Near-perfect Reconstruction Research Articles

Integrated top-down process and voxel-based microstructure modeling for Ti-6Al-4 V in laser wire direct energy deposition process

Laser-wire metal additive manufacturing (AM) is one of the ideal direct energy deposition (DED) processes for creating large-scale parts with a medium level of complexity. However, the DED process involves complex thermal signatures and wide length scales making the fabrication of realistic AM components and part qualification often reliant on experimental trial-and-error optimization. While experimental measurements over the full volume of a part are valuable and necessary, measuring the entire area of a part is significantly laborious and practically infeasible, particularly for large parts in terms of cost and rapid qualification. Therefore, in this work, we developed an effective thermal and microstructure modeling framework based on the Johnson–Mehl-Avrami-Kolmogorov (JMAK) and Koistinen & Marburger (KM) models through a top-down approach that considers plate distortion-affected thermal profiles. A voxel-by-voxel simulation method is used to predict individual phase fractions of Ti-6Al-4 V. The predicted results were validated through detailed metallurgical measurements. A combined voxel-by-voxel approach with a sparse data reconstruction technique produced a near-perfect reconstruction of the original data. This approach anticipates a significant reduction in data points and computation time and resources. Lastly, we conclude with potential extensions of this work to other modeling efforts.

Empowering quadrature mirror filter bank architectures: dynamic-grey wolf optimization approach for elevated filter orders

The present study introduces a revised version of the Grey Wolf Optimization (GWO) algorithm called Dynamic-GWO, which integrates a dynamic parameter adaptation mechanism for population diversity enhancement. This mechanism implements the real-time adjustment of control parameters throughout the optimization procedure. The algorithm's effectiveness is demonstrated by its consistent performance across a variety of intricate benchmark functions. Further, the suggested approach is employed to determine the eminent filter tap coefficients of the Quadrature-Mirror-Filter (QMF) bank that enables the configuration with filter orders of 120 and 150, which have yet to be achieved using existing methods. The uniqueness of the proposed approach lies in its capability to overcome the inherent difficulties associated with higher-order filter design, including increased filter length and computational complexity. The primary objective function is to minimize the algebraic sum of three types of distortion: pass-band error, excess power of stop-band, and squared error of the overall transfer function at the quadrature frequency ω q = π / 2 , which generally occur in the procedure of Near-Perfect-Reconstruction (NPR) QMF bank design. In addition, the measured maximum reconstruction errors are 1.303 × 10 − 15 , 2.93 × 10 − 16 and 2.18 × 10 − 06 dB, and aliasing distortions are A L = 85.80 , 128.49 and 153.52 dB for filter orders N = 100, 120 and 150, correspondingly. The proposed algorithm yields significant improvements with an 86.68% reduction in the ripple factor and a 10.45% increase in attenuation compared to the baseline GWO for filter order 120, underscoring its effectiveness in enhancing filter performance. The observed outcomes indicate that the Dynamic-GWO algorithm consistently surpasses the baseline GWO and other Nature-Inspired Algorithms (NIAs) regarding computational ease and convergence speed.

Accelerating breast MRI acquisition with generative AI models.

To investigate the use of the score-based diffusion model to accelerate breast MRI reconstruction. We trained a score-based model on 9549 MRI examinations of the female breast and employed it to reconstruct undersampled MRI images with undersampling factors of 2, 5, and 20. Images were evaluated by two experienced radiologists who rated the images based on their overall quality and diagnostic value on an independent test set of 100 additional MRI examinations. The score-based model produces MRI images of high quality and diagnostic value. Both T1- and T2-weighted MRI images could be reconstructed to a high degree of accuracy. Two radiologists rated the images as almost indistinguishable from the original images (rating 4 or 5 on a scale of 5) in 100% (radiologist 1) and 99% (radiologist 2) of cases when the acceleration factor was 2. This fraction dropped to 88% and 70% for an acceleration factor of 5 and to 5% and 21% with an extreme acceleration factor of 20. Score-based models can reconstruct MRI images at high fidelity, even at comparatively high acceleration factors, but further work on a larger scale of images is needed to ensure that diagnostic quality holds. The number of MRI examinations of the breast is expected to rise with MRI screening recommended for women with dense breasts. Accelerated image acquisition methods can help in making this examination more accessible. Accelerating breast MRI reconstruction remains a significant challenge in clinical settings. Score-based diffusion models can achieve near-perfect reconstruction for moderate undersampling factors. Faster breast MRI scans with maintained image quality could revolutionize clinic workflows and patient experience.

