Three-dimensional (3-D) imaging plays a vital role in the recognition of spinning space debris. However, the image may be blurred due to the range migration caused by fast rotation of space debris. Moreover, the image quality, which depends on the estimation accuracy of Doppler frequency and chirp rate of scattering centers, is influenced by cross-terms and sidelobes. In this article, we propose a novel 3-D imaging method based on smoothed Lv distribution (SLVD). Firstly, the selection criterion for best imaging time based on the time–frequency moment is proposed to guarantee that the echo is approximated as a linear frequency modulation (LFM) signal. Then, we operate the Khatri–Rao product on the centroid frequency and chirp rate (CFCR) representation and the range-Doppler (RD) image to obtain the 3-D image. To decrease the influence of range migration, we process a short time window during the RD imaging procedure. For cross-term and sidelobe suppression, the SLVD is proposed to obtain the CFCR representation by expressing the Lv distribution (LVD) in a convolution form and introducing a centroid frequency window. Experimental results verify the effectiveness of the proposed imaging method and the good performance of the proposed SLVD for cross-term and sidelobe suppression.

Motivated by the problem of radar target recognition, we develop a label-aided factor analysis (LA-FA) model for statistical modeling of high-resolution range profile (HRRP) under the prerequisite that the HRRP data are Gaussian distributed. The LA-FA model is the extension of the multi-task learning based factor analysis (MTL-FA) model which is mainly applied to the recognition problem with small training data size. Compared to the MTL-FA model, our LA-FA model introduces the discrete class labels via Sigmoid-Bernoulli hierarchy to restrict the learning of model parameters, which offers the potential to enhance the separability of statistical models from different classes, thus beneficial to the improvement of recognition capability. In addition, since the noise level of a test sample is usually different from those of the training samples in the real application, we introduce a noise-robust modification method for Gaussian-based models. The proposed modification method is implemented by updating the noise level parameter of the statistical model according to the estimated signal-to-noise ratio (SNR) of test HRRP. Experiments on measured HRRP data demonstrate the better recognition performance of the LA-FA model with limited training data and our noise-robust model modification method under low test SNR. Especially, when there are 20 training HRRP samples per frame, the recognition rate of our LA-FA model is 7% higher than that of the MTL-FA model, and moreover, the recognition accuracy of the noise-robust LA-FA model is 3% higher than that of the LA-FA model without modification under the condition of SNR=15 dB.

Most existing synthetic aperture radar (SAR) target recognition methods based on deep learning are of black boxes structure and data-drive networks, which are faced with the issue of severe performance degradation under extended operating conditions (EOCs). To address the issue, this paper proposes an end-to-end mechanism-driven interpretable network (EMI-Net) for SAR target recognition under EOCs. The EMI-Net achieves the integration of scattering center feature extraction and target recognition in an end-to-end framework to avoid the mismatch between scattering center features with classifier and also explore the representative electromagnetic characteristics that are useful for recognition under EOCs. In EMI-Net, by unfolding a sparse solving algorithm and integrating scattering center model into deep networks, our model contains feature encoding and decoding procedures of SAR images. Thus, EMI-Net is an interpretable deep unfolding network that is driven by physical mechanism to precisely learn scattering center features reflecting locations and amplitude of SAR targets based on the deep learning mode. Our EMI-Net divides input images into multiple patches based on the image-domain scattering center model to reduce its computation and space complexities. In addition, EMI-Net treats the scattering centers as discrete three-dimensional point data and designs a point cloud network as classifier to explore permutation-invariant representations for recognition. Results on the measured dataset validate that EMI-Net gains superior scattering center extraction and target recognition results under EOCs, and also shows high time-efficiency and low memory requirement.

In this article, a deep probability model, called the discriminative mixture variational autoencoder (DMVAE), is developed for the feature extraction in semisupervised learning. The DMVAE consists of three parts: 1) the encoding; 2) decoding; and 3) classification modules. In the encoding module, the encoder projects the observation to the latent space, and then the latent representation is fed to the decoding part, which depicts the generative process from the hidden variable to data. In particular, the decoding module in our DMVAE partitions the observed dataset into some clusters via multiple decoders whose number is automatically determined via the Dirichlet process (DP) and learns a probability distribution for each cluster. Compared to the standard variational autoencoder (VAE) describing all data with a single probability function, the DMVAE has the capacity to give a more accurate description for observations, thus improving the characterization ability of the extracted features, especially for the data with complex distribution. Moreover, to obtain a discriminative latent space, the class labels of labeled data are introduced to restrict the feature learning via a softmax classifier, with which the minimum entropy of the predicted labels for the features from unlabeled data can also be guaranteed. Finally, the joint optimization of the marginal likelihood, label, and entropy constraints makes the DMVAE have higher classification confidence for unlabeled data while accurately classifying the labeled data, ultimately leading to better performance. Experiments on several benchmark datasets and the measured radar echo dataset show the advantages of our DMVAE-based semisupervised classification over other related methods.

Sound field separation technique has been proposed, which overcomes the limitati on on applications of near_field acoustic holography (NAH). The limitation is th at the sound field on one side of holographic plane must be free，that is to say , all the sound sources must be confined to the other side. Sound field separation technique with double holographic planes has been built according to the wave field extrapolation theorem and the superposition theorem of sound pressure scalar in wave_number domain, and the technique with single holographic planes has also been built according to Euler's formulation and the vector superposition theorem of particle velocity in wave_number domain. A particular feature of the technique is that the influence of background noise on reconstructed results can be removed while retaining the background noise in the holographic measurements. The derivation of the principle verifies the technique theoretically, and the computer simulations and experiment demonstrate its feasibility and effectiveness.

Aiming at the signal reconstruction problem for the conventional narrowband radar system, we propose a new statistical compressive sensing (SCS) method to achieve the reconstruction of superresolution time-frequency spectrum from the corrupted time-domain measurement. The proposed method assumes that the signal obeys complex Gaussian distribution and develops a hierarchical Bayesian model. Variational Bayesian expectation maximization (VBEM) is used to perform inference for the posterior distributions of the model parameters. In order to fully exploit the superresolution characteristics of reconstructed spectrum, a novel superresolution time-frequency feature vector is extracted for subsequent classification of ground moving targets, i.e., walking person and a moving wheeled vehicle. Experimental results on measured data show that the proposed reconstruction method can obtain good reconstruction results and the superresolution feature has good classification performance for human and vehicle targets.