Alternating Direction Algorithm Research Articles

Reconstruction of transient acoustic field using sparse real-time near-field acoustic holography

A sparse real-time near-field acoustic holography method is proposed to precisely and stably reconstruct a transient sound field. By a time-domain impulse response function, a time domain convolution equation between the pressure time-wavenumber spectra on the hologram and reconstruction planes is first established. Then, a smoothed ℓ0-norm optimization algorithm is applied to solve the serious ill-conditioned problem of the inverse process to get the pressure time-wavenumber spectrum of the reconstruction plane. The key part of solving this problem is to approximate replace the discontinuous ℓ0-norm by using a suitable continuous Gaussian function family, and a steepest ascent algorithm is introduced to minimize the continuous function for obtaining the optimal solution. Finally, the pressure time-wavenumber spectra of the reconstruction plane for all wavenumbers at all times are solved, and the corresponding time-dependent pressures are gained by the two-dimensional space inverse Fourier transform. A numerical simulation is conducted to observe the reconstruction capacity of the proposed method. The simulation effect prove that the proposed method can accurately reconstruct the transient sound field, and its reconstruction results are compared to those of the real-time near-field acoustic holography (RTNAH) with Tikhonov regularization and YALL1 modal for verifying the superiority of the proposed method. The YALL1 module utilizes an alternating direction algorithm for solving the ℓ1 minimization problems. Several parameters including the noise, position of the holograph plane and two initialization values are discussed in the simulation. The comparison and discussion results show that the reconstruction effect of the proposed method is much better than those of RTNAH with Tikhonov regularization and YALL1 modal under different parameter configurations. An experiment with a percussive steel plate is implemented for further validating the effectivity of the proposed method.

Adaptive Parameter Alternating Direction Algorithm for Centrosymmetric Solutions of a Class of Generalized Coupled Sylvester-transpose Matrix Equations

Adaptive Parameter Alternating Direction Algorithm for Centrosymmetric Solutions of a Class of Generalized Coupled Sylvester-transpose Matrix Equations

Regolith mineral detection and abundance estimation based on the LMS spectral data of Chang’E-5 lander

<p indent="0mm">Determining the mineral components of the lunar regolith is key to understanding the Moon’s genesis and evolution, and it is one of the important scientific objectives of the Chang’E-5 Mission. The <italic>in-situ</italic> spectra collected by the lunar mineralogical spectrometer (LMS) of Chang’E-5 provide valuable data for interpreting the mineral composition of the landing site. However, little work has been performed to analyze the LMS data, and the traditional lunar mineral detection method based on the radiation transfer model cannot simultaneously obtain information on the mineral end-member, abundance, and particle size. To achieve the multiple goals, we propose a sparse unmixing method based on the spectral library of various particle-size minerals. The mineral detection problem is transformed into a sparse optimization problem and solved by the alternating direction algorithm. We have analyzed eight sets of LMS reflectance spectra and found that the lunar soil in the sampling area is composed of agglutinates and glass (49.36%), pyroxene (14.08%), plagioclase (18.58%), ilmenite (16.11%), and olivine (1.86%). The detected mineral composition is consistent with the composition of young lunar mare basalts. In addition, 79.83% of the detected minerals have a small particle size of less than 75 μm, of which the average particle size of olivine, plagioclase, pyroxene, ilmenite, agglutinates, and glass is 48, 205, 59, 37.4, and 9.7 μm, respectively. Differences in mineral particle size suggest that the effects of space weathering on the lunar surface vary by the component minerals. Moreover, the LMS data provide <italic>in-situ</italic> spectral evidence of water existence on the lunar surface, i.e., the spectral absorption at <sc>2850 nm.</sc> We estimate the water content of the sampling area using the effective single-particle absorption-thickness (ESPAT) value and the temperature derived from an improved lunar thermal model that has been cross-validated with the temperature records of several thermal sensors on the Chang’E-5 lander. The result shows that rocks are more hydrous than the regolith at the Cheng’E-5 landing site. The water content of the rock is as high as <sc>201 ppm,</sc> while the average water content of the sampling area is <sc>67 ppm.</sc>

