Alternating Projection Algorithm Research Articles

ECCM Scheme for Countering Main-Lobe Interrupted Sampling Repeater Jamming via Signal Reconstruction and Mismatched Filtering

Digital radio frequency memory (DRFM)-based main-lobe interrupted sampling repeater jamming (ISRJ) can achieve the effects of both deception and suppression, which cause serious performance degradation in modern radar systems. In this article, we propose an electronic counter-countermeasure (ECCM) scheme based on signal reconstruction and mismatched filtering (SC-MMF). The ECCM scheme consists of two steps: time-domain signal reconstruction and mismatched filter (MMF) design. First, the time-domain signal without noise is reconstructed using the provided jamming perception information. Then, an MMF corresponding to the reconstructed signal is designed to suppress ISRJ targets. The MMF design problem is formulated as a problem of minimizing the peak false target level (PFTL) and is solved with an improved alternating projection algorithm. After mismatched filtering, ISRJ targets are suppressed. Numerical simulations validate the effectiveness of the proposed method and explore the impacts of various parameters on its performance. Moreover, results obtained on measured data show that the proposed method has practical value in engineering applications.

A Spatial–Temporal Joint Radar-Communication Waveform Design Method with Low Sidelobe Level of Beampattern

A joint radar-communication (JRC) system utilizes the integrated transmit waveform and a single platform to perform radar and communication functions simultaneously. Admittedly, the multibeam waveform design approach could transmit the assigned waveforms in different beams with the aid of spatial and temporal degrees of freedom. However, a high sidelobe level (SLL) in the beampattern reduces energy efficiency and expands exposure probability. In this study, we propose a novel spatial–temporal joint waveform design method based on the beamforming algorithm to form a low SLL beampattern. Waveform synthesis constraints are considered to synthesize desired radar and communication waveforms at designated directions. Furthermore, we impose the constant modulus constraint to lessen the impact of the high peak-to-average ratio (PAPR). The optimization process of the whole model can be summarized as two stages. First, the covariance matrix is created by convex optimization with respect to the minimum SLL. Second, the integrated transmit waveform is tuned through an alternating projection algorithm. Based on the simulation findings, we demonstrate that the proposed method outperforms the traditional methods in terms of low SLL and waveform synthesis. Meanwhile, we validate the effectiveness of the proposed method using semi-physical experiment results.

Low-dose sinogram restoration enabled by conditional GAN with cross-domain regularization in SPECT imaging.

In order to generate high-quality single-photon emission computed tomography (SPECT) images under low-dose acquisition mode, a sinogram denoising method was studied for suppressing random oscillation and enhancing contrast in the projection domain. A conditional generative adversarial network with cross-domain regularization (CGAN-CDR) is proposed for low-dose SPECT sinogram restoration. The generator stepwise extracts multiscale sinusoidal features from a low-dose sinogram, which are then rebuilt into a restored sinogram. Long skip connections are introduced into the generator, so that the low-level features can be better shared and reused, and the spatial and angular sinogram information can be better recovered. A patch discriminator is employed to capture detailed sinusoidal features within sinogram patches; thereby, detailed features in local receptive fields can be effectively characterized. Meanwhile, a cross-domain regularization is developed in both the projection and image domains. Projection-domain regularization directly constrains the generator via penalizing the difference between generated and label sinograms. Image-domain regularization imposes a similarity constraint on the reconstructed images, which can ameliorate the issue of ill-posedness and serves as an indirect constraint on the generator. By adversarial learning, the CGAN-CDR model can achieve high-quality sinogram restoration. Finally, the preconditioned alternating projection algorithm with total variation regularization is adopted for image reconstruction. Extensive numerical experiments show that the proposed model exhibits good performance in low-dose sinogram restoration. From visual analysis, CGAN-CDR performs well in terms of noise and artifact suppression, contrast enhancement and structure preservation, particularly in low-contrast regions. From quantitative analysis, CGAN-CDR has obtained superior results in both global and local image quality metrics. From robustness analysis, CGAN-CDR can better recover the detailed bone structure of the reconstructed image for a higher-noise sinogram. This work demonstrates the feasibility and effectiveness of CGAN-CDR in low-dose SPECT sinogram restoration. CGAN-CDR can yield significant quality improvement in both projection and image domains, which enables potential applications of the proposed method in real low-dose study.

