Showing papers on "Fourier transform published in 2022"

Resolution-robust Large Mask Inpainting with Fourier Convolutions

Abstract: Modern image inpainting systems, despite the significant progress, often struggle with large missing areas, complex geometric structures, and high-resolution images. We find that one of the main reasons for that is the lack of an effective receptive field in both the inpainting network and the loss function. To alleviate this issue, we propose a new method called large mask inpainting (LaMa). LaMa is based on i) a new inpainting network architecture that uses fast Fourier convolutions (FFCs), which have the image-wide receptive field; ii) a high receptive field perceptual loss; iii) large training masks, which unlocks the potential of the first two components. Our inpainting network improves the state-of-the-art across a range of datasets and achieves excellent performance even in challenging scenarios, e.g. completion of periodic structures. Our model generalizes surprisingly well to resolutions that are higher than those seen at train time, and achieves this at lower parameter&time costs than the competitive baselines. The code is available at https://github.com/saic-mdal/lama.

An analytical solution of equivalent elastic modulus considering confining stress and its variables sensitivity analysis for fractured rock masses

Abstract: The equivalent elastic modulus is a parameter for controlling the deformation behavior of fractured rock masses in the equivalent continuum approach. The confining stress, whose effect on the equivalent elastic modulus is of great importance, is the fundamental stress environment of natural rock masses. This paper employs an analytical approach to obtain the equivalent elastic modulus of fractured rock masses containing random discrete fractures (RDFs) or regular fracture sets (RFSs) while considering the confining stress. The proposed analytical solution considers not only the elastic properties of the intact rocks and fractures, but also the geometrical structure of the fractures and the confining stress. The performance of the analytical solution is verified by comparing it with the results of numerical tests obtained using the three-dimensional distinct element code (3DEC), leading to a reasonably good agreement. The analytical solution quantitatively demonstrates that the equivalent elastic modulus increases substantially with an increase in confining stress, i.e. it is characterized by stress-dependency. Further, a sensitivity analysis of the variables in the analytical solution is conducted using a global sensitivity analysis approach, i.e. the extended Fourier amplitude sensitivity test (EFAST). The variations in the sensitivity indices for different ranges and distribution types of the variables are investigated. The results provide an in-depth understanding of the influence of the variables on the equivalent elastic modulus from different perspectives.

Dual-plane coupled phase retrieval for non-prior holographic imaging

Abstract: Abstract Accurate depiction of waves in temporal and spatial is essential to the investigation of interactions between physical objects and waves. Digital holography (DH) can perform quantitative analysis of wave–matter interactions. Full detector-bandwidth reconstruction can be realized based on in-line DH. But the overlapping of twin images strongly prevents quantitative analysis. For off-axis DH, the object wave and the detector bandwidth need to satisfy certain conditions to perform reconstruction accurately. Here, we present a reliable approach involving a coupled configuration for combining two in-line holograms and one off-axis hologram, using a rapidly converging iterative procedure based on two-plane coupled phase retrieval (TwPCPR) method. It realizes a fast-convergence holographic calculation method. High-resolution and full-field reconstruction by exploiting the full bandwidth are demonstrated for complex-amplitude reconstruction. Off-axis optimization phase provides an effective initial guess to avoid stagnation and minimize the required measurements of multi-plane phase retrieval. The proposed strategy works well for more extended samples without any prior assumptions of the objects including support, non-negative, sparse constraints, etc. It helps to enhance and empower applications in wavefront sensing, computational microscopy and biological tissue analysis.

Fourier Transform Infrared (FTIR) Spectroscopy to Analyse Human Blood over the Last 20 Years: A Review towards Lab-on-a-Chip Devices

Abstract: Since microorganisms are evolving rapidly, there is a growing need for a new, fast, and precise technique to analyse blood samples and distinguish healthy from pathological samples. Fourier Transform Infrared (FTIR) spectroscopy can provide information related to the biochemical composition and how it changes when a pathological state arises. FTIR spectroscopy has undergone rapid development over the last decades with a promise of easier, faster, and more impartial diagnoses within the biomedical field. However, thus far only a limited number of studies have addressed the use of FTIR spectroscopy in this field. This paper describes the main concepts related to FTIR and presents the latest research focusing on FTIR spectroscopy technology and its integration in lab-on-a-chip devices and their applications in the biological field. This review presents the potential use of FTIR to distinguish between healthy and pathological samples, with examples of early cancer detection, human immunodeficiency virus (HIV) detection, and routine blood analysis, among others. Finally, the study also reflects on the features of FTIR technology that can be applied in a lab-on-a-chip format and further developed for small healthcare devices that can be used for point-of-care monitoring purposes. To the best of the authors’ knowledge, no other published study has reviewed these topics. Therefore, this analysis and its results will fill this research gap.