Acceleration techniques for adaptive robust optimization transmission network expansion planning problems

The computational burden of two-stage adaptive robust optimization transmission network expansion planning problems increases when accurately representing the operation of power systems, i.e., when operational variability, inter-temporal operational constraints, and non-convex operational constraints are considered in the decision-making model. This motivates the use of acceleration techniques in order to avoid computationally intractable problems. The adaptive robust optimization problem is specifically solved using the nested column-and-constraint generation algorithm. We propose the application of two new acceleration techniques to this algorithm. On the one hand, the variables that model the uncertainty realizations are initialized to the solution obtained by using the alternating direction algorithm. On the other, the master problems of the solution procedure are relaxed by considering only certain cutting planes and including more constraints if the evolution of the bounds of the algorithm is not appropriate. Numerical results show that the use of the proposed acceleration techniques leads to reductions in the computational time of over 93%.

Graph regularized non-negative matrix factorization with prior knowledge consistency constraint for drug–target interactions prediction

BackgroundIdentifying drug–target interactions (DTIs) plays a key role in drug development. Traditional wet experiments to identify DTIs are expensive and time consuming. Effective computational methods to predict DTIs are useful to narrow the searching scope of potential drugs and speed up the process of drug discovery. There are a variety of non-negativity matrix factorization based methods to predict DTIs, but the convergence of the algorithms used in the matrix factorization are often overlooked and the results can be further improved.ResultsIn order to predict DTIs more accurately and quickly, we propose an alternating direction algorithm to solve graph regularized non-negative matrix factorization with prior knowledge consistency constraint (ADA-GRMFC). Based on known DTIs, drug chemical structures and target sequences, ADA-GRMFC at first constructs a DTI matrix, a drug similarity matrix and a target similarity matrix. Then DTI prediction is modeled as the non-negative factorization of the DTI matrix with graph dual regularization terms and a prior knowledge consistency constraint. The graph dual regularization terms are used to integrate the information from the drug similarity matrix and the target similarity matrix, and the prior knowledge consistency constraint is used to ensure the matrix decomposition result should be consistent with the prior knowledge of known DTIs. Finally, an alternating direction algorithm is used to solve the matrix factorization. Furthermore, we prove that the algorithm can converge to a stationary point. Extensive experimental results of 10-fold cross-validation show that ADA-GRMFC has better performance than other state-of-the-art methods. In the case study, ADA-GRMFC is also used to predict the targets interacting with the drug olanzapine, and all of the 10 highest-scoring targets have been accurately predicted. In predicting drug interactions with target estrogen receptors alpha, 17 of the 20 highest-scoring drugs have been validated.

High precision reconstruction for compressed femtosecond dynamics images based on the TVAL3 algorithm

Compressed sensing (CS) has been successfully demonstrated to reconstruct ultrafast dynamic scenes in ultrafast imaging techniques with large sequence depth. Since compressed ultrafast imaging used a two-step iterative shrinkage/thresholding (TwIST) algorithm in previous image reconstruction, some details of the object will not be recovered when the amount of data compression is large. Here we applied a more efficient Total Variation (TV) minimization scheme based on augmented Lagrangian and alternating direction algorithms (TVAL3) to reconstruct the ultrafast process. In order to verify the effectiveness of the TVAL3 algorithm, we experimentally compare the reconstruction quality of TVAL3 algorithm and TwIST algorithm in an ultrafast imaging system based on compressed-sensing and spectral-temporal coupling active detection with highest frame rate of 4.37 trillion Hz. Both dynamic and static experimental results show that, TVAL3 algorithm can not only reconstruct a rapidly moving light pulse with a more precise profile and more fitted trajectory, but also improve the quality of static objects and the speed of reconstruction. This work will advance the ultrafast imaging techniques based on compressed sensing in terms of image reconstruction quality and reconstruction speed, which finally helps promoting the application of these techniques in areas where high spatial precision is required, such as phase transitions and laser filamentation in nonlinear solids, etc.