Research on Leakage Location of Pipeline Based on Module Maximum Denoising

Leak detection and location of water supply pipelines is an important area of research, and it is especially important to find the leakage location in time and repair them. In view of the problem, that a large amount of noise is mixed in the detection signal when the pipeline leaks, it will inevitably affect the detection and positioning effect. In this paper, a denoising algorithm based on improved module maximum is proposed. Firstly, a discrete binary wavelet transform is carried out on the noisy signal, and the module maximum point corresponding to the wavelet transform coefficients, on each scale, is obtained. Secondly, different thresholds are used for the module maximum of different scale layers and the wavelet coefficients are reconstructed according to the retained module maximum and their extremums. Thirdly, the alternative projection algorithm is used to effectively suppress the false oscillations in the reconstructed signal, improve the quality of the reconstructed signal, and obtain the noise reduction signal. Finally, according to the theory of the negative pressure wave, the inflection point of the negative pressure wave is identified by the wavelet decomposition method, and the location of leakage point is determined. In order to verify the effectiveness of the proposed algorithm, a leakage simulation experiment system of water supply pipeline is built. The analysis of the results shows that, compared with the wavelet denoising method and the EMD-based method, the method proposed in this paper achieves a better denoising effect, obtains a smoother pressure signal, retains the signal waveform characteristics, and identifies the obvious inflexion point of the negative pressure wave. The minimum relative error of leakage point location is 0.9%, and the maximum relative error is 2.5%.

Low-Photon Counts Coherent Modulation Imaging via Generalized Alternating Projection Algorithm

Phase contrast imaging is advantageous for mitigating radiation damage to samples, such as biological specimens. For imaging at nanometer or atomic resolution, the required flux on samples increases dramatically and can easily exceed the sample damage threshold. Coherent modulation imaging (CMI) can provide quantitative absorption and phase images of samples at diffraction-limited resolution with fast convergence. When used for radiation-sensitive samples, CMI experiments need to be conducted under low illumination flux for high resolution. Here, an algorithmic framework is proposed for CMI involving generalized alternating projection and total variation constraint. A five-to-ten-fold lower photon requirement can be achieved for near-field or far-field experiment dataset. The work would make CMI more applicable to the dynamics study of radiation-sensitive samples.

Second-order cone and semidefinite methods for the bisymmetric matrix approximation problem

Approximating the closest positive semi-definite bisymmetric matrix using the Frobenius norm to a data matrix is important in many engineering applications, communication theory and quantum physics. In this paper, we will use the interior point method to solve this problem. The problem will be reformulated into various forms, in the beginning as a semi-definite programming problem and later, into the form of a mixed semidefintie and second-order cone optimization problem. Numerical results comparing the efficiency of these methods with the alternating projection algorithm will be reported.

Topological Pilot Assignment in Large-Scale Distributed MIMO Networks

We consider the pilot assignment problem in large-scale distributed multi-input multi-output (MIMO) networks, where a large number of remote radio head (RRH) antennas are randomly distributed in a wide area, and jointly serve a relatively smaller number of users (UE) coherently. By artificially imposing structures on the UE-RRH connectivity, we model the network by a partially-connected interference network, so that the pilot assignment problem can be cast as a topological interference management problem with multiple groupcast messages. Building upon such connection, we formulate the topological pilot assignment (TPA) problem in two different ways with respect to whether or not the to-be-estimated channel connectivity pattern is known <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> . When it is known, we formulate the TPA problem as a low-rank matrix completion problem that can be solved by a simple alternating projection algorithm. Otherwise, we formulate it as a sequential maximum weight induced matching problem that can be solved by either a mixed integer linear program or a simple yet efficient greedy algorithm. With respect to two different formulations of the TPA problem, we evaluate the efficiency of the proposed algorithms under the cell-free massive MIMO setting.

