Vector Reconstruction Research Articles

Sparse Bayesian Learning Based Multi Trajectory Tracking Algorithm For Direction of Arrival Trajectory Estimation

One of the applications of sequential sparse signal reconstruction is multi-target Direction of Arrival (DoA) trajectory estimation. In fact, each member of the support set is equivalent to the DoA of a moving target at each time instant. There is a mapping between the indices of the sparse vector and DoA values in continuous angle space. The key idea of this paper is to use the dynamic information of the continuous angular space to more accurately track sparse vectors and estimate the DoA trajectories of moving sources with time-varying acceleration based on the Sparse Bayesian Learning (SBL) framework. For this purpose, the members of the estimated support set are mapped to the continuous angular space at each instant. Then, the obtained DoAs are assigned to the available DoA trajectories using the Predictive-Description-Length (PDL) algorithm. In the following, the DoA of each source is predicted for the next time using the Kalman filter. Finally, the predicted DoAs are mapped to a sparse vector. The obtained sparse vector is used as the prior information for SBL-based sparse reconstruction. Simulation results show that the proposed algorithm, which is called SBL-MTT (Multi Trajectory Tracking), leads to an accurate reconstruction of successive sparse vectors in application of DoA trajectory estimation of moving sources.

Attack stage detection method based on vector reconstruction error autoencoder and explainable artificial intelligence

Attack stage detection method based on vector reconstruction error autoencoder and explainable artificial intelligence

The relationship between singular value decomposition orthogonal space vector and sound field reconstruction in equivalent source method

In acoustic holography, the equivalent source method represents a typical ill-posed inverse problem, characterized by the significant impact of measurement errors on the sought solution. To minimize the interference of noise with the sought solution, we analyze the relationship between orthogonal space vectors obtained through singular value decomposition and acoustic field reconstruction. The research findings indicate that the primary information of the acoustic field exhibits strong correlation with a small number of space vectors, while noise information demonstrates random correlation with all space vectors. Therefore, we retain the space vectors with higher correlation to the acoustic field while filtering out redundant ones, thereby stabilizing and accurately reconstructing the acoustic field. Numerical analysis of the acoustic field reconstruction demonstrates that compared to regularization methods such as Tikhonov and truncated singular value decomposition (TSVD), this approach achieves higher computational accuracy. Furthermore, the text combines practical examples to further explain the reasons behind the superior accuracy of this method.

Observation vector reconstruction-based nonparametric nonlinear restoring force identification for granules-structures coupled vibrating system

The nonlinear restoring force (NRF) generated by the collision and friction between particles and structures is the leading cause of the complex dynamic response of the granules-structures coupled vibrating system (GSCVS). Identification of NRF can provide critical information for post-event damage diagnosis and structural design of immersed structures. However, the spatial distribution and dynamic response of the particles near the structures are diverse and complex, making it difficult to describe the NRF with an accurate mathematical model. This paper proposed a data-based nonparametric method to estimate the NRF in the GSCVS. A nonparametric model of NRF that considered the additional effects of particles on both sides of the structures and consisted of system response and undetermined coefficients was developed. The observation vector of the conventional Extended Kalman Filter (EKF) was reconstructed by the sparse measurement of the strain response. The reconstructed observation vector contains three response components: translational displacement, translational acceleration, and rotational acceleration, in which the rotational acceleration response is difficult to measure in engineering applications. The proposed EKF based on observation vector reconstruction (EKF-OVR) can identify the undetermined coefficients in the nonparametric model, and then the NRF can be calculated. Numerical studies showed that EKF-OVR achieved higher accuracy and noise robustness than the conventional EKF and the data fusion based EKF. A dynamic experimental study on granules-beam coupled vibrating system (GBCVS) was conducted, and the proposed algorithm was employed to identify the NRF of the GBCVS. The effects of excitation amplitude, particle size, and immersed depth on NRF are analyzed, and it is found that higher harmonic components in the NRF led to period doubling and chaos of the beam response.