Diagnosis of Early Cervical Cancer with a Multimodal Magnetic Resonance Image under the Artificial Intelligence Algorithm.

This research was conducted to explore the value of multimodal magnetic resonance imaging (MRI) based on the alternating direction algorithm in the diagnosis of early cervical cancer. 64 patients diagnosed with early cervical cancer clinicopathologically were included, and according to the examination methods, they were divided into A group with conventional multimodal MRI examination and B group with the multimodal MRI examination under the alternating direction algorithm. The diagnostic results of two types of multimodal MRI for early cervical cancer staging were compared with the results of clinicopathological examination to judge the application value in the early diagnosis of cervical cancer. The results showed that in the 6 randomly selected samples of early cervical cancer patients, the peak signal-to-noise ratio (PSNR) and structural similarity image measurement (SSIM) of multimodal MRI images under the alternating direction algorithm were significantly higher than those of conventional multimodal MRI images and the image reconstruction was clearer under this algorithm. By comparing MRI multimodal staging, statistical analysis showed that the staging accuracy of B group was 75%, while that of A group was only 59.38%. For the results of postoperative medical examinations, the examination consistency of B group was better than that of A group, with a statistically significant difference (P < 0.05). The area under the receiver operating characteristic (ROC) curve (AUC) of B group was larger than that of A group; thus, sensitivity was improved and misdiagnosis was reduced significantly. Multimodal MRI under the alternating direction algorithm was superior to conventional multimodal MRI examination in the diagnosis of early cervical cancer, as the lesions were displayed more clearly, which was conducive to the detection rate of small lesions and the staging accuracy. Therefore, it could be used as an ideal MRI method for the assistant diagnosis of cervical cancer staging.

Adaptive AFM imaging based on object detection using compressive sensing

Atomic force microscopy (AFM) is a kind of high-precision nanoscale instrument to measure the surface morphology of various samples. Nevertheless, the standard AFM scanning process takes a very long time to obtain high-resolution images. Compressive sensing (CS) can be used to achieve fast AFM imaging. But, the traditional CS-AFM imaging is difficult to balance the image quality of each local area, resulting in poor quality in the object area at low sampling rate. Therefore, a novel imaging scheme of adaptive CS-AFM is proposed. The fast scanning is first used to generate a low resolution image in a short time, and then bicubic interpolation is performed to obtain a high resolution image. Afterwards, an advanced detection algorithm is used to realize the accurate detection and positioning of the objects. Furthermore, the supplementary scanning is carried out to achieve adaptive sampling on the objects. After sampling, the measurement matrix corresponding to the measurement points is constructed. Finally, Total Variation Minimization by Augmented Lagrangian and Alternating Direction Algorithm (TVAL3) is used to reconstruct the whole AFM image. The imaging quality of the sample is analyzed and assessed by image evaluation metrics (PSNR and SSIM) and visual effect. Compared with two non-adaptive imaging schemes, the proposed scheme is characterized by high automation, short time, and high quality.

Depth-aware total variation regularization for underwater image dehazing

Underwater images often show severe quality degradation due to the light absorption and scattering effects in water medium. This paper introduces a scene depth regularized underwater image dehazing method to obtain high-quality underwater images. Unlike previous underwater image dehazing methods that usually calculate a transmission map or a scene depth map using priors, we construct an exponential relationship between transmission map and normalized scene depth map. An initial scene depth is first estimated by the difference between color channels. Then it is refined by total variation regularization to keep structures while smoothing excessive details. An alternating direction algorithm is given to solve the optimization problem. Extensive experiments demonstrate that the proposed method can effectively improve the visual quality of degraded underwater images, and yields high-quality results comparative to the state-of-the-art underwater image enhancement methods quantitatively and qualitatively.