Fast Processing Approach for Near-Field Terahertz Imaging With Linear Sparse Periodic Array

Abstract: The benefits of terahertz (THz) radiation have increased its use, especially in imaging systems. Recently, the use of a linear sparse periodic array (SPA) has been proposed as an effective solution for two-dimensional (2D) scanning in THz imaging systems. However, the special multistatic structure of the SPA is such that it is not possible to apply fast Fourier transform-based techniques directly in the near-field (NF). Therefore, in this paper, a fast processing approach based on two Fourier techniques compatible with linear SPA is presented for NF THz imaging. In this approach, we first employ a multistatic-to-monostatic conversion to reduce phase errors due to NF multistatic imaging. Then, to improve the quality of the results, we mathematically derive an interpolation formula to counteract the non-uniform spacing of the virtual array. The modified data is then processed by three rapid techniques (fast Fourier transform (FFT)-inverse fast Fourier transform, matched filtering and a novel 1D FFT-based technique with low computational complexity) to obtain reconstructed images of the scene. Numerical and experimental results confirm the satisfactory performance of the proposed approach in terms of both the computational time and the quality of the reconstructed images.

Experimental and FLUKA evaluation on structure and optical properties and γ-radiation shielding capacity of bismuth borophosphate glasses

Abstract: For 662, 1173, 1275, and 1333 keV gamma-ray energy, photon transmissions, linear attenuation coefficients, half value layer, tenth value layer, and mean free path values of bismuth-borophosphate glasses were measured experimentally. Then, the measured findings were compared to the FLUKA code. The FLUKA code findings agreed well with the experimental results. Furthermore, the findings show that adding Bi 2 O 3 to the glass network improves the shielding properties. The current data reveal that when the Bi 2 O 3 content rises, so does the absorbance. Furthermore, the optical constants of the present gasses, such as optical band gap, phonon energy, and tails of localized states, were examined. Fourier transform infrared (FTIR) spectrometer was used to analyze the Fourier transform infrared (FTIR) spectra of our samples at room temperature in the 4000–400 cm −1 wavenumber range. From a shielding standpoint, bismuth-borophosphate glasses offer excellent gamma-ray shielding properties.

Specific Emitter Identification Based on Complex Fourier Neural Network

Abstract: Specific emitter identification (SEI) is a well-established approach to providing precise target information for civilian and military applications. For most deep learning (DL) based SEI schemes, neural operators directly learn mappings from the raw baseband waveform or its transformed representation. Different from existing schemes, we propose a novel complex Fourier neural operator (CFNO) in this letter, which introduces a time and frequency domain attention mechanism. With the CFNO block, features are fully learned from different domain perspectives. We evaluate the proposed method based on the joint distortion model of the transmitter and compare it with several state-of-the-art SEI algorithms. Simulation results demonstrate its excellent performance, making the CFNO block a good candidate for extracting fingerprints.

A Kaiser Window-Based S-Transform for Time-Frequency Analysis of Power Quality Signals

Abstract: The accurate time-frequency (TF) positioning of power quality (PQ) disturbances is the basis of dealing with PQ problems in power systems. To accurately detect PQ disturbances, this article proposes a Kaiser window-based S-transform (KST) that provides better time resolution at fundamental frequency to detect the amplitude information for voltage swell, sag, interrupt, flicker, and better frequency resolution at higher frequencies to detect the frequency of time-varying harmonics and oscillatory transient. Based on short-time Fourier transform and S-transform, KST uses a Kaiser window with the characteristic of inherent optimal energy concentration as the kernel function. The Kaiser window can be adjusted adaptively according to the detection demand of PQ disturbances by the designed control function. This allows KST to easily accommodate different detection requirements at different frequencies. The utilization of Fourier transform ensures that KST can be realized quickly. The complex TF matrix is generated after a signal is transformed by KST, where the column vector is expressed as the distribution of amplitude and phase with time at a certain frequency, and the row vector represents the distribution of amplitude and phase with frequency at a certain sampling time. Experimental results demonstrate that the proposed KST significantly outperforms the state-of-the-art techniques in TF analysis of PQ signals, especially for the energy concentration and the detection of fundamental wave.

Precise Longitudinal Power Monitoring over 2,080 km Enabled by Step Size Selection of Split Step Fourier Method

Abstract: We propose a step-size optimization scheme of the split-step Fourier method for longitudinal power profile monitoring. We observe only a 1.06-dB root-mean-square error from the theoretical power profile for a 2,080-km transmission link. © 2022 The Author(s)

Batch processing and data streaming Fourier-based convolutional neural network accelerator

Abstract: Decision-making through artificial neural networks with minimal latency is critical for numerous applications such as navigation, tracking, and real-time machine action systems. This requires machine learning hardware to process multidimensional data at high throughput. Unfortunately, handling convolution operations, the primary computational tool for data classification tasks, obeys challenging runtime complexity scaling laws. However, homomorphically implementing the convolution theorem in a Fourier optics display light processor can achieve a non-iterative O(1) runtime complexity for data inputs beyond 1,000 × 1,000 large matrices. Following this approach, here we demonstrate data streaming multi-kernel image batching using a Fourier Convolutional Neural Network (FCNN) accelerator. We show image batch processing of large-scale matrices as 2 million dot product multiplications performed by a digital light processing module in the Fourier domain. Furthermore, we further parallelize this optical FCNN system by exploiting multiple spatially parallel diffraction orders, achieving a 98x throughput improvement over state-of-the-art FCNN accelerators. A comprehensive discussion of the practical challenges associated with working at the edge of system capabilities highlights the problem of crosstalk and resolution scaling laws in the Fourier domain. Accelerating convolution by exploiting massive parallelism in display technology brings non-Van Neumann-based machine learning acceleration.