Real space iterative reconstruction for vector tomography (RESIRE-V)

Tomography has had an important impact on the physical, biological, and medical sciences. To date, most tomographic applications have been focused on 3D scalar reconstructions. However, in some crucial applications, vector tomography is required to reconstruct 3D vector fields such as the electric and magnetic fields. Over the years, several vector tomography methods have been developed. Here, we present the mathematical foundation and algorithmic implementation of REal Space Iterative REconstruction for Vector tomography, termed RESIRE-V. RESIRE-V uses multiple tilt series of projections and iterates between the projections and a 3D reconstruction. Each iteration consists of a forward step using the Radon transform and a backward step using its transpose, then updates the object via gradient descent. Incorporating with a 3D support constraint, the algorithm iteratively minimizes an error metric, defined as the difference between the measured and calculated projections. The algorithm can also be used to refine the tilt angles and further improve the 3D reconstruction. To validate RESIRE-V, we first apply it to a simulated data set of the 3D magnetization vector field, consisting of two orthogonal tilt series, each with a missing wedge. Our quantitative analysis shows that the three components of the reconstructed magnetization vector field agree well with the ground-truth counterparts. We then use RESIRE-V to reconstruct the 3D magnetization vector field of a ferromagnetic meta-lattice consisting of three tilt series. Our 3D vector reconstruction reveals the existence of topological magnetic defects with positive and negative charges. We expect that RESIRE-V can be incorporated into different imaging modalities as a general vector tomography method. To make the algorithm accessible to a broad user community, we have made our RESIRE-V MATLAB source codes and the data freely available at https://github.com/minhpham0309/RESIRE-V.

Full‐Space Near‐ and Far‐Field Jones Vector Reconstruction by Global Organization of Bidirectional Non‐Interleaved Linear‐Polarized Meta‐Radiators

AbstractIntegrated radiation‐type metasurfaces (RA‐M) have gained importance in the development of next‐generation wireless communications and integrated electronics. They facilitate advanced electromagnetic (EM) wave control with a single radiation aperture. However, most RA‐Ms fail to simultaneously decouple the amplitude, phase, and polarization information of the spatial radiation wavefront owing to the intrinsic restrictions of the meta‐radiator and limited design strategy. This study proposes and demonstrates a full‐space non‐interleaved RA‐M platform capable of precise complex‐vector‐field (CVF) Jones vector reconstruction of both near and far fields in the microwave region. The method is based on the global interaction of linear‐polarized (LP) meta‐radiators, which are organized via the LP‐basis inverse design methodology; thus, the near‐ and far‐field Jones vectors of the radiated wavefront can be subjected to customized reconstruction. The existing unidirectional meta‐radiators are further pushed to bidirectional spaces, facilitating diverse full‐space multiplexing integrated meta‐devices, such as bidirectional multi‐polarization routers and full‐space vectorial hologram modulators. The proposed RA‐M unlocks the unequaled potential of radiated CVF, thereby paving a promising pathway for integrated electronic device technologies.

New method for analysing spatial relationships of facial muscles on MRI: a pilot study

Dysfunction of the facial musculature can have significant physical, social, and psychological consequences. In surgeries such as cleft surgery or craniofacial bimaxillary osteotomies, the perioral facial muscles may be detached or severed, potentially altering their functional vectors and mimicry capabilities. Ensuring correct reconstruction and maintenance of anatomical sites and muscle vectors is crucial in these procedures. However, a standardized method for perioperative assessment of the facial musculature and function is currently lacking. The aim of this study was to develop a workflow to analyse the three-dimensional vectors of the facial musculature using magnetic resonance imaging (MRI) scans. A protocol for localizing the origins and insertions of these muscles was established. The protocol was implemented using the 3DMedX computer program and tested on 7 Tesla MRI scans obtained from 10 healthy volunteers. Inter- and intra-observer variability were assessed to validate the protocol. The absolute intra-observer variability was 2.6 mm (standard deviation 2.0 mm), and absolute inter-observer variability was 2.6 mm (standard deviation 1.5 mm). This study presents a reliable and reproducible method for analysing the spatial relationships and functional significance of the facial muscles. The workflow developed facilitates perioperative assessment of the facial musculature, potentially aiding clinicians in surgical planning and potentially enhancing the outcomes of midface surgery.

Three-dimensional reconstruction of industrial parts from a single image

This study proposes an image-based three-dimensional (3D) vector reconstruction of industrial parts that can generate non-uniform rational B-splines (NURBS) surfaces with high fidelity and flexibility. The contributions of this study include three parts: first, a dataset of two-dimensional images is constructed for typical industrial parts, including hexagonal head bolts, cylindrical gears, shoulder rings, hexagonal nuts, and cylindrical roller bearings; second, a deep learning algorithm is developed for parameter extraction of 3D industrial parts, which can determine the final 3D parameters and pose information of the reconstructed model using two new nets, CAD-ClassNet and CAD-ReconNet; and finally, a 3D vector shape reconstruction of mechanical parts is presented to generate NURBS from the obtained shape parameters. The final reconstructed models show that the proposed approach is highly accurate, efficient, and practical.