Non-line-of-sight transparent object detection and reconstruction based on passive single-pixel imaging

Single-pixel imaging (SPI) uses point detectors instead of expensive array sensors to capture images under low light conditions. It therefore provides a solution in detecting objects with weak signals. In this research, we propose a non-line-of-sight (NLOS) 2D transparent object inspection system based on SPI technique. The 2D shape of the transparent object is reconstructed using Total Variation Augmented Lagrangian and Alternating Direction Algorithm (TVAL3) approach by collecting indirect light reflected from the object surface. Theoretical analysis shows that 300 illumination patterns are required to reconstruct a pixel image, and those patterns are streamed to the digital micromirror device at high speed. Compared to TVAL3 with other methods, better image quality can be obtained with only one-third of illumination patterns. Also, experimental results confirm that this system can obtain transparent object information from reflected light even at a sampling rate of 24%. Furthermore, adjusting the laser wavelength and laser power can improve image quality. The proposed SPI detection system for NLOS transparent objects is an effective method that requires fewer illumination patterns and provides new insights for the detection and reconstruction of NLOS transparent object.

Fast AFM Imaging Based on Compressive Sensing Using Undersampled Raster Scan

Atomic force microscope (AFM), which has nanoscale precision, is a widely used instrument in material science and biomedical science. Nevertheless, conventional AFM scanning is a time-consuming procedure. Compressive sensing (CS) and undersampling techniques have been introduced to accomplish fast AFM imaging in recent years. At present, existing undersampled scan patterns cannot simultaneously guarantee imaging efficiency and quality well. Therefore, a novel one called undersampled raster (USR) scan is put forward in this article. It has higher imaging efficiency than most existing scan patterns, which is drawn by calculating the scanning time with the proposed estimation formulas. Experimental results show that the imaging quality is obviously better than using other combinations of fast scan patterns and reconstruction algorithms when the regular form of the USR scan is employed with Total Variation Minimization by Augmented Lagrangian and Alternating Direction Algorithm (TVAL3). The universality of this imaging scheme is verified by using a variety of samples. In the end, the applications of regular USR scan or its variant for super-resolution AFM imaging and predicting appropriate sampling rates are proposed. In conclusion, applying regular USR scan and TVAL3 algorithm to CS-based AFM can effectively realize fast and high-quality imaging.

Ghost imaging enhancement for detections of the low-transmittance objects

The underwater environment is extremely complex and variable, which makes it difficult for underwater robots detecting or recognizing surroundings using images acquired with cameras. Ghost imaging as a new imaging technique has attracted much attention due to its special physical properties and potential for imaging of objects in optically harsh or noisy environments. In this work, we experimentally study three categories of image reconstruction methods of ghost imaging for objects of different transmittance. For high-transmittance objects, the differential ghost imaging is more efficient than traditional ghost imaging. However, for low-transmittance objects, the reconstructed images using traditional ghost imaging and differential ghost imaging algorithms are both exceedingly blurred and cannot be improved by increasing the number of measurements. A compressive sensing method named augmented Lagrangian and alternating direction algorithm (TVAL3) is proposed to reduce the background noise imposed by the low-transmittance. Experimental results show that compressive ghost imaging can dramatically subtract the background noise and enhance the contrast of the image. The relationship between the quality of the reconstructed image and the complexity of object itself is also discussed.

An Algorithm of l 1-Norm and l 0-Norm Regularization Algorithm for CT Image Reconstruction from Limited Projection.

