Two-dimensional Fast Fourier Transform Research Articles

Quantitative gait analysis and prediction using artificial intelligence for patients with gait disorders

Quantitative Gait Analysis (QGA) is considered as an objective measure of gait performance. In this study, we aim at designing an artificial intelligence that can efficiently predict the progression of gait quality using kinematic data obtained from QGA. For this purpose, a gait database collected from 734 patients with gait disorders is used. As the patient walks, kinematic data is collected during the gait session. This data is processed to generate the Gait Profile Score (GPS) for each gait cycle. Tracking potential GPS variations enables detecting changes in gait quality. In this regard, our work is driven by predicting such future variations. Two approaches were considered: signal-based and image-based. The signal-based one uses raw gait cycles, while the image-based one employs a two-dimensional Fast Fourier Transform (2D FFT) representation of gait cycles. Several architectures were developed, and the obtained Area Under the Curve (AUC) was above 0.72 for both approaches. To the best of our knowledge, our study is the first to apply neural networks for gait prediction tasks.

Geometric Properties of Water-ice Clouds as Observed from Jezero Crater in the First 600 sols with the NavCam Instrument On Board the Mars2020 Rover, Perseverance

In the first 600 sols of the Mars2020 mission, LS 5.6o – 316.8o, 46 cloud movies and 145 cloud surveys were collected to observe clouds at Jezero Crater, the landing site of the Perseverance Rover. Cloud movies were processed using the Mean-Frame Subtraction (MFS) method for revealing cloud structures, which were subsequently analyzed using digital-image processing. Two-dimensional Fast Fourier Transforms (2D-FFT) were used to compute cloud structure sizes ranging from 2.90 to 15.25 km for clouds between 30 and 50 km altitude, based on coincident Mars Climate Sounder vertical profiles of atmospheric water-ice. Same-value thresholding was used to detect the cloud structures in MFS-processed and projected cloud movies. The resolution dependence that was needed to resolve these structures over various thresholds was examined to find multifractal scaling of Mars clouds for resolutions between 0.1 and 1.6 km. We characterize the multiscaling observed in the images and its implications for the design of cloud-tracking cameras from the surface as well as for cloud-resolving models.

Evolution of Plumage Patterns in a Pattern Morphospace: A Phylogenetic Analysis of Melanerpine Woodpeckers.

AbstractPlumage patterns of melanerpine (Melanerpes-Sphyrapicus) woodpeckers are strikingly diverse. Understanding the evolution and function of this diversity is challenging because of the difficulty of quantifying plumage patterns. We use a three-dimensional space to characterize the evolution of melanerpine achromatic plumage patterns. The axes of the space are three pattern features (spatial frequency, orientation, and contrast) quantified using two-dimensional fast Fourier transformation of museum specimen images. Mapping plumage in pattern space reveals differences in how species and subclades occupy the space. To quantify these differences, we derive two new measures of pattern: pattern diversity (diversity across plumage patches within a species) and pattern uniqueness (divergence of patterns from those of other species). We estimate that the melanerpine ancestor had mottled plumage and find that pattern traits across patches and subclades evolve at different rates. We also find that smaller species are more likely to display horizontal face patterning. We promote pattern spaces as powerful tools for investigating animal pattern evolution.

Use of 2D FFT and DTW in Protein Sequence Comparison.

Protein sequence comparison remains a challenging work for the researchers owing to the computational complexity due to the presence of 20 amino acids compared with only four nucleotides in Genome sequences. Further, protein sequences of different species are of different lengths; it throws additional changes to the researchers to develop methods, specially alignment-free methods, to compare protein sequences. In this work, an efficient technique to compare protein sequences is developed by a graphical representation. First, the classified grouping of 20 amino acids with a cardinality of 4 based on polar class is considered to narrow down the representational range from 20 to 4. Then a unit vector technique based on a two-quadrant Cartesian system is proposed to provide a new two-dimensional graphical representation of the protein sequence. Now, two approaches are proposed to cope with the varying lengths of protein sequences from various species: one uses Dynamic Time Warping (DTW), while the other one uses a two-dimensional Fast Fourier Transform (2D FFT). Next, the effectiveness of these two techniques is analyzed using two evaluation criteria-quantitative measures based on symmetric distance (SD) and computational speed. An analysis is performed on five data sets of 9 ND4, 9 ND5, 9 ND6, 12 Baculovirus, and 24 TF proteins under the two methods. It is found that the FFT-based method produces the same results as DTW but in less computational time. It is found that the result of the proposed method agrees with the known biological reference. Further, the present method produces better clustering than the existing ones.