Feasibility and validity of using deep learning to reconstruct 12-lead ECG from three‑lead signals

BackgroundIn the field of mobile health, portable dynamic electrocardiogram (ECG) monitoring devices often have a limited number of lead electrodes due to considerations, such as portability and battery life. This situation leads to a contradiction between the demand for standard 12‑lead ECG information and the limited number of leads collected by portable devices. MethodsThis study introduces a composite ECG vector reconstruction network architecture based on convolutional neural network (CNN) combined with recurrent neural network by using leads I, II, and V2. This network is designed to reconstruct three‑lead ECG signals into 12‑lead ECG signals. A 1D CNN abstracts and extracts features from the spatial domain of the ECG signals, and a bidirectional long short-term memory network analyzes the temporal trends in the signals. Then, the ECG signals are inputted into the model in a multilead, single-channel manner. ResultsUnder inter-patient conditions, the mean reconstructed Root mean squared error (RMSE) for precordial leads V1, V3, V4, V5, and V6 were 28.7, 17.3, 24.2, 36.5, and 25.5 μV, respectively. The mean overall RMSE and reconstructed Correlation coefficient (CC) were 26.44 μV and 0.9562, respectively. ConclusionThis paper presents a solution and innovative approach for recovering 12‑lead ECG information when only three‑lead information is available. After supplementing with comprehensive leads, we can analyze the cardiac health status more comprehensively across 12 dimensions.

Determination of optimal experimental conditions for accurate 3D reconstruction of the magnetization vector via XMCD-PEEM.

This work presents a detailed analysis of the performance of X-ray magnetic circular dichroism photoemission electron microscopy (XMCD-PEEM) as a tool for vector reconstruction of magnetization. For this, 360° domain wall ring structures which form in a synthetic antiferromagnet are chosen as the model to conduct the quantitative analysis. An assessment is made of how the quality of the results is affected depending on the number of projections that are involved in the reconstruction process, as well as their angular distribution. For this a self-consistent error metric is developed which allows an estimation of the optimum azimuthal rotation angular range and number of projections. This work thus proposes XMCD-PEEM as a powerful tool for vector imaging of complex 3D magnetic structures.

Noise-robust latent vector reconstruction in ptychography using deep generative models.

Computational imaging is increasingly vital for a broad spectrum of applications, ranging from biological to material sciences. This includes applications where the object is known and sufficiently sparse, allowing it to be described with a reduced number of parameters. When no explicit parameterization is available, a deep generative model can be trained to represent an object in a low-dimensional latent space. In this paper, we harness this dimensionality reduction capability of autoencoders to search for the object solution within the latent space rather than the object space. We demonstrate what we believe to be a novel approach to ptychographic image reconstruction by integrating a deep generative model obtained from a pre-trained autoencoder within an automatic differentiation ptychography (ADP) framework. This approach enables the retrieval of objects from highly ill-posed diffraction patterns, offering an effective method for noise-robust latent vector reconstruction in ptychography. Moreover, the mapping into a low-dimensional latent space allows us to visualize the optimization landscape, which provides insight into the convexity and convergence behavior of the inverse problem. With this work, we aim to facilitate new applications for sparse computational imaging such as when low radiation doses or rapid reconstructions are essential.

High-accuracy reconstruction of Stokes vectors via spatially modulated polarimetry using deep learning at low light field

Polarization measurement is generally performed in scenes with a low signal-to-noise ratio (SNR) such as remote sensing and biological tissue detection. The spatially modulated polarimeter can satisfy the real-time measurement requirements in low SNR scenes by establishing the mapping between photon spatial distribution and polarization information. However, accurately measuring the polarization state under low-light illumination becomes highly challenging owing to the interference of background noise. In this paper, a deep learning method is proposed and applied to the high-accuracy reconstruction of polarization information at low light field. A reinforced two-layer deep convolutional neural network is designed to respectively extract global and local features of noise in this method. Accurate photon spatial distribution can be obtained by fusing and processing these features. Experimental results illustrate the excellent accuracy achieved by the proposed method with a maximum average value of the absolute measured error below 0.04. More importantly, the proposed method is well-performed for the reconstruction of Stokes vectors at low light fields of various levels without requiring changes to the model, enhancing its practicality and simplicity.

