Two-dimensional Fast Fourier Transform Research Articles

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.

Evaluation of FORMOSAT-2 and PlanetScope Imagery for Aboveground Oil Palm Biomass Estimation in a Mature Plantation in the Congo Basin

The present study developed methods using remote sensing for estimation of total dry aboveground biomass (AGB) of oil palm in the Congo Basin. To achieve this, stem diameters at breast height (DBH, 1.3 m) and stem heights were measured in an oil palm plantation located in Gabon (Congo Basin, Central Africa). These measurements were used to determine AGB in situ. The remote sensing approach that was used to estimate AGB was textural ordination (FOTO) based upon Fourier transforms that were applied, respectively, to PlanetScope and FORMOSAT-2 satellite images taken from the area. The FOTO method is based on the combined use of two-dimensional (2D) Fast Fourier Transform (FFT) and Principal Component Analysis (PCA). In the context of the present study, it was used to characterize the variation in canopy structure and to estimate the aboveground biomass of mature oil palms. Two types of equations linking FOTO indices to in situ biomass were developed: multiple linear regressions (MLR); and multivariate adaptive spline regressions (MARS). All best models developed yielded significant results, regardless of whether they were derived from PlanetScope or from FORMOSAT-2 images. Coefficients of determination (R2) varied between 0.80 and 0.92 (p ≤ 0.0005); and relative root mean-square-errors (%RMSE) were less than 10.12% in all cases. The best model was obtained using MARS approach with FOTO indices from FORMOSAT-2 (%RMSE = 6.09%).

Correction of amplitude scintillation effect in fully polarimetric SAR coherency matrix data

In this paper, we investigate the correction of ionospheric amplitude scintillations appearing as image artifacts in low frequency synthetic aperture radar (SAR) data. A method has been proposed to separate amplitude and phase components of fully polarimetric SAR (POLSAR) coherency matrix [T], and then implement a combination of multi-level, two-dimensional Discrete Wavelet Transform and Fast Fourier Transform (DWT-FFT) to correct the amplitude scintillation-induced stripes in [T] matrix. In the methodology, [T] is decomposed into component matrices of amplitude and relative phases. To the amplitude [T] matrix, a combination of 2-D DWT is performed, using the Haar wavelet, followed by a non-linear 2-D FFT correction strategy to remove amplitude scintillation stripes. Using DWT, each amplitude [T] matrix element is decomposed into low- and high-frequency components known as approximate and detailed coefficients respectively. On applying a 2-D FFT on the detailed coefficients, amplitude scintillation-induced stripes are easily identified in the frequency spectrum and then removed using 2-D FFT correction strategy of averaging-post-thresholding. The proposed method is tested on the [T] matrix of several POLSAR datasets acquired from Advanced Land Observation Satellite/Phased Array type L-band synthetic aperture radar (ALOS/PALSAR) and Advanced Land Observation Satellite-2/Phased Array type L-band synthetic aperture radar-2 (ALOS-2/PALSAR-2) satellites. The performance of the correction technique is analysed both, qualitatively and quantitatively. While improvements in the post-correction datasets are visually observed, a supervised Wishart classification also performed on the [T] matrices of undisturbed (reference), disturbed and corrected data indicates significant increase in overall accuracy (OA) and kappa coefficient (k̂) parameters. The classification accuracies of the disturbed data (OA = 69.31%, k̂=0.54) improved to OA = 76.49%, k̂=0.68 after applying the proposed correction approach, which is comparable to the reference data values (OA = 81.57%, k̂=0.71). The proposed method performs significantly better than the existing technique of a simple 2-D FFT approach (OA = 73.49%, k̂=0.62). The contribution of dominant scattering powers, obtained from the seven-component scattering power decomposition of POLSAR coherency matrix (7SD) model, also demonstrates post-correction improvements. The dominant scattering power for targets increased by ~3–9% using the proposed approach, shows an improvement of ~3% over the existing 2-D FFT technique.