Real-time computing for a holographic 3D display based on the sparse distribution of a 3D object and requisite Fourier spectrum.

In holographic three-dimensional (3D) displays, the surface structures of 3D objects are reconstructed without their internal parts. In diffraction calculations using 3D fast Fourier transform (FFT), this sparse distribution of 3D objects can reduce the calculation time as the Fourier transform can be analytically solved in the depth direction and the 3D FFT can be resolved into multiple two-dimensional (2D) FFTs. Moreover, the Fourier spectrum required for hologram generation is not the entire 3D spectrum but a partial 2D spectrum located on the hemispherical surface. This sparsity of the required Fourier spectrum also reduces the number of 2D FFTs and improves the acceleration. In this study, a fast calculation algorithm based on two sparsities is derived theoretically and explained in detail. Our proposed algorithm demonstrated a 24-times acceleration improvement compared with a conventional algorithm and realized real-time hologram computing at a rate of 170Hz.

Performance improvement of non-orthogonal multiple access with a 3D constellation and a 2D IFFT modulator.

In this paper, we propose a performance improvement of non-orthogonal multiple access (NOMA) with a three-dimensional (3D) constellation and a two-dimensional Inverse Fast Fourier Transform IFFT modulator (2D-IFFT) for the passive optical network (PON). Two kinds of 3D constellation mapping are designed for the generation of a three-dimensional NOMA (3D-NOMA) signal. Higher-order 3D modulation signals can be obtained by superimposing signals of different power levels by pair mapping. Successive interference cancellation (SIC) algorithm is implemented at the receiver to remove interference from different users. Compared with the traditional two-dimensional NOMA (2D-NOMA), the proposed 3D-NOMA can increase the minimum Euclidean distance (MED) of constellation points by 15.48%, which enhances the bit error rate (BER) performance of the NOMA. The peak-to-average power ratio (PAPR) of NOMA can be reduced by 2 dB. A 12.17 Gb/s 3D-NOMA transmission over 25 km single-mode fiber (SMF) is experimentally demonstrated. The results show that at the bit error rate (BER) of 3.8 × 10-3, the sensitivity gain of the high-power signals of the two proposed 3D-NOMA schemes is 0.7 dB and 1 dB compared with that of 2D-NOMA under the condition of the same rate. Low-power level signal also has 0.3 dB and 1 dB performance improvement. Compared with 3D orthogonal frequency-division multiplexing (3D-OFDM), the proposed 3D-NOMA scheme could potentially expand the number of users without obvious performance degradation. Due to its good performance, 3D-NOMA is a potential method for future optical access systems.

Low Complexity Radar Gesture Recognition Using Synthetic Training Data

Developments in radio detection and ranging (radar) technology have made hand gesture recognition feasible. In heat map-based gesture recognition, feature images have a large size and require complex neural networks to extract information. Machine learning methods typically require large amounts of data and collecting hand gestures with radar is time- and energy-consuming. Therefore, a low computational complexity algorithm for hand gesture recognition based on a frequency-modulated continuous-wave (FMCW) radar and a synthetic hand gesture feature generator are proposed. In the low computational complexity algorithm, two-dimensional Fast Fourier Transform is implemented on the radar raw data to generate a range-Doppler matrix. After that, background modelling is applied to separate the dynamic object and the static background. Then a bin with the highest magnitude in the range-Doppler matrix is selected to locate the target and obtain its range and velocity. The bins at this location along the dimension of the antenna can be utilised to calculate the angle of the target using Fourier beam steering. In the synthetic generator, the Blender software is used to generate different hand gestures and trajectories and then the range, velocity and angle of targets are extracted directly from the trajectory. The experimental results demonstrate that the average recognition accuracy of the model on the test set can reach 89.13% when the synthetic data are used as the training set and the real data are used as the test set. This indicates that the generation of synthetic data can make a meaningful contribution in the pre-training phase.

Photoacoustic imaging a PDT response marker for monitoring vasculature changes

Photoacoustic imaging (PAI) is an evolving modality for studying and imaging tumor hypoxia. The experimental results from animals treated with ALA for Pre-PDT, Post-PDT, 4hr PDT, 24 hr PDT show a short-term increase in the BV followed by a strong decrease; however, no complete stasis. An alternate method is created by looking at the spatial and frequency domain histogram to observe the tumor vasculature. The images are represented in frequency domains by application of two-dimensional Fast Fourier Transform (FFT) on spatial domain images. The variations in acoustic impedance after Photodynamic Therapy (PDT) are studied. The photoacoustic signals implemented on tumor models indicated PDT influenced variations in the hemoglobin levels against different time periods and studied their outcome on the tumor necrosis.