Hybrid technique for crop image compression using discrete wavelet transform and sparse singular vector reconstruction

In this paper, a hybrid compression technique, based on discrete wavelet transform (DWT) and singular vector sparse reconstruction (SVSR), is proposed. In the initial phase, an original image has been divided into four sub-band by using the DWT technique. After that, SVSR is utilized for boosting the compression ratio and to improve reconstruction using piecewise cubic Hermite interpolation (PCHIP). Inverse discrete wavelet transform (IDWT) process has been applied to obtain a compressed crop image. The first time, this developed technique has been applied for compression. The performance of proposed hybrid techniques has been assessed in terms of several evaluation parameters, which are compression ratio (CR), peak signal-to-noise ratio (PSNR), structural similarity index measure (SSIM), and mean square error (MSE) on ten crop image data sets. It is observed from the results that the proposed technique is quite effective in compression of different types of crop images. Further, the experimental results show that the proposed hybrid method achieved significantly higher compression over the existing techniques. The proposed technique with Haar wavelet provides 412.5% and 94.97% higher CR as compared to Singular Value Decomposition (SVD), and SVSR respectively with desirable image quality. Further, other wavelets Db4 provide 396.48% and 88.88% and Bior3.5 also provides 306.74% and 54.74% higher CR as compared to SVD, and SVSR respectively with similar image quality.

Reconstruction of flow field with missing experimental data of a circular cylinder via machine learning algorithm

In this study, artificial neural networks (ANNs) have been implemented to recover missing data from the particle image velocimetry (PIV), providing quantitative measurements of velocity fields. Due to laser reflection or lower intensity of particles in the interrogation area, the reconstruction of erroneous velocity vectors is required. Therefore, the distribution of time-averaged and normalized flow characteristics around a circular cylinder has been demonstrated as streamwise and cross-stream velocities at Re = 8000. These velocity components have been given for different regions at x/D = 0.5, x/D = 1.25, x/D = 2, and y/D = 0. These stations have been chosen to estimate missing data for near-wake, mid-wake, far-wake, and symmetry regions. The missing data ratios (A*) for 0.5 ≤ x/D ≤ 2 are A* = 3.5%, 7%, and 10%. In addition, these values are A* = 4%, 8%, and 12% for y/D = 0, while A* = 7.5% for the shaded region. The increment of area positively affects the estimation results for near-wake and mid-wake regions. Moreover, the errors tend to decrease by moving away from the body. At y/D = 0, increasing the area negatively influences the prediction of the results. The mean velocity profiles of predicted and experimental data have also been compared. The missing data have been predicted with a maximum percentage error of 3.63% for horizontal stations. As a result, the ANN model has been recommended to reconstruct PIV data.

Observation and formation mechanism of 360° domain wall rings in synthetic anti-ferromagnets with interlayer chiral interactions

The interlayer Dzyaloshinskii–Moriya interaction (IL-DMI) chirally couples spins in different ferromagnetic layers of multilayer heterostructures. So far, samples with IL-DMI have been investigated utilizing magnetometry and magnetotransport techniques, where the interaction manifests as a tunable chiral exchange bias field. Here, we investigate the nanoscale configuration of the magnetization vector in a synthetic anti-ferromagnet (SAF) with IL-DMI, after applying demagnetizing field sequences. We add different global magnetic field offsets to the demagnetizing sequence in order to investigate the states that form when the IL-DMI exchange bias field is fully or partially compensated. For magnetic imaging and vector reconstruction of the remanent magnetic states, we utilize x-ray magnetic circular dichroism photoemission electron microscopy, evidencing the formation of 360° domain wall rings of typically 0.5–3.0 μm in diameter. These spin textures are only observed when the exchange bias field due to the IL-DMI is not perfectly compensated by the magnetic field offset. From a combination of micromagnetic simulations, magnetic charge distribution, and topology arguments, we conclude that a non-zero remanent effective field with components both parallel and perpendicular to the anisotropy axis of the SAF is necessary to observe the rings. This work shows how the exchange bias field due to IL-DMI can lead to complex metastable spin states during reversal, important for the development of future spintronic devices.