Employing a U-net convolutional neural network for segmenting impact damages in optical lock-in thermography images of CFRP plates

ABSTRACT Carbon fibre reinforced plastics (CFRPs) are replacing metals in fields such as aerospace due to their high mechanical strength and low weight. They have an anisotropic behaviour, which hinders the analysis of structural impairment caused by damages like impacts. Optical lock-in thermography (OLT) can be used to assess CFRP integrity and image processing tools can be applied to measure the area affected by impacts on the thermal images. There are several alternatives for segmenting those images and this work proposes a transfer learning approach with a U-Net neural network used in characterisations of neuronal structures in microscopy for segmenting OLT images of CFRP plates with impact damages. After training and testing this tool with OLT images, using as ground truth their manual segmentation, the results were compared with four image processing combinations of methods: a filter based on two-dimensional Fast Fourier Transform with an adaptive threshold tool; an absolute thermal contrast (ATC) with a global threshold (GT) tool; the image overflow difference with GT; and principal component analysis (PCA) with GT. The results show that the U-Net was the most reliable for the proposed conditions for defective area assessment, allowing a higher safety in maintenance tasks.

A Comparison of Supermassive Black Hole Mass of NGC 4151 Using Different Methods

We found a new value of supermassive black hole (SMBH) mass in the middle of type 1 Seyfert, NGC 4151 galaxy. In this Study, the image of NGC 4151 galaxy was deprojected to face-on, using spiral galaxy of face-on, and applied IRAF to calculate the ellipticity and position angle of major-axis. A two-dimensional (2D) Fast Fourier Transform (FFT) applied to the deprojected image to calculate the spiral arm of NGC 4151 galaxy, and, in that way, find a central mass AGN 4151 galaxy. We compared our results of the mass of SMBH in in the center of NGC 4151 galaxy with the mass of SMBH calculated using different methods ((direct method: stellar dynamics, gas dynamics, reverberation mapping), and indirect method: MBH-σ*, MBH-Vrot, MBH-n, MBH-Lbulge, and MBH-P correlations). We concluded that the results of mass for these methods are in agreement with the estimated ones, i.e. using direct methods.

Using satellite altimetry leveling to assess the marine geoid

Based on the concept of Global Position System (GPS)/leveling, the satellite altimetry leveling (SAL) is first proposed to evaluate the marine geoid. SAL is derived by the difference among the mean sea surface (MSS), mean dynamic ocean topography (MDT), and leveling origin. In this study, (1) the original satellite altimetry data are processed to infer the vertical deflection and gravity anomaly, (2) the Chinese coastal marine geoids (CMG) are determined by using the different methods (including Molodensky, least square collocation, Stokes formula, and two-dimensional fast Fourier transformation (FFT) with the vertical deflection and gravity anomaly data), (3) CMG are evaluated by using the results from above different methods, the Gravity field and steady-state Ocean Circulation Explorer (GOCE) gravity potential model (GGPM), and SAL. The results show that (1) CMG from the Molodensky method has the highest precision by using vertical deflection data, (2) the accuracy of CMG indicate good consistency between the SAL and GGPM, (3) SAL can be used as a new method for assessing marine geoid.

Highly Parallel Vector Radix FFT for High Throughput Video Applications

The Vector Radix Fast Fourier Transform, with the inherent amenity for parallel implementation is very favourable for high throughput video processing applications. The conventional implementation of two-dimensional Fast Fourier Transform as one dimensional transforms of rows and columns can be replaced with this approach. This brief presents a novel Single Instruction Multiple Data architecture for the 8 × 8 vector radix Fast Fourier Transform implemented in Field-Programmable Gate Array with Digital Signal Processing Slice as the processing element. The performance metrics of the design is compared to the two dimensional Fast Fourier Transform implemented using one dimensional Fast Fourier Transform Intellectual Property from Xilinx. The analysis demonstrates the dominance of the design for high throughput low latency video applications.

Detection improvement of off-pin targets in FMCW radars

Frequency Modulated Continuous Wave (FMCW) radars get target range and Doppler information by extracting the target beat frequency and phase exchange based on the well-known Two-Dimensional Fast Fourier Transform (2D-FFT) processing algorithm. Target whose beat frequency does not lie on the FFT grids suffers from great detection degradation. Doubling the number of FFT points, and consequently, the hardware processing complexity is a common solution to solve this problem. In this paper, a proposed method to increase the detection performance of these targets and avoid increasing system complexity is introduced. The proposed method depends on applying a proposed filter following the first and second FFT algorithms. The filter order and weights are chosen so that only one peak form the adjacent peaks of off-pin targets are distinguished. The superiority of the proposed method over the traditional one is validated for different scenarios through the Receiver Operating Characteristic (ROC).