Spirality: A Novel Way to Measure Spiral Arm Pitch Angle

We present the MATLAB code Spirality, a novel method for measuring spiral arm pitch angles by fitting galaxy images to spiral templates of known pitch. Computation time is typically on the order of 2 min per galaxy, assuming 8 GB of working memory. We tested the code using 117 synthetic spiral images with known pitches, varying both the spiral properties and the input parameters. The code yielded correct results for all synthetic spirals with galaxy-like properties. We also compared the code’s results to two-dimensional Fast Fourier Transform (2DFFT) measurements for the sample of nearby galaxies defined by DMS PPak. Spirality’s error bars overlapped 2DFFT’s error bars for 26 of the 30 galaxies. The two methods’ agreement correlates strongly with galaxy radius in pixels and also with i-band magnitude, but not with redshift, a result that is consistent with at least some galaxies’ spiral structure being fully formed by z=1.2, beyond which there are few galaxies in our sample. The Spirality code package also includes GenSpiral, which produces FITS images of synthetic spirals, and SpiralArmCount, which uses a one-dimensional Fast Fourier Transform to count the spiral arms of a galaxy after its pitch is determined. All code is freely available.

Mitigation of Systematic Noise in F16 SSMIS LAS Channels Observations for Tropical Cyclone Applications

The Special Sensor Microwave Imager Sounder (SSMIS) onboard the Defense Meteorological Satellite Program (DMSP) F16, launched on 18 October 2003, was the first conical-scanning radiometer to combine the Special Sensor Microwave/Imagers (SSM/I), Special Sensor Microwave/Temperature Sounder (SSM/T), and the Special Sensor Microwave/Water Vapor Sounder (SSM/T2). Nearly 20 years of F16 SSMIS data are available to the general public, providing many opportunities to study the atmosphere at both the synoptic and decadal scales. However, data noise from complicated structures has occurred in the brightness temperature (TB) observations of lower atmospheric sounding (LAS) channels since 25 April 2013. We used a two-dimensional Fast Fourier Transform to analyze the characteristic features of data noise in cross-track and along-track directions. We found that the data noise is around 1–2 K and occurs at certain cross-track wavelengths (Δλ)noise. A latitudinal variation was found for (Δλ)noise. Due to noise interference, TB observations reflecting rain, clouds, tropical cyclone warm core, temperature, and water vapor distributions are not readily distinguishable, especially in channels above the middle troposphere (channels 4–7 and 24), whose dynamic TB range is smaller than low tropospheric channels 1–3. Examples are provided to show the impact of the proposed noise mitigation for conical-scanning TB observations to capture 3D structures of hurricanes directly. Once the noise in F16 SSMIS LAS channels from 25 April 2013to the present is eliminated, we may investigate the decadal change of many features of tropical cyclones derivable from these TB observations.

Human Activity Recognition Using Wearable Sensors Based on Image Classification

Two-Dimensional Fast Fourier Transform (2-D FFT) and Wigner-Ville Transform (WVT) are two popular transforms applied to find frequency and time-frequency representations, respectively. By using them, signals acquired from different axes or sensors are mapped to these representations, considered 2D images. Based on this opinion, three novel methods are presented in this paper. The first two methods are called basic methods. The 2D images based on the magnitude of the 2-D FFT are constructed in method 1 and a fine-tuned CNN is also applied for classifying. WVT is used for constructing 2D compressed images in method 2, and classifying is done like method 1. Fusing two basic methods is presented as the proposed method. It attains the accuracies of 93.45%, 96.47%, 99.00%, and 98.20% for UCI HAR, MOTIONSENSE, MHEALTH, and WISDM datasets, respectively. Achieved results show the superiority of the proposed method compared with the state-of-the-art approaches.

Optimised gravity anomaly fields from along-track multi-mission satellite altimeter over Malaysian seas

Marine gravity anomalies are crucial parameters and elements for determining coastal and ocean geoid, tectonics and crustal structures, as well as offshore studies. This study aims to derive and develop a marine gravity anomaly model over Malaysian seas from multi-mission altimetry data. Universiti Teknologi Malaysia 2020 Mean Sea Surface Model is computed based on along-track data from nine satellite missions, incorporating TOPEX, Jason-1, Jason-2, ERS-2, Geosat Follow on (GFO), Envisat-1, CryoSat-2, SARAL/AltiKa, and Sentinel-3A. The data exploited are from 1993 to 2019 (27 years). Residual gravity anomaly is computed using Gravity Software, and two-dimensional planar Fast Fourier Transformation method is applied. The evaluation, selection, blunder detection, combination, and re-gridding of the altimetry-derived gravity anomalies and Global Geopotential Model data are demonstrated. Cross-validation procedure is employed for data cleaning and quality control using the Kriging interpolation method. Then, cross-validation procedure is applied to the tapering window width 200, which adopting the GECO model denotes the optimum gravity anomaly with root mean square errors in the range of ± 4.2472 mGal to ± 6.0202 mGal. The findings suggest that the estimated marine gravity anomaly is acceptable to be implemented in the marine geoid determination and bathymetry estimation over Malaysian seas. In addition, the results of this study are valuable for geodetic and geophysical applications in marine areas.