Sparse and Low-Rank Optimization for Pliable Index Coding via Alternating Projection

Pliable index coding (PICOD) has recently been regarded as a promising solution that exploits the coding advantage to improve communication efficiency of content-type systems (e.g., recommendation system), where clients are pliable and are interested in receiving any new message that they do not have. PICOD aims to find an effective coding strategy that satisfies the demands of all clients with the minimum number of transmissions. However, most of the previous works mainly provided theoretical understanding on PICOD in special instances based on greedy algorithms. In contrast, in this paper, we present a flexible sparse and low-rank matrix modeling approach to minimize the number of transmissions for the general PICOD problems. This is achieved by establishing generalized pliable alignment conditions to guarantee the requirements of all clients. As the resulting non-convex problem is highly intractable, we further develop an alternating pursuit framework to detect the rank of the matrix to be recovered by using the rank-increasing strategy. To address the feasibility-detection issues in the existing methods, we propose an alternating projection algorithm, which admits closed-form expressions and avoids excessive sparsity inducing. Moreover, we establish the global convergence of the alternating projection algorithm with random initial points. Simulation results demonstrate that the proposed alternating pursuit algorithm significantly reduces the number of transmissions compared to the state-of-the-art methods.

Color computational ghost imaging based on a plug-and-play generalized alternating projection.

Computational ghost imaging (CGI), in which an image is retrieved from the known speckle patterns that illuminate the object and the total transmitted intensity, has shown great advances because of its advantages and potential applications at all wavelengths. However, high-quality and less time-consuming imaging has been proven challenging especially in color CGI. In this paper, we will present a new color CGI method that can achieve the reconstruction of high-fidelity images at a relatively low sampling rate (0.0625) by using plug-and-play generalized alternating projection algorithm (PnP-GAP). The spatial distribution and color information of the object are encoded into a one-dimensional light intensity sequence simultaneously by combining randomly distributed speckle patterns and a Bayer color mask as modulation patterns, which is measured by a single-pixel detector. A pre-trained deep denoising network is utilized in the PnP-GAP algorithm to achieve better results. Furthermore, a joint reconstruction and demosaicking method is developed to restore the target color information more realistically. Simulations and optical experiments are performed to verify the feasibility and superiority of our proposed scheme by comparing it with other classical reconstruction algorithms. This new color CGI scheme will enable CGI to obtain information in real scenes more effectively and further promote its practical applications.

Interference Nulling Using Reconfigurable Intelligent Surface

This paper investigates the interference nulling capability of reconfigurable intelligent surface (RIS) in a multiuser environment where multiple single-antenna transceivers communicate simultaneously in a shared spectrum. From a theoretical perspective, we show that when the channels between the RIS and the transceivers have line-of-sight and the direct paths are blocked, it is possible to adjust the phases of the RIS elements to null out all the interference completely and to achieve the maximum <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> degrees-of-freedom (DoF) in the overall <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> -user interference channel, provided that the number of RIS elements exceeds some finite value that depends on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> . Algorithmically, for any fixed channel realization we formulate the interference nulling problem as a feasibility problem, and propose an alternating projection algorithm to efficiently solve the resulting nonconvex problem with local convergence guarantee. Numerical results show that the proposed alternating projection algorithm can null all the interference if the number of RIS elements is only slightly larger than a threshold of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2K(K-1)$ </tex-math></inline-formula> . For the practical sum-rate maximization objective, this paper proposes to use the zero-forcing solution obtained from alternating projection as an initial point for subsequent Riemannian conjugate gradient optimization and shows that it has a significant performance advantage over random initializations. For the objective of maximizing the minimum rate, this paper proposes a subgradient projection method which is capable of achieving excellent performance at low complexity.