Designing optimal prototype filters for maximally decimated Cosine Modulated filter banks with rapid convergence

An analytic design of a prototype filter for M-channel maximally decimated cosine-modulated Near Perfect Reconstruction (NPR) filter banks is proposed in this work. The prototype filter is created using the least-square (CLS) method with weighted constraints, which is one-dimensional and requires single-parameter optimization. Compared to existing approaches, this suggested method achieves rapid convergence by analytically determining the optimal step size, ensuring the 3 dB cutoff frequency at π/2 M. The simulation results for design examples outperform the techniques in the available literature in terms of amplitude and aliasing distortion, reaching distortion around 2.4489 × 10−4 and 3.4907 × 10−9, respectively. This optimization algorithm's usefulness is further demonstrated with the sub-band coding of ECG signals. Implementing optimal prototype filters has tangible real-world effects, especially in critical sectors like healthcare and communications, improving diagnostics accuracy, data transmission efficiency, and overall performance.

Augmentation of degranulation mechanism for high-dimensional data with a multi-round optimization strategy

Various fuzzy clustering-based granulation–degranulation techniques have been developed for constructing and optimizing information granules, which help reveal the underlying structure of experimental data in Granular Computing (GrC). Basically, a well-performing granulation–degranulation mechanism runs with a low degranulation (reconstruction) error. However, the increasingly high-dimensional characteristics of data bring great challenges to achieve accurate of reconstruction of high-dimensional data. As such, for the reconstruction of high-dimensional data, an important issue is how to reduce the reconstruction error such that the data could be reconstructed more accurately. In order to address the challenge of unacceptable high reconstruction error posed by the increase in data dimensions and improve the inefficient fuzzy clustering-based granulation in existing techniques, this study develops a multi-round iterative optimization strategy with the use of Fuzzy C-Means (FCM) to enhance reconstruction performance for high-dimensional data. First, we propose a Feature Sampling-based FCM (FS-FCM) scheme served as the granulation mechanism in the framework. The proposed scheme draws on the idea of ensemble learning, where the granulation of original high-dimensional data is accomplished by generating and training low-dimensional sub-datasets through multiple times of feature random sampling. Then, a multi-round iterative granulation–degranulation mechanism is proposed along with its algorithmic framework. Within the proposed framework, we attempt to reduce the reconstruction error by iteratively reconstructing the residual data generated in each round of granulation–degranulation. Finally, we validate the developed strategy framework over twelve publicly available datasets with varying dimension scales. A set of ablation experiments verifies the effectiveness of the FS-FCM granulation scheme. The near-perfect reconstruction performance achieved by the proposed iterative framework on the given datasets further demonstrates its superiority.

Transfer learning and generalization of a neural-network-based multimode fiber position and imaging sensor under thermal perturbations

Fiber specklegrams created through multimode fibers have been utilized in a wide variety of imaging and sensing applications. In a practical environment it is useful to have a system that, after an initial calibration, produces reconstructed images and tracks the current state of relevant physical quantities such as the position or shape of the fiber. Neural networks provide the ability to extract and generalize the information contained in the specklegrams in order to produce accurate predictions even when experimental conditions are altered from their calibration state. Using a single-layer fully-connected network, we demonstrate the capability to perform robust image reconstruction under discrete position and temperature perturbations, as well as to classify the fiber position for different reconstructed images and thermal perturbations. On a test set with the same thermal state and bend configuration as for the training data, the network achieves near-perfect reconstruction and classification accuracy. Further, our neural network can generalize its position classification and image reconstruction capabilities across a 30 °C temperature perturbation with a high degree of accuracy, providing measurements that are robust to these variations, as well as calibrations that are stable and effective for several days. Moreover, using a low-temperature training set to initialize network weights, transfer learning is demonstrated by re-calibrating on a small set of data and shown to significantly improve robustness and performance of the imaging system on a high-temperature perturbation test set.

