No Arabic abstract
Layover separation has been fundamental to many synthetic aperture radar applications, such as building reconstruction and biomass estimation. Retrieving the scattering profile along the mixed dimension (elevation) is typically solved by inversion of the SAR imaging model, a process known as SAR tomography. This paper proposes a nonlinear blind scatterer separation method to retrieve the phase centers of the layovered scatterers, avoiding the computationally expensive tomographic inversion. We demonstrate that conventional linear separation methods, e.g., principle component analysis (PCA), can only partially separate the scatterers under good conditions. These methods produce systematic phase bias in the retrieved scatterers due to the nonorthogonality of the scatterers steering vectors, especially when the intensities of the sources are similar or the number of images is low. The proposed method artificially increases the dimensionality of the data using kernel PCA, hence mitigating the aforementioned limitations. In the processing, the proposed method sequentially deflates the covariance matrix using the estimate of the brightest scatterer from kernel PCA. Simulations demonstrate the superior performance of the proposed method over conventional PCA-based methods in various respects. Experiments using TerraSAR-X data show an improvement in height reconstruction accuracy by a factor of one to three, depending on the used number of looks.
For 3D Synthetic Aperture Radar (SAR) imaging, one typical approach is to achieve the cross-track 1D focusing for each range-azimuth pixel after obtaining a stack of 2D complex-valued images. The cross-track focusing is the main difficulty as its aperture length is limited and the antenna positions are usually non-uniformly distributed. Sparsity regularization methods are widely used to tackle these problems. However, these methods are of obvious limitations. The most well-known ones are their heavy computational burdens and unsatisfied stabilities. In this letter, an efficient deep network-based cross-track imaging method is proposed. When trained, the imaging process, i.e. the forward propagation of the network, is made up of simple matrix-vector calculations and element-wise nonlinearity operations, which significantly speed up the imaging. Also, we find that the deep network is of good robustness against noise and model errors. Comprehensive simulations and experiments have been carried out, and the superiority of the proposed method can be clearly seen.
Existing SAR tomography (TomoSAR) algorithms are mostly based on an inversion of the SAR imaging model, which are often computationally expensive. Previous study showed perspective of using data-driven methods like KPCA to decompose the signal and reduce the computational complexity. This paper gives a preliminary demonstration of a new data-driven method based on sparse Bayesian learning. Experiments on simulated data show that the proposed method significantly outperforms KPCA methods in estimating the steering vectors of the scatterers. This gives a perspective of data-drive approach or combining it with model-driven approach for high precision tomographic inversion of large areas.
We propose and experimentally demonstrate an optical pulse sampling method for photonic blind source separation. The photonic system processes and separates wideband signals based on the statistical information of the mixed signals and thus the sampling frequency can be orders of magnitude lower than the bandwidth of the signals. The ultra-fast optical pulse functions as a tweezer that collects samples of the signals at very low sampling rates, and each sample is short enough to maintain the statistical properties of the signals. The low sampling frequency reduces the workloads of the analog to digital conversion and digital signal processing systems. In the meantime, the short pulse sampling maintains the accuracy of the sampled signals, so the statistical properties of the undersampling signals are the same as the statistical properties of the original signals. With the optical pulses generated from a mode-locked laser, the optical pulse sampling system is able to process and separate mixed signals with bandwidth over 100GHz and achieves a dynamic range of 30dB.
The family of constant-modulus algorithms is widely used in wireless communication systems and in radar. The classical constant-modulus adaptive (CMA) algorithm, however, fails to lock onto a single mode when used in conjunction with an antenna array. Instead, it equalizes the entire spatial spectrum. In this paper, we describe in full detail our recently proposed approach for the separation of multiple users in a radio system with frequency reuse, such as a cellular network, making use of the CMA algorithm. Based on the observation that the differential filter weights resemble a superposition of the array steering vectors, we cast the original task to a direction-of-arrival estimation problem. With rigorous theoretical analysis of the array response based on the discrete-space Fourier transform we elaborate a solution that solves the problem by finding the roots of a polynomial equation. We provide a numerical example to demonstrate the validity of the approach under high-SNR conditions. In addition, we propose a more general preprocessor for the CMA array which allows the modulated signals to differ in amplitude. As a byproduct, the preprocessor yields a low-cost estimate of the number of concurrent users, i.e. the model order, by simply counting the roots with the strongest response.
In this work, we consider the problem of blind source separation (BSS) by departing from the usual linear model and focusing on the linear-quadratic (LQ) model. We propose two provably robust and computationally tractable algorithms to tackle this problem under separability assumptions which require the sources to appear as samples in the data set. The first algorithm generalizes the successive nonnegative projection algorithm (SNPA), designed for linear BSS, and is referred to as SNPALQ. By explicitly modeling the product terms inherent to the LQ model along the iterations of the SNPA scheme, the nonlinear contributions of the mixing are mitigated, thus improving the separation quality. SNPALQ is shown to be able to recover the ground truth factors that generated the data, even in the presence of noise. The second algorithm is a brute-force (BF) algorithm, which is used as a post-processing step for SNPALQ. It enables to discard the spurious (mixed) samples extracted by SNPALQ, thus broadening its applicability. The BF is in turn shown to be robust to noise under easier-to-check and milder conditions than SNPALQ. We show that SNPALQ with and without the BF postprocessing is relevant in realistic numerical experiments.