/s18040951 pmid:29570641 pmcid:PMC5948648 fatcat:hphswyh7wjbcxbldyq6ogypzay