The l1-norm regularization has attracted attention for image reconstruction in computed tomography. The l0-norm of the gradients of an image provides a measure of the sparsity of gradients of the image. In this paper, we present a new combined l1-norm and l0-norm regularization model for image reconstruction from limited projection data in computed tomography. We also propose an algorithm in the algebraic framework to solve the optimization effectively using the nonmonotone alternating direction algorithm with hard thresholding method. Numerical experiments indicate that this new algorithm makes much improvement by involving l0-norm regularization.

Terahertz Meta-Holograms Reconstruction Based on Compressed Sensing

The introduction of single-pixel imaging and compressed sensing (CS) techniques into terahertz (THz) imaging has sped up image acquisition and avoided raster scanning. At present, most single-pixel terahertz imaging developments are based on simple metal samples, researchers rarely study the reconstruction of complex structural samples with large attenuation in the terahertz domain, such as metasurface holographic images. Here, we present an implementation of the single-pixel compressed sensing approach into THz metasurface holography reconstruction. By laser projecting a set of binary patterns on a 500-μm thick silicon wafer using a digital micromirror device (DMD), THz wavefront of the holographic metasurface is spatially encoded. Single-element detector is used to measure electric field amplitude of the transmitted THz radiation for each pattern, and then the hologram is reconstructed by Total variation Augmented Lagrangian and Alternating Direction Algorithm (TVAL3). Besides, the reconstruction effects are also analyzed by reducing measurement number, it can maintain more than 95% of the image information under 20% compression. The demonstrated combination of terahertz holography and single-pixel compressed sensing imaging provides new possibilities for metasurface imaging, verifies the stability of terahertz single-pixel imaging, and the scheme may lead to advances in fast terahertz imaging.

Reducing uncertainty in conceptual prior models of complex geologic systems via integration of flow response data

A major source of uncertainty in subsurface flow modeling is related to the conceptual model of geologic continuity that is adopted by geologists and hydrogeologists. Traditional model calibration methods usually rely on a given model of geologic continuity that is used to constrain the spatial distribution of aquifer properties. Flow response data, however, may also be used as additional source of information to constrain and revise conceptual geologic models or parameters that control them. The problem is more complicated when models that exhibit complex non-Gaussian spatial connectivity patterns are considered. We formulate the problem of flow data integration to select conceptual geologic scenarios with complex lithofacies as a regularized least-squares problem. The solution approach combines learning with model selection regularization techniques, where the former imposes geological feasibility while the latter eliminates scenarios that do not contribute to reproducing the flow response data. Geologic feasibility constraint to preserve complex connectivity patterns is enforced through supervised machine learning while geologic scenario selection is implemented via a mixed l1/l2-norm regularization term. The least-squares minimization is performed using an alternating directions algorithm that involves a sequence of model selection steps followed by geologic feasibility mapping, the latter implemented by combining k nearest neighbor (k-NN) algorithm with a pattern-learning method. Several examples with complex fluvial channel models are used to illustrate the performance of this approach.

An adaptive algorithm for restoring image corrupted by mixed noise

Image denoising is one of the fundamental problems in image processing. Digital images are often contaminated by noise due to the image acquisition process under poor conditions. In this paper, we propose an effective approach to remove mixed Poisson-Gaussian noise in digital images. Particularly, we propose to use a spatially adaptive total variation regularization term in order to enhance the ability of edge preservation. We also propose an instance of the alternating direction algorithm to solve the proposed denoising model as an optimization problem. The experiments on popular natural images demonstrate that our approach achieves superior accuracy than other recent state-of-the-art techniques.

An augmented Lagrangian alternating direction method for overlapping community detection based on symmetric nonnegative matrix factorization

In this paper, we present an augmented Lagrangian alternating direction algorithm for symmetric nonnegative matrix factorization. The convergence of the algorithm is also proved in detail and strictly. Then we present a modified overlapping community detection method which is based on the presented symmetric nonnegative matrix factorization algorithm. We apply the modified community detection method to several real world networks. The obtained results show the capability of our method in detecting overlapping communities, hubs and outliers. We find that our experimental results have better quality than several competing methods for identifying communities.