Determination of aflatoxin B1 value in corn based on Fourier transform near-infrared spectroscopy: Comparison of optimization effect of characteristic wavelengths

Abstract: Aflatoxin B1 (AFB1) is an important cause of human liver cancer. This study proposes a quantitative detection method for the AFB1 in corn based on Fourier transform near-infrared (FT-NIR) spectroscopy technology. First, we acquired spectral data of corn samples with different degrees of mildew using FT-NIR spectrometer; then, we used the ant colony optimization (ACO) and the NSGA-Ⅱ algorithms to optimize the characteristic wavelengths of the spectra after SNV treatment respectively; Finally, the back propagation neural network (BPNN) models were established using the optimized characteristic wavelengths to realize the accurate detection of the AFB1 in corn. The results obtained showed that the prediction performance of the BPNN model established using the four characteristic wavelength variables optimized by NSGA-Ⅱ algorithm is the best, and the best NSGA-Ⅱ-BPNN model's correlation coefficient of prediction (RP) is 0.9951, the root mean square error of prediction (RMSEP) is 1.5606 μg ⋅ kg−1. The overall results demonstrate that the quantitative detection of AFB1 in corn by FT-NIR technique is feasible; in addition, the NSGA-Ⅱ algorithm has its unique advantages in the optimization of spectral characteristics, and it can obtain characteristic wavelength variables with strong pertinence and a small number.

Automated Emotion Identification Using Fourier–Bessel Domain-Based Entropies

Abstract: Human dependence on computers is increasing day by day; thus, human interaction with computers must be more dynamic and contextual rather than static or generalized. The development of such devices requires knowledge of the emotional state of the user interacting with it; for this purpose, an emotion recognition system is required. Physiological signals, specifically, electrocardiogram (ECG) and electroencephalogram (EEG), were studied here for the purpose of emotion recognition. This paper proposes novel entropy-based features in the Fourier–Bessel domain instead of the Fourier domain, where frequency resolution is twice that of the latter. Further, to represent such non-stationary signals, the Fourier–Bessel series expansion (FBSE) is used, which has non-stationary basis functions, making it more suitable than the Fourier representation. EEG and ECG signals are decomposed into narrow-band modes using FBSE-based empirical wavelet transform (FBSE-EWT). The proposed entropies of each mode are computed to form the feature vector, which are further used to develop machine learning models. The proposed emotion detection algorithm is evaluated using publicly available DREAMER dataset. K-nearest neighbors (KNN) classifier provides accuracies of 97.84%, 97.91%, and 97.86% for arousal, valence, and dominance classes, respectively. Finally, this paper concludes that the obtained entropy features are suitable for emotion recognition from given physiological signals.

Fourier-based Radar Processing for Multistatic Millimetre-wave Imaging with Sparse Apertures

Abstract: Fourier-based radar processing algorithms have attracted a lot of interest among imaging techniques mostly because they are extremely fast. Moreover, such techniques can be integrated with a Multiple-Input Multiple-Output (MIMO) effective aperture to form a cost-effective imaging system that can retrieve an estimation of the scene in real-time. The proposed technique leverages the phase center approximation and a multistatic-to-monostatic data conversion to render the back-scattered measurements compatible with fast Fourier processing. Whereas the phase center approximation is applicable for imaging in the far-field of the synthesized aperture, in the near-field, a more sophisticated aperture design should be considered to reduce the distortion in the reconstructed images. This paper presents a theoretical study for a sparse aperture design and the optimization of the aperture layout for near-field imaging. Furthermore, it proposes a GPU accelerated reconstruction algorithm able to form 3D images in a few milliseconds with low-cost hardware.

Integrated photodetectors for compact Fourier-transform waveguide spectrometers

Abstract: Extreme miniaturization of infrared spectrometers is critical for their integration into next-generation consumer electronics, wearables and ultrasmall satellites. In the infrared, there is a necessary compromise between high spectral bandwidth and high spectral resolution when miniaturizing dispersive elements, narrow band-pass filters and reconstructive spectrometers. Fourier-transform spectrometers are known for their large bandwidth and high spectral resolution in the infrared; however, they have not been fully miniaturized. Waveguide-based Fourier-transform spectrometers offer a low device footprint, but rely on an external imaging sensor such as bulky and expensive InGaAs cameras. Here we demonstrate a proof-of-concept miniaturized Fourier-transform waveguide spectrometer that incorporates a subwavelength and complementary-metal-oxide-semiconductor-compatible colloidal quantum dot photodetector as a light sensor. The resulting spectrometer exhibits a large spectral bandwidth and moderate spectral resolution of 50 cm-1 at a total active spectrometer volume below 100 μm × 100 μm × 100 μm. This ultracompact spectrometer design allows the integration of optical/analytical measurement instruments into consumer electronics and space devices.