In this paper, based on sum-difference co-array analysis, a new fourth-order sparse array called sum-difference-FODC (SD-FODC) is proposed, allowing the construction of a fourth-order DCA with long consecutive lags using the continuous segments in the second-order DCA and SCA of the original array. It has a closed-form expression for sensor positions that can be generated by two arbitrary nonuniform linear arrays (NLAs) called generators. If the second-order SCA and DCA of the generators have long consecutive segments, the designed fourth-order sparse array can achieve a large number of uDOFs. Numerical results are provided to demonstrate the superior performance of the proposed design.

A tensor-based wideband direction of arrival (DOA) estimation method is proposed in this paper. Virtual arrays are initially generated and extended into a unified ULA across all frequencies of interest. Next, the covariance matrices of these virtual array models are computed and stacked to form a three-dimensional tensor. Then, tensor completion with a denoising step is presented, and DOAs can be obtained after tensor decomposition. Simulations demonstrate that improved performance can be achieved by the proposed method in scenarios with varying source power ratios across frequencies.

Two-dimensional (2-D) direction of arrival (DOA) estimation with a circular array based on the difference co-array has attracted considerable attention in past years. In this paper, the difference co-array position set of a circular array with arbitrary sensor arrangement is derived, and condition under which the maximum number of virtual co-array sensors can be provided by a circular array is presented. Then, an augmented uniform circular array (AUCA) is proposed, providing the maximum number of DOFs for arbitrary number of physical sensors. Compressive sensing based focusing method for the one-dimensional case is extend to 2-D wideband DOA estimation, where focusing on the difference co-array is adopted for performance improvement. Simulations show that better performance can be achieved by our proposed AUCA.

Hyperspectral videos (HSVs) offer not only spatial information but also diagnostic spectral features. Due to the fact that spectral features are only related to the material of the object, this advantage can address the issue of RGB video tracking failure when the object and background are visually similar. However, the effectiveness of deep learning models is limited due to insufficient HSV training data. Existing methods tend to divide a hyperspectral image (HSI) into several three-channel false-color images to leverage the existing RGB trackers for transfer learning. Nonetheless, these methods lack adequate exploration of band interrelations and overlook correlation among objects prior to similarity calculation. In this article, a transformer-based band regrouping and feature refinement network (TBR-Net) is introduced, which is specifically tailored for hyperspectral object tracking. To maximize the potential of the RGB tracker and enhance the use of available training data, we propose a transformer-based band regrouping (TBR) method. By modeling long-range spectral dependencies, the inherent context information among bands is captured, which is subsequently utilized to reorganize bands into several false-color images. Furthermore, to combine the relationship of the template and the search (T & S) frames into a correlation calculation, a feature refinement module (FRM) is designed. The cross-attention mechanism enables mutual relation modeling, allowing similar regions to be perceived and form discriminative feature representation. As a result, a hyperspectral tracker can be efficiently trained via transfer learning to address the data insufficiency challenge, while the mutual perception between objects further enhances the tracking performance. Its effectiveness is validated by extensive benchmark experiments, which demonstrate that the TBR-Net surpasses state-of-the-art methods.

Multi-baseline circular synthetic aperture radar (C-SAR) tomography is an important three-dimensional (3-D) radar imaging mode since it allows for omni-directional 3-D reconstruction of targets. Typically, this imaging mode splits the full-aperture data into multiple narrow-apertures to be processed separately due to the sensitivity to elevation angle and imaging height. However, the repeated one-dimensional (1-D) elevation inversion of all imaged pixels for each sub-aperture also leads to more processing time and more parameter estimation uncertainties. In this paper, a new C-SAR tomography framework based on scattering phase correction (SPC) is presented. Our main idea is to use 1-D elevation inversion to estimate the exact height of the distorted scattering points in two-dimensional (2-D) full-aperture image, and derive the imaging height transformation formula. Then these distorted scattering points of different heights are transformed to the proper heights respectively. As a result, the elevation inversion only needs to be done once for the whole framework and does not need to be done for each sub-aperture. Besides, a combination of two separate processing chains (i.e., fast coherent imaging and slices transform imaging) is used to minimize the 3-D reconstruction errors caused by the imaging height transformation and 1-D elevation inversion. Numerical and outdoor measurement results of real-world complex targets are presented to demonstrate the usefulness of the proposed framework.

In this paper, we consider the underdetermined two dimensional (2-D) source localization problem for wideband sources based on a distributed sensor array network, where a sparse sub-array is placed on each observation platform and the source number is larger than the sensor number of each sub-array. The received signals are first decomposed into different frequency bins via discrete Fourier transform (DFT), followed by the vectorization process to obtain the virtual array model with a larger aperture. Then, focusing is applied to the virtual array instead of the physical array for performance improvement, and a group sparsity based 2-D localization method exploiting the difference co-array is proposed, with increased DOFs for localization. Improved performance is achieved as demonstrated by computer simulations.