Millimeter‐wave metasurface lens aided phaseless characterization for quiet zone of compact antenna test range

AbstractThe quiet zone of compact antenna test range (CATR) is typically required as uniform as possible with a low phase deviation error. Here, we propose a novel phaseless CATR characterization method by combining a single millimeter‐wave metasurface lens‐based technique and an alternating projection algorithm. The metasurface lens provides two sets of weakly correlated amplitude‐only data to the algorithm by changing the propagation path of the pseudo‐plane wave, hence realizing the phase retrieval of the quiet zone with low complexity of measures. In addition, initial phase preprocessing is adopted to further improve the precision of phase retrieval. Furthermore, different alternating projection algorithms are compared to validate the effectiveness of the proposed method, showing the maximum phase error in the effective quiet zone reaches 0.75° at 220 GHz. In the end, the simulation results show that the proposed method can be applied in the ultra‐broadband frequency range of 120 GHz. In a nutshell, this paper provides new insights for the applications of metasurface lens in the phaseless characterization of CATR.

Robust Beamforming Based on Covariance Matrix Reconstruction in FDA-MIMO Radar to Suppress Deceptive Jamming.

Frequency diverse array (FDA)-multiple-input multiple-output (MIMO) radars can generate a range-angle two-dimensional transmit steering vector (SV), which is capable of suppressing mainbeam deceptive jamming in the transmit–receive frequency domain by utilizing additional degrees of freedom (DOFs) in the range dimension. However, when there are target SV mismatch, covariance matrix estimation error and target contamination, the jamming suppression performance degrades severely. In this paper, a robust adaptive beamforming algorithm for anti-jammer application based on covariance matrix reconstruction is proposed in FDA-MIMO radar. In this method, the residual noise is further determined by using the spatial power spectrum estimation approach, which results in improved estimation accuracy of the signal covariance matrix and the desired target SV. The jamming SV is obtained from vectors in the intersection of two subspaces (namely, the signal-jamming subspace derived from the sample covariance matrix (SCM) and the jamming subspace generated from the jamming covariance matrix) by an alternating projection algorithm. Furthermore, the jamming power is obtained by exploiting the orthogonality between the different SVs. With the obtained parameters of target and jamming, the optimal adaptive beamformer weight vector is calculated. Simulation results demonstrate that the proposed algorithm can cope with the mainbeam deceptive jamming suppression under various model mismatches and has excellent performance over a wide range of signal-to-noise ratios (SNRs).

LU-Net: combining LSTM and U-Net for sinogram synthesis in sparse-view SPECT reconstruction.

Lowering the dose in single-photon emission computed tomography (SPECT) imaging to reduce the radiation damage to patients has become very significant. In SPECT imaging, lower radiation dose can be achieved by reducing the activity of administered radiotracer, which will lead to projection data with either sparse projection views or reduced photon counts per view. Direct reconstruction of sparse-view projection data may lead to severe ray artifacts in the reconstructed image. Many existing works use neural networks to synthesize the projection data of sparse-view to address the issue of ray artifacts. However, these methods rarely consider the sequence feature of projection data along projection view. This work is dedicated to developing a neural network architecture that accounts for the sequence feature of projection data at adjacent view angles. In this study, we propose a network architecture combining Long Short-Term Memory network (LSTM) and U-Net, dubbed LU-Net, to learn the mapping from sparse-view projection data to full-view data. In particular, the LSTM module in the proposed network architecture can learn the sequence feature of projection data at adjacent angles to synthesize the missing views in the sinogram. All projection data used in the numerical experiment are generated by the Monte Carlo simulation software SIMIND. We evenly sample the full-view sinogram and obtain the 1/2-, 1/3- and 1/4-view projection data, respectively, representing three different levels of view sparsity. We explore the performance of the proposed network architecture at the three simulated view levels. Finally, we employ the preconditioned alternating projection algorithm (PAPA) to reconstruct the synthesized projection data. Compared with U-Net and traditional iterative reconstruction method with total variation regularization as well as PAPA solver (TV-PAPA), the proposed network achieves significant improvement in both global and local quality metrics.