Evaluation of the sensitivity of higher order modes cluster (HOMC) guided waves to plate defects

Higher Order Modes Cluster (HOMC) guided waves are non-dispersive wave packets consisting of higher order Lamb wave modes. This paper investigates the effect of frequency and dominant mode(s) of an HOMC guided wave on its sensitivity to plate defects. The propagation of HOMC guided waves in a 10-mm thick mild steel plate is simulated by two-dimensional finite element model. The level of contribution of Lamb wave modes to the wave cluster is analyzed by using a two-dimensional Fast Fourier Transform (2D FFT) at various frequency-thickness products ranging from 15 to 35 MHz-mm. The normal stress profiles of the HOMC guided waves are plotted and used to show the changes in normal stress as a function of frequency-thickness product. The HOMC guided waves interactions with notches of 5%, 10%, 30% and 50% depths relative to the plate thickness are examined at various frequency-thickness products ranging from 15 to 35 MHz-mm. It is observed that the reflected energy from these notches decreases with increase in frequency-thickness product. Experimental measurements are also conducted on a similar plate. The experimental results are in line with simulations and confirm the changes observed in the reflection coefficient of notches at different frequency-thickness products.

Associations between acoustic features of maternal speech and infants' emotion regulation following a social stressor.

Caregiver voices may provide cues to mobilize or calm infants. This study examined whether maternal prosody predicted changes in infants' biobehavioral state after the still face, a stressor in which the mother withdraws and reinstates social engagement. Ninety-four dyads participated in the study (infant age 4-8months). Infants' heart rate and respiratory sinus arrhythmia (measuring cardiac vagal tone) were derived from an electrocardiogram (ECG). Infants' behavioral distress was measured by negative vocalizations, facial expressions, and gaze aversion. Mothers' vocalizations were measured via a composite of spectral analysis and spectro-temporal modulation using a two-dimensional fast Fourier transformation of the audio spectrogram. High values on the maternal prosody composite were associated with decreases in infants' heart rate (β=-.26, 95% CI: [-0.46, -0.05]) and behavioral distress (β=-.23, 95% CI: [-0.42, -0.03]), and increases in cardiac vagal tone in infants whose vagal tone was low during the stressor (1 SD below mean β=.39, 95% CI: [0.06, 0.73]). High infant heart rate predicted increases in the maternal prosody composite (β=.18, 95% CI: [0.03, 0.33]). These results suggest specific vocal acoustic features of speech that are relevant for regulating infants' biobehavioral state and demonstrate mother-infant bi-directional dynamics.

Hw/Sw Co-Design technique for 2D fast fourier transform algorithm on Zynq SoC

The Two-Dimensional Fast Fourier Transform (2D-FFT) algorithm is used for the study of many modern systems applied for security and biometrics. The adoption of this algorithm, which is a compute intensive task, is limited due to its hardware design complexity. The first objective of this paper is to underline the effect of the hardware/software co-design (Hw/Sw co-design) for the reduction of the processing time and power consumption. Secondly, we propose an innovative architecture for the 2D-FFT algorithm tested on Zynq Soc, which requires less processing time and memory compared to the traditional algorithm. Three implementations (one software and two Hw/Sw co-designs) of the 2D-FFT algorithm using the Zynq SoC are presented in this paper. The first is based on ARM processor. A speedup of 29x is obtained compared to the original implementation thanks to many optimizations. The second is a Hw/Sw co-design solution of the traditional 2D-FFT algorithm introduced on a hybrid platform combining an ARM Cortex-A9 processor with an FPGA. The third is also a Hw/Sw co-design solution using our optimized 2D-FFT algorithm to reach the real-time contraints for high-resolution images (1920 × 1080). It provides a speedup of 1.13x, 3.31x and 96.21x faster than the Hw/Sw co-design implementation of the traditional RC algorithm, the pure software implementations with and without optimizations, respectively.