LidarCSNet: A Deep Convolutional Compressive Sensing Reconstruction Framework for 3D Airborne Lidar Point Cloud

Lidar scanning is a widely used surveying and mapping technique ranging across remote-sensing applications involving topological, and topographical information. Typically, lidar point clouds, unlike images, lack inherent consistent structure and store redundant information thus requiring huge processing time. The Compressive Sensing (CS) framework leverages this property to generate sparse representations and accurately reconstructs the signals from very few linear, non-adaptive measurements. The reconstruction is based on valid assumptions on the following parameters- (1) sampling function governed by sampling ratio for generating samples, and (2) measurement function for sparsely representing the data in a low-dimensional subspace. In our work, we address the following motivating scientific questions- Is it possible to reconstruct dense point cloud data from a few sparse measurements? And, what could be the optimal limit for CS sampling ratio with respect to overall classification metrics? Our work proposes a novel Convolutional Neural Network based deep Compressive Sensing Network (named LidarCSNet) for generating sparse representations using publicly available 3D lidar point clouds of the Philippines. We have performed extensive evaluations for analysing the reconstruction for different sampling ratios {4%, 10%, 25%, 50% and 75%} and we observed that our proposed LidarCSNet reconstructed the 3D lidar point cloud with a maximum PSNR of 54.47 dB for a sampling ratio of 75%. We investigate the efficacy of our novel LidarCSNet framework with 3D airborne lidar point clouds for two domains - forests and urban environment on the basis of Peak Signal to Noise Ratio, Haussdorf distance, Pearson Correlation Coefficient and Kolmogorov-Smirnov Test Statistic as evaluation metrics for 3D reconstruction. The results relevant to forests such as Canopy Height Model and 2D vertical profile are compared with the ground truth to investigate the robustness of the LidarCSNet framework. In the urban environment, we extend our work to propose two novel 3D lidar point cloud classification frameworks, LidarNet and LidarNet++, achieving maximum classification accuracy of 90.6% as compared to other prominent lidar classification frameworks. The improved classification accuracy is attributed to ensemble-based learning on the proposed novel 3D feature stack and justifies the robustness of using our proposed LidarCSNet for near-perfect reconstruction followed by classification. We document our classification results for the original dataset along with the point clouds reconstructed by using LidarCSNet for five different measurement ratios - based on overall accuracy and mean Intersection over Union as evaluation metrics for 3D classification. It is envisaged that our proposed deep network based convolutional sparse coding approach for rapid lidar point cloud processing finds huge potential across vast applications, either as a plug-and-play (reconstruction) framework or as an end-to-end (reconstruction followed by classification) system for scalability.

Performance of Oversampled Polyphase Filterbank Inversion via Fourier Transform

Frequency channelization is a fundamental signal processing operation employed across various domains, including communications and radio astronomy. The polyphase filterbank (PFB) represents an efficient and versatile means of channelization. When strict constraints are placed on the allowable spectral leakage between neighboring channels, an oversampled PFB design is advantageous. A helpful consequence of the oversampling is that inversion of the PFB to recover high temporal resolution is simplified and can be accomplished accurately using Fourier transforms. We describe this inversion approach and identify key design considerations. We examine the residual error and spectral/temporal leakage behavior when a channelizer and its corresponding inverter are cascaded, concluding that near-perfect reconstruction can be approached with appropriate selection of PFB and inverter design parameters.