Theoretical investigation for the relation (supermassive black hole mass)–(spiral arm pitch angle): a correlation for galaxies with classical bulges

In this work, the determination of the masses of supermassive black holes (SMBHs) and the properties of their host spiral galaxies are focused for the purposes of constraining scaling relations and with the aim of understanding the role of SMBHs in the evolution of galaxies.The measurements of SMBHs mass for a sample of 40 spiral galaxies were studied by applying indirect techniques (the SMBHs mass versus stellar/gas velocity dispersion relation). In addition, spiral arm pitch angle of a sample of nearly face-on spiral galaxies were measured using IRAF (The Image Reduction and Analysis Facility) and two-dimensional Fast Fourier Transform (2DFFT) program.Finally, we present a new correlation between spiral arm pitch angle (a measure of the tightness of spiral structure) and the mass of supermassive black holes (BHs) in the nuclei of classical galaxies.

Maximum Likelihood Delay and Doppler Estimation for Passive Sensing

We consider the problem of delay and Doppler frequency estimation of a moving target in passive radar using a non-cooperative illuminator of opportunity (IO). The passive radar consists of a reference channel (RC), i.e., an antenna steered to the IO, and a surveillance channel (SC) that collects target echoes. We examine the maximum-likelihood estimator (MLE) for the passive estimation problem by modeling the unknown IO waveform as a deterministic process. Under this condition, the passive MLE is shown to reduce to a cross-correlation and search process using the surveillance signal and a delay-Doppler compensated version of the reference signal. We present two implementations for the passive MLE, including a direct and, respectively, a fast implementation based on a two-dimensional Fast Fourier Transform. In addition, the Cramer-Rao Bound is derived to benchmark the passive estimation performance. The passive MLE is compared via numerical simulation with its active counterpart, which has the exact knowledge of the waveform and uses it for cross-correlation. Our results show that the signal-to-noise ratio (SNR) in the RC relative to the SNR in the SC has a significant impact on the passive MLE. Specifically, if the former is notably higher than the latter (by, e.g., 5 dB), there is a minor difference between the passive and active MLEs for the delay and Doppler estimation; otherwise, the difference is non-negligible and increases with the SNR.

Mechanical inactivation of Staphylococcus aureus and Pseudomonas aeruginosa by titanium substrata with hierarchical surface structures

Titanium is the material of choice for the manufacture of orthopaedic and dental implants because of excellent corrosion resistance and proven biocompatibility. The occurrence of premature implant failure due to implant-associated infections, however, remains a prominent concern for clinicians. In this work, titanium substrata possessing micron-scale surface architectures were fabricated using a process of mask-less plasma etching of bulk titanium for periods of 5, 10, 20, 30 and 40 minutes. The resultant surfaces were characterised using two-dimensional Fast-Fourier Transforms (2D-FFT), scanning electron microscopy (SEM) and atomic force microscopy (AFM), which highlighted the formation of a two-tier pillared surface topology at the maximum etch period. Each of the substrata were assessed for antibacterial efficiency against two common human pathogens, Pseudomonas aeruginosa and Staphylococcus aureus bacteria, achieving maximum antibacterial efficiencies of 87.2 ± 2% and 72.5 ± 13%, respectively. Significantly, the formation of these three-dimensional (3D) hierarchical features was found to minimise the extent of attachment of S. aureus cells, directionally trapping the cells inside the micron size pillars with the second tier of pillars acting to kill the cells. The results of this work shed new light on the development of smart mechano-bactericidal surfaces based on tuning their micron-scale surface topology and suggest that such complex hierarchical surfaces can be particularly effective towards inactivation of cocci bacteria, such as S. aureus.

