Dimensional Fast Fourier Transform Research Articles

Implementation of Secured and Robust DFT-Based Image Watermark Through Hybridization with Decomposition Algorithm

Robust as well as secure image watermarking is capable of providing a promising solution in many copyright protection applications. In this paper, an improved image watermarking scheme based on DFT with a decomposition algorithm is proposed. First, two dimensional (2D) Fast Fourier Transform (FFT) is applied to the host image, and then its singular value decomposition (SVD) is performed. Second, the watermark image is encrypted with a chaotic map for ensuring security against unauthorized detection, and then its 2D FFT and SVD are also performed. Third, the singular values of the watermark image are embedded into the singular values of the host image. The hybridization of DFT with SVD ensures the increasing performance of the watermarking system from the perspectives of visual distortion and robustness. Experimental results show that our proposed method is highly robust and also imperceptible with a large watermark size and increased security than the classical DFT-based methods.

Classification of Brainwaves for Sleep Stages by High-Dimensional FFT Features from EEG Signals

Manual classification of sleep stage is a time-consuming but necessary step in the diagnosis and treatment of sleep disorders, and its automation has been an area of active study. The previous works have shown that low dimensional fast Fourier transform (FFT) features and many machine learning algorithms have been applied. In this paper, we demonstrate utilization of features extracted from EEG signals via FFT to improve the performance of automated sleep stage classification through machine learning methods. Unlike previous works using FFT, we incorporated thousands of FFT features in order to classify the sleep stages into 2–6 classes. Using the expanded version of Sleep-EDF dataset with 61 recordings, our method outperformed other state-of-the art methods. This result indicates that high dimensional FFT features in combination with a simple feature selection is effective for the improvement of automated sleep stage classification.

Complexity Analysis and Accuracy of Image Recovery Based on Signal Transformation Algorithms

In this paper we compare and analyze the complexity of three functions: Fast Fourier transform (FFT), Discrete Cosine Transform (DCT) and Discrete Wavelet Transform (DWT), used in image transformation. The purpose of all the algorithms is to shift the signal from space or time domain to frequency domain for de-noising or compression. We compare the simulated process time of both one and two dimensional FFT, DCT and DWT (Symlet and Debauches 1) using image and speech signal. The process time is found lowest for FFT and highest for DWT, provided its basis function governs the process time and DCT provide the moderate result. Finally the quality of compressed image under the three mathematical functions are compared, where DWT is found as the best and FFT yields worst result.

Fast and Robust Matching for Multimodal Remote Sensing Image Registration

While image registration has been studied in remote sensing community for decades, registering multimodal data [e.g., optical, LiDAR, SAR, and map] remains a challenging problem because of significant nonlinear intensity differences between such data. To address this problem, this paper presents a fast and robust matching framework integrating local descriptors for multimodal registration. In the proposed framework, a local descriptor, such as Histogram of Oriented Gradient (HOG), Local Self Similarity (LSS), or Speeded-Up Robust Feature (SURF), is first extracted at each pixel to form a pixel-wise feature representation of an image. Then we define a similarity measure based on the feature representation in frequency domain using the 3 Dimensional Fast Fourier Transform (3DFFT) technique, followed by a template matching scheme to detect control points between images. In this procedure, we also propose a novel pixel-wise feature representation using orientated gradients of images, which is named channel features of orientated gradients (CFOG). This novel feature is an extension of the pixel-wise HOG descriptors, and outperforms that both in matching performance and computational efficiency. The major advantage of the proposed framework includes: (1) structural similarity representation using the pixel-wise feature description and (2) high computational efficiency due to the use of 3DFFT. Experimental results on different types of multimodal images show the superior matching performance of the proposed framework than the state-of-the-art methods.The proposed matching framework have been used in the software products of a Chinese listed company. The matlab code is available in this manuscript.

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.