Near‐perfect reconstruction short length pulses for FBMC systems: re‐optimising OFDP design via semi‐definite programming

Here, the authors develop a prototype filter design for filter bank multi-carrier (FBMC) systems focusing on shortlength pulses (K ≤ 3) with near-perfect reconstruction features, favouring operational conditions for FBMC systems. The proposed design is formulated as the optimisation of the weights of a discrete prototype filter that takes into account high symbol reconstruction rates and desirable spectrum features. Despite not being convex, the formulated optimisation problem is relaxed via semi-definite programming (SDP), enabling solutions that can over-perform other popular prototype filters. Numerical results show that the proposed design considering overlapping factors K = {1,2,3} can deliver prototype filters with a good signal-to-interference ratio (SIR) versus spectrum performance trade-off. Indeed, for K ≤ 2, the proposed methodology delivered prototype filters with the highest SIR levels among the available options. Furthermore, the proposed methodology can be extended and combined with other filter optimisation criteria, enabling to comply with different FBMC design requirements.

Review of Channel Estimation for Candidate Waveforms of Next Generation Networks

The advancement in wireless communication applications encourages the use of effective and efficient channel estimation (CE) techniques because of the varying behaviour of the Rayleigh fading channel. In most cases, the emphasis of most proposed CE schemes is to improve the CE performance and complexity for ensuring quality signal reception and improved system throughput. Candidate waveforms whose designs are based on filter bank multi-carrier (FBMC) modulation techniques such as filter bank orthogonal frequency division multiplexing based on offset quadrature amplitude modulation (OFDM-OQAM), universal filtered multicarrier (UFMC) and generalised frequency division multiplexing based on offset quadrature amplitude modulation (GFDM-OQAM) are no exception to the use of these proposed CE techniques in the literature. These schemes are considered as potential waveform candidates for the physical/media access control layer of the emerging fifth generation (5G) networks. Therefore, pinpoint CE techniques represent an important requirement for these waveforms to attain their full potentials. In this regard, this paper reviews the concept of CE as applicable to these waveforms as well as other waveform candidates under consideration in the emerging 5G networks. Since the design of the majority of the waveform candidates is filter based, a review of the general filter design considerations is presented in this paper. Secondly, we review general CE techniques for candidate waveforms of next generation networks and classify some of the studied CE techniques. In particular, we classify the CE schemes used in filter bank OFDM-OQAM and GFDM-OQAM based transceivers and present a performance comparison of some of these CE schemes. Besides, the paper reviews the performances of two linear CE schemes and three adaptive based CE schemes for two FBMC based waveform candidates assuming near perfect reconstruction (NPR) and non-perfect reconstruction (Non-PR) filter designs over slow and fast frequency selective Rayleigh fading channels. The results obtained are documented through computer simulations, where the performances of the studied CE schemes in terms of the normalised mean square error (NMSE) are analysed. Lastly, we summarise the findings of this work and suggest possible research directions in order to improve the potentials of the studied candidate waveforms over Rayleigh fading channels.

Fast-convolution multicarrier based frequency division multiple access

Fast-convolution multicarrier (FCMC), the asynchronous waveform with ultra-low sidelobe, has appeared to be a promising waveform technique for future wireless communications. In this paper, we investigate the filter bank optimization as well as receiver design including low-complexity channel estimator and equalizer for FCMC based frequency division multiple access (FDMA). Starting from the conventional multi-carrier signals, we first derive a vectorized signal model as a framework to systematically design the FCMC transceiver. For nearly perfect reconstruction (NPR) filter banks design, an optimization criterion which consists of minimizing received signal segments mean square error (MSE) is proposed. From the fact that Toeplitz matrices can be asymptotically diagonalized by discrete Fourier transform (DFT) matrix, the channel equalizer can be simplified to one-tap frequency domain equalizer when DFT size is large enough. The minimum mean square error (MMSE) criterion is then applied to calculate the coefficients of one-tap frequency domain equalizer. In practice, due to the channel fading, the channel estimation has to be performed to obtain the channel state information (CSI) which is required by the channel equalization. To this end, we propose a combined cyclic prefix (CP) and cyclic suffix (CS) pilot structure which facilitates to estimate the frequency domain CSI directly in the receiver end. The proposed FCMC based FDMA features low-complexity receiver, adjustable users bandwidth and low peak-to-average power ratio. Simulation results confirm the performance of the proposed scheme.