Delamination Localization in Sandwich Skin Using Lamb Waves by Finite Element Method

In this work we model by finite element method (FEM) the Lamb waves’ propagation and their interactions with symmetric and asymmetric delamination in sandwich skin. The simulations were carried out using ABAQUS CAE by exciting the fundamental A0 Lamb mode in the frequency 300 kHz. The delamination was then estimated by analysing the signal picked up at two sensors using two technics: Two-Dimensional Fast Fourier Transform (2D-FFT) to identify the propagating and converted modes, and wavelet transform (WT) to measure the arrival times. The results showed that the mode A0 is sensible to symmetric and asymmetric delamination. Besides, based on signal changes with the delamination edges, a localization method is proposed to estimate the position and the length of the delamination. In the last section an experimental FEM verification is provided to validate the proposed method.

Photoluminescence enhancement and morphological properties of nanoporous anodic alumina prepared in oxalic acid with varying time and temperature

We report on the photoluminescence (PL) enhancement and morphological properties of highly ordered Nanoporous anodic alumina (NAA) fabricated by two-step anodization for 2–10 h at 5 °C and 25 °C anodization temperatures. Structural features and pore arrangements of NAA were characterized. Pore-properties such as pore-diameter, porosity and growth rate showed an increase with rising in temperature whereas pore-wall thickness and barrier layer thickness decreased, however, interpore distance and pore density were not affected. Two-dimensional fast Fourier Transform (FFT) analysis was used to study the pore arrangement. The average pore regularity ratio was higher at 5 °C. The Photoluminescence (PL) spectra of NAA samples exhibited a strong visible blue emission at room temperature. The broad PL peak was deconvoluted into two Gaussian sub-bands attributed to luminescent F+ and F centers. Experimental results showed that NAA prepared at elevated temperature showed PL enhancement by about 3.6–4.8 fold due to the increased anodizing current which leads to the increased density of F centers compared to F+ centers.

Dynamics and density distribution of laser-produced plasma using optical interferometry

Dynamic evolution and spatio-temporally resolved density profiles of laser-produced plasma in air were investigated using optical interferometry. A series of interferograms were obtained with a pulse energy of 50 mJ and delay times from 50 ns to 2650 ns. With increasing delay time, the expansion profiles of the shock wave change from a flat ellipsoid to a spheroid. The phase shift has been extracted using a two-dimensional (2D) fast Fourier transformation algorithm and the radial distribution of the refractive index is calculated using the inverse Abel transformation assuming that the plasma is axisymmetric along the direction of the incident laser beam. Interferograms of the 2D expansion and evolution of the plasma plume and the shock wave were obtained by exploiting the spatial dependence of the refractive index. The electron densities in the plasma region and the air densities in the compressed air region were calculated from the refractive-index distributions obtained. Our results provided further understanding of the expansion and the dynamic evolution of the laser-produced plasma and the shock wave and of the spatio-temporal evolution of the density of plasma in air.

A fast numerical algorithm for a basic dual integral equation of the flapping wing in a flow of non-viscous incompressible fluid

The present paper proposes a new approach to the classical problem of the harmonic oscillations of a thin wing in a flow of non-viscous incompressible fluid. The problem is reduced to a dual integral equation, permitting application of numerical methods. The numerical experiments are performed by using some advanced fast non-stationary iterative methods, with the help of the two-dimensional Fast Fourier Transform. There is given a brief survey on the iterative methods, to evaluate the most efficient algorithms in application to the considered problem of the flapping wing theory.

Experimental and Computational Studies on the Scattering of an Edge-Guided Wave by a Hidden Crack on a Racecourse Shaped Hole.