Observer and fault reconstruction-based control design for interval type-2 fuzzy systems

In this study, the finite-time stabilization and multiple faults reconstruction issues are scrutinized for nonlinear control systems in the presence of time-varying state delay, actuator faults and sensor faults in which the underlying system is approximated by dint of fuzzy approach. To be specific, the interval type-2 (IT2) fuzzy technique is deployed in tandem with a non-parallel distribution compensation scheme to linearize such a faulty system. Further, the existence of unknown inputs in both the system and its output are effectively reconstructed with the aid of IT2 fuzzy-based observer, namely the IT2 fuzzy unknown input (UI) observer. Simultaneously, the designed observer also ensures the reconstruction of system state vectors that are not able to be measured. With the help of this reconstruction information, a fault-tolerant control scheme is established to maintain the performance of the addressed system even in the occurrence of unknown faults. Particularly, in this work, the sampling strategy is incorporated with the developed controller design. Overall, the proposed IT2 fuzzy UI observer-based sampled fault-tolerant controller guarantees the stability of the resulting system within a finite-time duration. Furthermore, the Lyapunov stability theory enables to formulate the delay-dependent adequate constraints in the framework of linear matrix inequalities. On the grounds of established criteria, the relations are also constructed for obtaining the controller and observer gain matrices. Eventually, the simulation study is conducted with two numerical examples to validate the theoretical and practical significance of the developed control procedure.

Complex buildings orientation recognition and description based on vector reconstruction

Complex buildings orientation recognition and description based on vector reconstruction

Efficient Compressed Sensing Reconstruction Algorithm for Nonnegative Vectors in Wireless Data Transmission

With the rapid development of 5G communication and wireless Internet of Things technology, the application of intelligent wearable devices based on wireless data transmission technology is becoming more and more popular. However, due to the bandwidth of wireless data transmission nodes and the power consumption of the device system, the use time and data storage of wearable devices are severely restricted. The compressed sensing (CS) technology has become an effective method to tackle this problem. CS technology includes data compressive sensing at the transmission end and data reconstruction at the receiving end. In this paper, we consider the reconstruction of nonnegative sparse vectors, an important problem in the area of CS for wireless data transmission. It is known that the interval-passing (IP) algorithm is a low-complexity message-passing type method for the problem. However, the reconstruction performance of the IP algorithm is inferior to that of the other state-of-the-art CS reconstruction algorithms such as the orthogonal matching pursuit (OMP) algorithm. In order to address the problem, we propose a two-stage reconstruction algorithm in this paper. The proposed algorithm applies the IP algorithm for the first stage of reconstruction. If the reconstruction fails, the OMP algorithm is then used on the basis of the results in the first stage. The proposed algorithm is evaluated and compared with other state-of-the-art algorithms by the probability of perfect reconstruction under the given sparsity order value. Simulation results suggest that the proposed two-stage algorithm can greatly improve the reconstruction performance of the IP algorithm and can even outperform the OMP algorithm. In addition, the low-complexity advantages of the IP algorithm are maintained in the proposed algorithm.

Swan-Neck Correction by FDS Tenodesis and Dynamic Lateral Band Volar Relocation in the Setting of Cerebral Palsy.

While there are many proposed surgical treatment options for the correction of swan-neck deformities, none are perfect. We describe a partial flexor digitorum superficialis tenodesis that combines both a static volar plate with a dynamic oblique retinacular ligament vector reconstruction. This is performed through a single, short mid-lateral incision and requires no tendon grafts. The protected early active exercises are encouraged postoperatively, and our long-term results have been promising. The technique was designed for children with cerebral palsy, but the indications have since expanded. Level of Evidence: Level V (Therapeutic).

Exploring Neural Dynamics in Source Code Processing Domain

Deep neural networks have proven to be able to learn rich internal representations, including for features that can also be used for different purposes than those the networks are originally developed for. In this paper, we are interested in exploring such ability and, to this aim, we propose a novel approach for investigating the internal behavior of networks trained for source code processing tasks. Using a simple autoencoder trained in the reconstruction of vectors representing programs (i.e., program embeddings), we first analyze the performance of the internal neurons in classifying programs according to different labeling policies inspired by real programming issues, showing that some neurons can actually detect different program properties. We then study the dynamics of the network from an information-theoretic standpoint, namely by considering the neurons as signaling systems and by computing the corresponding entropy. Further, we define a way to distinguish neurons according to their behavior, to consider them as formally associated with different abstract concepts, and through the application of nonparametric statistical tests to pairs of neurons, we look for neurons with unique (or almost unique) associated concepts, showing that the entropy value of a neuron is related to the rareness of its concept. Finally, we discuss how the proposed approaches for ranking the neurons can be generalized to different domains and applied to more sophisticated and specialized networks so as to help the research in the growing field of explainable artificial intelligence.