A generalized sum-difference expansion scheme is proposed to construct sparse arrays based on the fourth-order difference co-array with increased degrees of freedom (DOFs). Different from existing structures, both the second-order sum and difference co-arrays are exploited in array construction under this scheme, leading to a large consecutive fourth-order difference co-array with its number of uniform DOFs (uDOFs) derived. To optimize the provided uDOFs, required design properties of the initial prototype arrays are discussed. Three examples are then provided to demonstrate its superior performance over existing structures in both resolution capacity and estimation accuracy.

We present extended Cantor arrays based on fourth- order difference co-arrays (E-FO-Cantor). These arrays result from extending the recently proposed fractal arrays to fourth- order difference co-arrays, and lead to fourth-order difference co-arrays that are hole-free. The set of sensor positions of the E-FO-Cantor is expressed in a simple and recursive form. The proposed Cantor arrays lead to O(N2log23) ≈ O(N3.17) degrees of freedom compared to O(N2) that can be achieved by existing sparse arrays with the hole-free property. Compared with other sparse arrays with the hole-free property in their fourth-order co-arrays, the proposed Cantor arrays provide a longer uniform linear array with more virtual sensors, leading to better DOA estimation performance.

The Cramér-Rao bound (CRB) for direction of arrival (DOA) estimation exploiting both auto-correlation and cross-correlation information within multiple frequencies of the received array signals is derived. It provides a tighter bound than the existing CRB for the dual-frequency scenario. For the multiple frequencies, it is much lower than its dual-frequency counterpart, and also exists for a greater number of sources, thereby validating that exploiting multiple frequency pairs can improve both estimation accuracy and target resolvability.

The generalized linear moving sampling scheme (MSS) exploiting the second-order statistics and also the high-order cumulants is studied, where the set of MSS is defined as the shifted distance offsets involved in estimation based on a moving platform. Then, sparse physical arrays (SPAs) with nonuniform linear moving sampling schemes (NL-MSS), referred to as SPA-NL-MSS, are proposed to optimize the consecutive difference co-arrays. For the same number of sensors and data samples, better performance in terms of both the number of degrees of freedom (DOFs) and estimation accuracy can be achieved by SPA-NL-MSS than existing array structures exploiting array motions at the second order level.

The target localization problem for distributed sensor array networks where a sub-array is placed at each receiver is studied, and under the compressive sensing (CS) framework, a group sparsity based two-dimensional localization method is proposed. Instead of fusing the separately estimated angles of arrival (AOAs), it processes the information collected by all the receivers simultaneously to form the final target locations. Simulation results show that the proposed localization method provides a significant performance improvement compared with the commonly used maximum likelihood estimator (MLE).

An expanding and shift scheme for efficient fourth-order difference coarray construction is proposed. It consists of two sparse subarrays, where one of them is modified and shifted according to the analysis provided. The number of consecutive lags of the proposed structure at the fourth order is consistently larger than two previously proposed methods. Two effective construction examples are provided with the second sparse subarray chosen to be a two-level nested array, as such a choice can increase the number of consecutive lags further. Simulations are performed to show the improved performance by the proposed method in comparison with existing structures.

Group-sparsity-based method is applied to the 2qth-order difference coarray for underdetermined wideband direction of arrival (DOA) estimation. For complexity reduction, a focused compressive-sensing-based approach is proposed, without sacrificing its performance. Different from the conventional focusing approach, in the proposed one, focusing is applied to the virtual arrays and no preliminary DOA estimation is required. Simulation results are provided to demonstrate the effectiveness of the proposed methods.

To reach a higher number of degrees of freedom by exploiting the fourth-order difference co-array concept, an effective structure extension based on two-level nested arrays is proposed. It increases the number of consecutive lags in the fourth-order difference coarray, and a virtual uniform linear array (ULA) with more sensors and a larger aperture is then generated from the proposed structure, leading to a much higher number of distinguishable sources with a higher accuracy. Compressive sensing based approach is applied for direction-of-arrival (DOA) estimation by vectorizing the fourth-order cumulant matrix of the array, assuming non-Gaussian impinging signals.

An effective sparse array extension method for maximizing the number of consecutive lags in the fourth-order difference co-array is proposed, leading to a novel enhanced sparse array structure based on co-prime arrays (CPAs) with significantly increased number of degrees of freedom (DOFs). One method to exploit the increased DOFs based on nonstationary signals is also proposed, with simulation results provided to demonstrate the effectiveness of the proposed structure.

A class of low-complexity compressive sensing-based direction-of-arrival (DOA) estimation methods for wideband co-prime arrays is proposed. It is based on a recently proposed narrowband estimation method, where a virtual array model is generated by directly vectorizing the covariance matrix and then using a sparse signal recovery method to obtain the estimation result. As there are a large number of redundant entries in both the auto-correlation and cross-correlation matrices of the two sub-arrays, they can be combined together to form a model with a significantly reduced dimension, thereby leading to a solution with much lower computational complexity without sacrificing performance. A further reduction in complexity is achieved by removing noise power estimation from the formulation. Then, the two proposed low-complexity methods are extended to the wideband realm utilizing a group sparsity based signal reconstruction method. A particular advantage of group sparsity is that it allows a much larger unit inter-element spacing than the standard co-prime array and therefore leads to further improved performance.