Reliable and quantitative non-destructive evaluation for small fatigue cracks, in particular those in hard-to-inspect locations, is a challenging problem. Guided waves are advantageous for structural health monitoring due to their slow geometrical decay of amplitude with propagating distance, which is ideal for rapid wide-area inspection. This paper presents a 3D laser vibrometry experimental and finite element analysis of the interaction between an edge-guided wave and a small through-thickness hidden edge crack on a racecourse shaped hole that occurs, in practice, as a fuel vent hole. A piezoelectric transducer is bonded on the straight edge of the hole to generate the incident wave. The excitation signal consists of a 5.5 cycle Hann-windowed tone burst of centre frequency 220 kHz, which is below the cut-off frequency for the first order Lamb wave modes (SH1). Two-dimensional fast Fourier transformation (2D FFT) is applied to the incident and scattered wave field along radial lines emanating from the crack mouth, so as to identify the wave modes and determine their angular variation and amplitude. It is shown experimentally and computationally that mid-plane symmetric edge waves can travel around the hole’s edge to detect a hidden crack. Furthermore, the scattered wave field due to a small crack length, a, (compared to the wavelength λ of the incident wave) is shown to be equivalent to a point source consisting of a particular combination of body-force doublets. It is found that the amplitude of the scattered field increases quadratically as a function of a/λ, whereas the scattered wave pattern is independent of crack length for small cracks a << λ. This study of the forward scattering problem from a known crack size provides a useful guide for the inverse problem of hidden crack detection and sizing.

Influence of pole and slot combinations on vibration and noise in external rotor axial flux in‐wheel motors

This study provides a detailed finding of the influence of pole and slot combinations on vibration and noise in external rotor axial flux in-wheel motors (AFWMs). Firstly, electromagnetic force exerted on the surface of permanent magnet is discussed and a two-dimensional fast Fourier transformation is implemented to analyse its spatial distribution and frequency characteristics. Then, a multiphysics model is developed to predict the vibration and noise and figure out the main origin from the perspective of electromagnetism. The influence of pole and slot combinations on vibration and noise is also analysed via the proposed model. Finally, the effect of load on vibration and noise in AFWMs is further investigated. It turns out that zeroth spatial order of axial electromagnetic force is the main origin of vibration and noise in axial flux motors, which is quite different from radial flux motors. Moreover, AFWMs with larger lowest common multiple (LCM) of pole number (2 p ) and slot number ( Q s ) show lower noise level and for the motors that satisfy LCM(2 p,Q s ) ≠ 6 p , vibration and noise are greatly influenced by load. This study provides guidance for the design of low noise AFWMs.

Biophysical properties of cardiomyocyte surface explored by multiparametric AFM.

PeakForce Quantitative Nanomechanical Mapping (PeakForce QNM) multiparametric AFM mode was adapted to qualitative and quantitative study of the lateral membrane of cardiomyocytes (CMs), extending this powerful mode to the study of soft cells. On living CM, PeakForce QNM depicted the crests and hollows periodic alternation of cell surface architecture previously described using AFM Force Volume (FV) mode. PeakForce QNM analysis provided better resolution in terms of pixel number compared to FV mode and reduced acquisition time, thus limiting the consequences of spontaneous living adult CM dedifferentiation once isolated from the cardiac tissue. PeakForce QNM mode on fixed CMs clearly visualized subsarcolemmal mitochondria (SSM) and their loss following formamide treatment, concomitant with the interfibrillar mitochondria climbing up and forming heaps at the cell surface. Interestingly, formamide-promoted SSM loss allowed visualization of the sarcomeric apparatus ultrastructure below the plasma membrane. High PeakForce QNM resolution led to better contrasted mechanical maps than FV mode and provided correlation between adhesion, dissipation, mechanical and topographical maps. Modified hydrophobic AFM tip enhanced contrast on adhesion and dissipation maps and suggested that CM surface crests and hollows exhibit distinct chemical properties. Finally, two-dimensional Fast Fourier Transform to objectively quantify AFM maps allowed characterization of periodicity of both sarcomeric Z-line and M-band. Overall, this study validated PeakForce QNM as a valuable and innovative mode for the exploration of living and fixed CMs. In the future, it could be applied to depict cell membrane architectural, mechanical and chemical defects as well as sarcomeric abnormalities associated with cardiac diseases.

Modification of a two-dimensional fast Fourier transform algorithm with an analog of the Cooley–Tukey algorithm for image processing

Two-dimensional fast Fourier transform (FFT) for image processing and filtering is widely used in modern digital image processing systems. This paper concerns the possibility of using a modification of two-dimensional FFT with an analog of the Cooley---Tukey algorithm, which requires a smaller number of complex addition and multiplication operations than the standard method of calculation by rows and columns.