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Hyperspectral image (HSI) unmixing is an increasingly studied problem in various areas, including remote sensing. It has been tackled using both physical model-based approaches and more recently machine learning-based ones. In this article, we propose a new HSI unmixing algorithm combining both model- and learning-based techniques, based on algorithm unrolling approaches, delivering improved unmixing performance. Our approach unrolls the alternating direction method of multipliers (ADMMs) solver of a constrained sparse regression problem underlying a linear mixture model. We then propose a neural network structure for abundance estimation that can be trained using supervised learning techniques based on a new composite loss function. We also propose another neural network structure for blind unmixing that can be trained using unsupervised learning techniques. Our proposed networks are also shown to possess a lighter and richer structure containing less learnable parameters and more skip connections compared with other competing architectures. Extensive experiments show that the proposed methods can achieve much faster convergence and better performance even with a very small training dataset size when compared with other unmixing methods, such as model-inspired neural network for abundance estimation (MNN-AE), model-inspired neural network for blind unmixing (MNN-BU), unmixing using deep image prior (UnDIP), and endmember-guided unmixing network (EGU-Net). [ABSTRACT FROM AUTHOR]

Airborne SAR tomography (TomoSAR) 3D image reconstruction can be realized with combination of 2D imaging algorithms and compressed sensing (CS) algorithms. However, most typical CS algorithms cannot achieve a balance between algorithm efficiency and 3D reconstruction accuracy. Due to difficulties in flight path control of airborne SAR, it is hard to realize registration of SAR images with frequency-domain imaging algorithms because of time-varying baseline. To address these problems, an efficient 3D image reconstruction method for airborne TomoSAR based on back projection (BP) algorithm and improved adaptive iterative shrinkage-thresholding algorithm (IA-ISTA) is proposed. First, 2D images are achieved with BP algorithm on the ground plane. After registration of SAR images, 3D image reconstruction results in the elevation direction are realized with IA-ISTA. Selection criterion of IA-ISTA parameters are given in this paper. At last, final 3D image reconstruction results are achieved after geometrical transformation based on geometric relationship. Both simulated data and measured data of a P-band airborne TomoSAR system are used. 3D image reconstruction results show that the proposed method outperforms traditional methods regarding efficiency and accuracy, which proves the validity and practicality of the proposed method.

Compressed sensing (CS) demonstrates significant potential to improve image quality in 3-D millimeter-wave imaging compared with conventional matched filtering (MF). However, existing sparsity-driven 3-D imaging algorithms always suffer from large-scale storage, excessive computational cost, and nontrivial tuning of parameters due to the huge-dimensional matrix–vector multiplication in complicated iterative optimization steps. In this article, we present a novel range migration (RM) kernel-based iterative-shrinkage thresholding network, dubbed as RMIST-Net, by combining the traditional model-based CS method and data-driven deep learning method for near-field 3-D millimeter-wave (mmW) sparse imaging. First, the measurement matrices in ISTA optimization steps are replaced by RM kernels, by which matrix–vector multiplication is converted to the Hadamard product. Then, the modified ISTA optimization is unrolled into a deep hierarchical architecture, in which all parameters are learned automatically instead of manually tuned. Subsequently, 1000 pairs of oracle images with randomly distributed targets and their corresponding echoes are simulated to train the network. A well-trained RMIST-Net produces high-quality 3-D images from range-focused echoes. Finally, we experimentally prove that RMIST-Net is capable process $512 \times 512$ large-scale imaging tasks within 1 s. Besides, we compare RMIST-Net with other state-of-the-art methods in near-field 3-D imaging applications. Both simulations and real-measured experiments demonstrate that RMIST-Net produces impressive reconstruction performance while maintaining high computational speed compared with conventional and sparse imaging algorithms. [ABSTRACT FROM AUTHOR]

Scanning radar can be used to obtain images of targets in forward-looking area, and has attracted much attention in many fields, such as ocean monitoring, air-to-ground attack, navigation, and so on. However, its azimuth resolution is extremely poor due to the limitation of the antenna size. In order to break through the limitation, many superresolution algorithms have been proposed, and iterative shrinkage-thresholding algorithm (ISTA) is one of the most famous methods because of its antinoise ability and simplicity. In the meantime, the slow convergence of iterative shrinkage-thresholding algorithm is also known to all. In this article, a second-order accelerated ISTA for scanning radar forward-looking superresolution imaging is proposed. In this algorithm, a prediction vector is constructed before each iteration by using the first and the second-order difference information of iteration vectors to reduce the number of iterations and get a faster convergence speed. In the end, simulations and experimental results are given to illustrate the effectiveness of the accelerated imaging algorithm.

The use of compressive sensing techniques has become predominant in signal processing applications when dealing with sparse signals. Theoretical results on these tools involve drastic conditions on the dictionaries used, which are usually not met in practice. Nevertheless, it has been recently shown that even in the case of very correlated dictionaries, such as dictionaries based on translated waveforms, information can be retrieved from the observations with good accuracy. However, in numerous fields the signals that we have to process are extremely large, making the direct use of standard algorithms impossible. This paper presents a fast version of the Iterative Shrinkage-Thresholding Algorithm (ISTA) for sparse reconstruction based on dictionaries built from translated waveforms. By rearranging the columns of the dictionary, we show that matrix-vector multiplications can be alternatively expressed as convolutions, which can be performed efficiently using standard Fast Fourier Transforms (FFTs). Results on synthetic data validate the proposed convolutional ISTA (CoSA) method. Furthermore, we also show that CoSA is able to attain good results in a real-world application, where ISTA cannot be applied directly: spike localization and activity estimation in a large spectroscopic signal. [ABSTRACT FROM AUTHOR]