On the Feasibility of Fast Fourier Transform Separability Property for Distributed Image Processing

Given the high algorithmic complexity of applied-to-images Fast Fourier Transforms (FFT), computational-resource-usage efficiency has been a challenge in several engineering fields. Accelerator devices such as Graphics Processing Units are very attractive solutions that greatly improve processing times. However, when the number of images to be processed is large, having a limited amount of memory is a serious problem. This can be faced by using more accelerators or using higher-capability accelerators, which implies higher costs. The separability property is a resource in hardware approaches that is frequently used to divide the two-dimensional FFT work into several one-dimensional FFTs, which can be simultaneously processed by several computing units. Then, a feasible alternative to address this problem is distributed computing through an Apache Spark cluster. However, determining the separability-property feasibility in distributed systems, when migrating from hardware implementations, is not evident. For this reason, in this paper a comparative study is presented between distributed versions of two-dimensional FFTs using the separability property to determine the suitable way to process large image sets using both Spark RRDs and DataFrame APIs.

An FFT-based visual quality metric robust to spatial shift

Measuring image visual quality is extremely important for many image processing tasks. In the past, several metrics have been proposed for measuring image visual quality such as structural similarity index (SSIM) and visual information fidelity (VIF). Nevertheless, these metrics are not robust to image spatial shifts when the reference and distorted images are misaligned by a few pixels. These metrics generate extremely low metric scores which is undesirable. It is well known that shifting the image by a few pixels does not affect the perceived image quality significantly. In this paper, we modify the SSIM metric to make it more robust to spatial shifts by pre-processing the input images with two-dimensional (2D) Fast Fourier Transform (FFT2). We then use the magnitudes of the Fourier coefficients in the existing metrics since these coefficients are shift-invariant. Experiments show that our proposed novel method is particularly good at measuring the visual quality of 2D images because it is far less complex than the existing methods and it offers better accuracy. Our new method is better than SSIM even when no spatial shifts are introduced to the images.

Diffusion representation for asymmetric kernels

We extend the diffusion-map formalism to data sets that are induced by asymmetric kernels. Analytical convergence results of the resulting expansion are proved, and an algorithm is proposed to perform the dimensional reduction.A coordinate system connected to the tensor product of Fourier basis is used to represent the underlying geometric structure obtained by the diffusion-map, thus reducing the dimensionality of the data set and making use of the speedup provided by the two-dimensional Fast Fourier Transform algorithm (2-D FFT).We compare our results with those obtained by other eigenvalue expansions, and verify the efficiency of the algorithms with synthetic data, as well as with real data from applications including climate change studies.

Four-Directional Total Variation With Overlapping Group Sparsity for Image Denosing

In this paper, a new model combining four-directional total variation with overlapping group sparsity is proposed, which not only suppresses the staircase effects introduced by traditional total variation, but also fully utilizes the gradient neighborhood information on each pixel of the image. In order to decrease the computation time of image denoising, the alternating direction method of multipliers (ADMM) is adopted to divide the complex optimization problem into separate subproblems that are easy to solve. At the same time, two-dimensional Fast Fourier Transform (FFT) and majorization-minimization (MM) are used to solve the subproblems alternatively. Then, the proposed new model is compared with other state-of-the-art models. Experiments show that the new model is robust in denoising. The new model not only excavates the gradient information of the four directions on the image to remove the noise more effectively, but also better in preserving image features, further reducing staircase artifacts.

Using the same type of IP-cores in the Virtex-6 family FPGA-architecture for distributed image processing

Distributed image processing in real time is a relevant task. An effective solution to this problem at the hardware level is possible on the basis of creating prototypes of devices on FPGA. In this regard, the paper solves the problem of distributed computation of two-dimensional fast Fourier transform (TDFFT) based on the same type of IP-cores implemented in the architecture of the Virtex-6 family_FPGA-architecture. The possibility of distributed implementation of each of the stages of the TDFFT, performed using four transformations of the “butterfly” type_(TrB) over four elements of the processed data array, is shown. When using a specialized CAD-system, estimates of the time and hardware complexity of the IP-core implementing TrB are_obtained. The estimated operating frequency of this_IP-core is approximately 108 MHz. Hardware complexity estimates by the number of configurable elements involved in the Virtex-6 family_FPGA-architecture are determined. TrB must be performed over an_array of N 2 elements a · N 2/4 once, where a = log2 N is the number of TDFFT stages, and N = 2 k . The ability to parallelize the specified operations at each of a stages by using_IP-cores that implement four TrB is shown. The results can be used to estimate hardware and time costs for distributed TDFFT execution over a square data array N × N - dimension.