Design of sparse cosine modulated filter banks based on Hopfield neural network

Cosine modulated filter bank (CMFB) is the most basic and important module in multi-rate signal processing system. Sparse FIR linear-phase CMFB can not only reduce the complexity of hardware design, but also ensure good performance. In this paper, a new design method of CMFB is proposed. First, the set of sparse coefficients of the prototype filter is found by using the orthogonal matching pursuit (OMP) algorithm. Then the Hopfield neural network (HNN) is employed to optimize the non-zero coefficients. The analytical and simulation results demonstrate that the new approach not only ensures that the sparse CMFBs satisfy near perfect reconstruction (NPR), but also improves the efficiency of hardware operation.

A Novel Design of Sparse Prototype Filter for Nearly Perfect Reconstruction Cosine-Modulated Filter Banks

Cosine-modulated filter banks play a major role in digital signal processing. Sparse FIR filter banks have lower implementation complexity than full filter banks, while keeping a good performance level. This paper presents a fast design paradigm for sparse nearly perfect-reconstruction (NPR) cosine-modulated filter banks. First, an approximation function is introduced to reduce the non-convex quadratically constrained optimization problem to a linearly constrained optimization problem. Then, the desired sparse linear phase FIR prototype filter is derived through the orthogonal matching pursuit (OMP) performed under the weighted l 2 norm. The simulation results demonstrate that the proposed scheme is an effective paradigm to design sparse NPR cosine-modulated filter banks.

Software for Complete Mode Structure Analysis of a Light Field

We present a software package aimed at simulating photon-number probability distributions of a range of classical and non-classical states of light. This software can generate arbitrary probability distributions from user-defined mode structure of a light field. It can also solve the reverse problem, i.e., reconstructing the mode structure of a light field from a given probability distribution. The mode structure fully defines a light field. Thus it provides information about the source of light without having to directly access the source. The multimode fields simulated by this software include those comprised of a number of thermal modes, a Poisson mode, and single-photon modes. In addition, conjugated multimode sources (such as those created via parametric downconversion (PDC) or four-wave mixing (FWM)) can be simulated. This software provides for a nearly-perfect reconstruction of multimode fields comprised of several correlated and uncorrelated thermal and Poisson modes. The code is particularly effective at characterizing mesoscopic quantum states of light. This software can be modified to include other types of modes (i.e., governed by other statistical distributions), as needed.

Design perfect reconstruction cosine-modulated filter banks via quadratically constrained quadratic programming and least squares optimization

In this paper, the design of perfect reconstruction (PR) cosine-modulated filter banks (CMFBs) is implemented via quadratically constrained quadratic programming (QCQP) and least squares (LS) optimization. To this end, a PR CMFB design problem is formulated as a nonconvex QCQP after re-arranging the coefficients of the prototype filter. Then a deep insight is offered into the algebraic relationship between the PR conditions and near-perfect reconstruction (NPR) ones for CMFB designs. Here we theoretically show that the NPR conditions are just the summations of the PR conditions. Firmly in the light of this relationship, a two-stage method is proposed for PR CMFB design. We firstly solve an NPR CMFB problem to obtain its optimal solution as a reference point, then model the PR CMFB design problem as a series of small-sized LS problems near the reference point. And we solve the LS problems in parallel with cheap iteration. Our analysis and numerical results show that the proposed method bears superior performance on effectiveness and efficiency, especially in the case of designing PR CMFBs with large number of channels.

Full statistical mode reconstruction of a light field via a photon-number-resolved measurement

We present a method to reconstruct the complete statistical mode structure and optical losses of multimode conjugated optical fields using an experimentally measured joint photon-number probability distribution. We demonstrate that this method evaluates classical and non-classical properties using a single measurement technique and is well-suited for quantum mesoscopic state characterization. We obtain a nearly-perfect reconstruction of a field comprised of up to 10 modes based on a minimal set of assumptions. To show the utility of this method, we use it to reconstruct the mode structure of an unknown bright parametric down-conversion source.