Phaseless Characterization of Compact Antenna Test Range via Improved Alternating Projection Algorithm

A practical compact antenna test range (CATR) requires good quiet zone quality for antenna characterization. This paper addresses the phase profile of the CATR quiet zone from the known intensity pattern of spatial domain and Fourier domain based on a combined alternating projection algorithm. The proposed algorithm is composed of Gerchberg–Saxton (GS) and Hybrid Input–Output (HIO) algorithms and the two algorithms with spatial phase perturbation (SPP) work collaboratively or independently under predesigned conditions. It is observed that the algorithm with random initial phase guess can always converge to an optimal solution by performing a series of hierarchical optimizations of the problem. The numerical results are in good agreement with simulated results in different frequency bands, overcoming the phase retrieval limitation of local convergence in the iterative process. Furthermore, to validate the effectiveness and robustness of the proposed procedure, the related discussions corresponding to different sampling areas in Fourier domain and different signal to noise ratios (SNRs) are given.

Least-squares support tensor data description

Multi-way arrays or tensors are becoming important tools to deal with multidimensional data. This paper is concerned with a one-class classification of second order tensor data. One-class classification problems arise when data from one class is the only data available. Typical vector based methods have limitations when dealing with tensor data. Least squares one-class support vector machine (LS-OCSVM) is a variant of the standard one-class support vector machine (OCSVM). It operates directly on patterns represented by vector and obtains an analytical solution directly from solving a set of linear equations instead of quadratic programming (QP). One-class support tensor machine (OCSTM) is a one-class classification tool for solving the one-class classification problem for tensors. It is based on alternating projection algorithms and quadratic programming to obtain solutions. In this paper, a new method to deal with one-classification of tensors is proposed, least squares support tensor data description (LS-STDD). The advantage of LS-STDD over one-class support tensor machine (OCSTM) is that LS-STDD has a closed form solution. It doesn’t use the alternating projection method of OCSTM and quadratic programming. Consequently, LS-STDD is easier and faster to implement than OCSTM. The efficiency of the proposed method over OCSTM is illustrated through simulations.

Small footprint phase locking system for a large tiled aperture laser array.

A phase sensing system fitted to the control of coherent laser beam array of large cross section is experimented. It is based on the use of a fiber bundle that collects a weak part of the synthetic wavefront, that scales it down (1/40) and that reshapes it in a more compact arrangement (2D to 1D array). Then, the reconfigured beam array can be analyzed by a small footprint system making the large laser beam array easier to phase-lock. The discrete laser array wavefront transmitted by the meter long fiber bundle was stabilized thanks to a multiple arm servo loop. Laser array phase locking was further ensured by random scattering through a diffuser, associated to an alternating projection algorithm. Six fiber laser beams constituting a 110 mm diameter synthetic aperture, were phase-locked with λ/16 accuracy.

On Cluster-Aware Supervised Learning: Frameworks, Convergent Algorithms, and Applications