A pattern-matching method for flow model calibration under training image constraint

Modern geostatistical modeling techniques are developed to simulate complex geologic connectivity patterns (e.g., curvilinear fluvial systems) at the grid-level using a training image (TI) that encodes multiple-point statistical (MPS) information. A challenging aspect of using MPS methods is conditioning the resulting models on nonlinear flow data. We develop a pattern-matching method for calibration of MPS-based facies models subject to the TI constraint. Since the exact statistical information in the TI can only be expressed empirically, flow data conditioning and pattern matching are carried out in two iterative steps, using an alternating-direction algorithm. Flow data integration is formulated through a regularized least-squares by taking advantage of learned k-SVD sparse parametrization and l1-norm sparsity-promoting regularization methods. The TI constraint is enforced through a MPS-based pattern-matching algorithm that uses the identified model calibration solution to generate a corresponding facies model that is consistent with the TI. The pattern-matching algorithm uses a local search template to scan the TI to find facies patterns with smallest distances from the corresponding local patterns in the parameterized approximate solution. The identified patterns for each location in the model are stored and used to estimate local conditional probabilities for assigning the facies types to each grid cell. The resulting solution is passed to the flow data conditioning step as a regularization term to perform the next iteration. The process is repeated until the MPS facies model provides an acceptable match to the data. Numerical experiments are presented to evaluate the performance of the pattern-matching method for calibration of complex facies models.

A Smoothed l0-Norm and l1-Norm Regularization Algorithm for Computed Tomography

The nonmonotone alternating direction algorithm (NADA) was recently proposed for effectively solving a class of equality-constrained nonsmooth optimization problems and applied to the total variation minimization in image reconstruction, but the reconstructed images suffer from the artifacts. Though by the l0-norm regularization the edge can be effectively retained, the problem is NP hard. The smoothed l0-norm approximates the l0-norm as a limit of smooth convex functions and provides a smooth measure of sparsity in applications. The smoothed l0-norm regularization has been an attractive research topic in sparse image and signal recovery. In this paper, we present a combined smoothed l0-norm and l1-norm regularization algorithm using the NADA for image reconstruction in computed tomography. We resolve the computation challenge resulting from the smoothed l0-norm minimization. The numerical experiments demonstrate that the proposed algorithm improves the quality of the reconstructed images with the same cost of CPU time and reduces the computation time significantly while maintaining the same image quality compared with the l1-norm regularization in absence of the smoothed l0-norm.

An alternating direction algorithm for hybrid precoding and combining in millimeter wave MIMO systems

Millimeter-wave (mmWave) technology is one of the most promising candidates for future wireless communication systems as it can offer large underutilized bandwidths and eases the implementation of large antenna arrays which are required to help overcome the severe signal attenuation that occurs at these frequencies. To reduce the high cost and power consumption of a fully digital mmWave precoder and combiner, hybrid analog/digital designs based on analog phase shifters are often adopted. In this work we derive an iterative algorithm for the hybrid precoding and combining design for spatial multiplexing in mmWave massive multiple-input multiple-output (MIMO) systems. To cope with the difficulty of handling the hardware constraint imposed by the analog phase shifters we use the alternating direction method of the multipliers (ADMM) to split the hybrid design problem into a sequence of smaller subproblems. This results in an iterative algorithm where the design of the analog precoder/combiner consists of a closed form solution followed by a simple projection over the set of matrices with equal magnitude elements. It is initially developed for the fully-connected structure and then extended to the partially-connected architecture which allows simpler hardware implementation. Furthermore, to cope with the more likely wideband scenarios where the channel is frequency selective, we also extend the algorithm to an orthogonal frequency division multiplexing (OFDM) based mmWave system. Simulation results in different scenarios show that the proposed design algorithms are capable of achieving performances close to the optimal fully digital solution and can work with a broad range of configuration of antennas, RF chains and data streams.