Interference-driven designs of nonlinear-phase FIR filter with application in FBMC system

In the forthcoming 5G systems, new technologies, such as amorphous networks and non-orthogonal filter bank multi-carriers (FBMC), provide an effective way to accommodate high-rate transmissions. Meanwhile, the prototype filter affects the adjacent channel interference, and therefore is important for FBMC systems. Besides, once the amorphous network is taken into account, the requirement for interference control must be much stricter. Accordingly, this paper focuses on the design of prototype filter with better ability of interference controlling, where we exploit the nonlinear phase FIR filter (NLPFF) instead of traditional linear phase FIR filter (LPFF) to achieve more optimization spaces under a small sacrifice of linear phase. In our designs, both the amplitude and phase responses are handled independently to approach the stop-band performance enhancements, in while the nearly perfect reconstruction (NPR) conditions are relaxed by pre-specified thresholds. Computer simulations confirm the effectiveness of the NLPFF designs, and demonstrate the advantages of the proposed NLPFF in FBMC applications.

Properties and achievable data rate of a cyclic prefix based imperfect reconstruction filter bank multiple access system

In this study, the authors propose a cyclic prefix (CP) based imperfect reconstruction (IPR) filter bank multicarrier (FBMC) system in the uplink of multiuser networks, known as filter bank multiple access (FBMA). The prototype filter in the system is a common low-pass filter without any perfect reconstruction (PR) or nearly perfect reconstruction (NPR) constraint. CP appended input signal format is applied to avoid inter-symbol interference and facilitate the equalisation task. The received signal is jointly processed by multi-subband equalisation. Besides, the input data symbols can be complex-valued due to IPR design. Some properties and achievable data rate of the proposed system are discussed. Simulations illustrate that the proposed system with uniformly/non-uniformly designed filter bank has a similar achievable data rate to orthogonal frequency division multiple access (OFDMA). Bit error rate performance of the proposed system is better than OFDMA and an error floor always exists when applying conventional PR FBMC to multi-user networks. In addition, OFDMA is more sensitive to carrier frequency offset than FBMA because of full synchronisation requirement. Therefore, it suggests that the proposed CP based IPR FBMA system works well without PR/NPR conditions and more extensive development is feasible for the filter banks in the foreseeable future.

A Comparison of Compressed Sensing and Sparse Recovery Algorithms Applied to Simulation Data

The move toward exascale computing for scientific simulations is placing new demands on compression techniques. It is expected that the I/O system will not be able to support the volume of data that is expected to be written out. To enable quantitative analysis and scientific discovery, we are interested in techniques that compress high-dimensional simulation data and can provide perfect or near-perfect reconstruction. In this paper, we explore the use of compressed sensing (CS) techniques to reduce the size of the data before they are written out. Using large-scale simulation data, we investigate how the sufficient sparsity condition and the contrast in the data affect the quality of reconstruction and the degree of compression. We provide suggestions for the practical implementation of CS techniques and compare them with other sparse recovery methods. Our results show that despite longer times for reconstruction, compressed sensing techniques can provide near perfect reconstruction over a range of data with varying sparsity.

Prototype filter design for QAM-based filter bank multicarrier system

In this paper, we provide conditions for a prototype filter design of filter bank multicarrier (FBMC) based on quadrature amplitude modulation (QAM). The conditions consist of a generalized Nyquist criterion (GNC) for nearly perfect reconstruction (NPR) and meeting the stopband condition for a small side-lobe. In a practical environment, a small side-lobe is a key aspect of achieving high spectral efficiency, which becomes an important factor in reducing the size of the guard band among channels. In addition, because the conventional GNC is derived under the assumption of an ideal channel, which can be easily broken over a practical multipath channel, we propose a relaxed NPR that considers the multipath delay using a 2L-oversampled discrete Fourier transform (DFT) in the frequency domain. Based on the relaxation of the GNC depending on a multipath channel, we formulate an optimization problem for a QAM-FBMC prototype filter design and propose a prototype filter with a small side-lobe and reliable BER performance. Simulation results show that the proposed prototype filter remarkably reduces the side-lobe compared to conventional QAM-FBMC based on two types of prototype filters and orthogonal frequency division multiplexing (OFDM) via the trade-off between GNC and side-lobe performance. The benefit of the side-lobe condition allows the proposed prototype filter, the Relaxed-NPR-F, to improve spectral efficiency by reducing the guard band in the frequency domain.