This paper proposes a cluster-aware supervised learning (CluSL) framework, which integrates the clustering analysis with supervised learning. The objective of CluSL is to simultaneously find the best clusters of the data points and minimize the sum of loss functions within each cluster. This framework has many potential applications in healthcare, operations management, manufacturing, and so on. Because CluSL, in general, is nonconvex, we develop a regularized alternating minimization (RAM) algorithm to solve it, where at each iteration, we penalize the distance between the current clustering solution and the one from the previous iteration. By choosing a proper penalty function, we show that each iteration of the RAM algorithm can be computed efficiently. We further prove that the proposed RAM algorithm will always converge to a stationary point within a finite number of iterations. This is the first known convergence result in cluster-aware learning literature. Furthermore, we extend CluSL to the high-dimensional data sets, termed the F-CluSL framework. In F-CluSL, we cluster features and minimize loss function at the same time. Similarly, to solve F-CluSL, a variant of the RAM algorithm (i.e., F-RAM) is developed and proven to be convergent to an [Formula: see text]-stationary point. Our numerical studies demonstrate that the proposed CluSL and F-CluSL can outperform the existing ones such as random forests and support vector classification, both in the interpretability of learning results and in prediction accuracy. Summary of Contribution: Aligned with the mission and scope of the INFORMS Journal on Computing, this paper proposes a cluster-aware supervised learning (CluSL) framework, which integrates the clustering analysis with supervised learning. Because CluSL is, in general, nonconvex, a regularized alternating projection algorithm is developed to solve it and is proven to always find a stationary solution. We further generalize the framework to the high-dimensional data set, F-CluSL. Our numerical studies demonstrate that the proposed CluSL and F-CluSL can deliver more interpretable learning results and outperform the existing ones such as random forests and support vector classification in computational time and prediction accuracy.

DOA Estimation in Non-Uniform Noise Using Matrix Completion via Alternating Projection

In this paper, direction-of-arrival (DOA) estimation in the presence of non-uniform noise is investigated. To achieve high estimation accuracy, the DOA estimation problem is solved with the use of a matrix completion approach. The matrix completion via alternating projection algorithm (APA) is firstly utilized to find the noise-free covariance matrix of the signal, which is then used to find the DOA by utilizing the conventional subspace-based method. Numerical simulations are performed to verify the accuracy and effectiveness of the proposed approach.

Low Rank Pure Quaternion Approximation for Pure Quaternion Matrices

Quaternion matrices are employed successfully in many color image processing applications. In particular, a pure quaternion matrix can be used to represent red, green, and blue channels of color images. A low-rank approximation for a pure quaternion matrix can be obtained by using the quaternion singular value decomposition. However, this approximation is not optimal in the sense that the resulting low-rank approximation matrix may not be pure quaternion, i.e., the low-rank matrix contains a real component which is not useful for the representation of a color image. The main contribution of this paper is to find an optimal rank-$r$ pure quaternion matrix approximation for a pure quaternion matrix (a color image). Our idea is to use a projection on a low-rank quaternion matrix manifold and a projection on a quaternion matrix with zero real component, and develop an alternating projections algorithm to find such optimal low-rank pure quaternion matrix approximation. The convergence of the projection algorithm can be established by showing that the low-rank quaternion matrix manifold and the zero real component quaternion matrix manifold has a nontrivial intersection point. Numerical examples on synthetic pure quaternion matrices and color images are presented to illustrate the projection algorithm can find optimal low-rank pure quaternion approximation for pure quaternion matrices or color images.

Fast and Accurate Amplitude Demodulation of Wideband Signals

Amplitude demodulation is a classical operation used in signal processing. For a long time, its effective applications in practice have been limited to narrowband signals. In this work, we generalize amplitude demodulation to wideband signals. We pose demodulation as a recovery problem of an oversampled corrupted signal and introduce special iterative schemes belonging to the family of alternating projection algorithms to solve it. Sensibly chosen structural assumptions on the demodulation outputs allow us to reveal the high inferential accuracy of the method over a rich set of relevant signals. This new approach surpasses current state-of-the-art demodulation techniques apt to wideband signals in computational efficiency by up to many orders of magnitude with no sacrifice in quality. Such performance opens the door for applications of the amplitude demodulation procedure in new contexts. In particular, the new method makes online and large-scale offline data processing feasible, including the calculation of modulator-carrier pairs in higher dimensions and poor sampling conditions, independent of the signal bandwidth. We illustrate the utility and specifics of applications of the new method in practice by using natural speech and synthetic signals.