Design and Evaluation of a Scalable Engine for 3D-FFT Computation in an FPGA Cluster

The Three Dimensional Fast Fourier Transform (3D-FFT) is commonly used to solve the partial differential equations describing the system evolution in several physical phenomena, such as the motion of viscous fluids described by the Navier-Stokes equations. Simulation of such problems requires the use of a parallel High-Performance Computing architecture since the size of the problem grows with the cube of the FFT size, and the representation of the single point comprises several double precision floating- point complex numbers. Modern High-Performance Computing (HPC) systems are considering the inclusion of FPGAs as components of this computing architecture because they can combine effective hardware acceleration capabilities and dedicated communication facilities. Furthermore, the network topology can be optimized for the specific calculation that the cluster must perform, especially in the case of algorithms limited by the data exchange delay between the processors. In this paper, we explore an HPC design that uses FPGA accelerators to compute the 3DFFT. We devise a scalable FFT engine based on a custom radix-2 double-precision core that is used to implement the Decimation in Frequency version of the Cooley-Tukey FFT algorithm. The FFT engine can be adapted to different technology constraints and networking topologies by adjusting the number of cores and configuration parameters in order to minimize the overall calculation time. We compare the various possible configurations with the technological limits of available hardware. Finally, we evaluate the bandwidth required for continuous FFT execution in the APEnet toroidal mesh network.

Radix‐4 3 based two‐dimensional FFT architecture with efficient data reordering scheme

Multi-dimensional Discrete Fourier Transforms (DFTs) play an important role in signal and image processing applications. Image reconstruction is a key component in signal processing applications like medical imaging, computer vision, face recognition etc. Two dimensional fast Fourier Transform (2D FFT) and Inverse FFT plays vital role in reconstruction. In this paper we present a fast 64 × 64 point 2D FFT architecture based on radix-43 algorithm using a parallel unrolled radix-4 3 FFT as the basic block. Our radix-4 3 architecture is a memory optimized parallel architecture which computes 64-point FFT, with least execution time. Proposed architecture produces reordered output of both 64-point one dimensional (1D) FFT and 64 × 64 point 2D FFT, without using any additional hardware for reordering. The proposed architecture has been implemented in UMC 40nm CMOS technology with clock frequency of 500 MHz and area of 0.841 mm 2 . The power consumption of proposed architecture is 358 mW at 500 MHz. Energy efficiency (FFTs computed per unit of energy) is 341 points/Joule. Computation time of 64 × 64 point FFT is 8.19 μs. ASIC implementation results shows better performance of proposed work in terms of computation time when compared with state-of-art implementation. Proposed architecture has also been implemented in Virtex-7 FPGA which gives comparable area.

Robust Digital Watermarking for High-definition Video using Steerable Pyramid Transform, Two Dimensional Fast Fourier Transform and Ensemble Position-based Error Correcting

In this paper, we propose a robust blind watermarking scheme for high-definition video. In the embedding process, luminance component of each frame is transformed by 2-dimensional fast Fourier transform (2D FFT). A secret key is used to generate a matrix of random numbers for the security of watermark information. The matrix is transformed by inverse steerable pyramid transform (SPT). We embed the watermark into the low and mid-frequency of 2D FFT coefficients with the transformed matrix. In the extraction process, the 2D FFT coefficients of each frame and the transformed matrix are transformed by SPT respectively, to produce two oriented sub-bands. We extract the watermark from each frame by cross-correlating two oriented sub-bands. If a video is degraded by some attacks, the watermarks of frames contain some errors. Thus, we use an ensemble position-based error correcting algorithm to estimate the errors and correct them. The experimental results show that the proposed watermarking algorithm is imperceptible and moreover is robust against various attacks. After embedding 64 bits of watermark into each frame, the average peak signal-to-noise ratio between original frames and embedded frames is 45.7 dB.

Study of Spatial Variation of Ocean Surface Waves by Using SAR Images in Coastal Area

A temporal pattern or characteristic of the ocean surface wave can be learned from bouy observation. In terms of spatial variations, the use of Synthetic Aperture Radar (SAR) image is considered to be the most efficient as SAR is not weather dependent. This paper aimed to study the pattern of ocean waves with study area in Jakarta coast by using SAR image. We focused on spatial variation so that we emphasized in the study of the wave pattern in the area close to the coastline and away from the coast. The low pass filter was applied to reduce the noise and the discontinuity in wave images can be removed as well. The two dimensional Fast Fourier Transform and the dispersion relation were applied to get the wave spectrum and then the amplitude of ocean wave was successfully obtained. By comparing the spectral ocean wave model, the pattern of ocean waves can be understood. The results showed that in the area close to the coastline, the random wave behavior was not dominant, where a single wave pattern as a result of the nonlinear process or the wave-wave interaction appeared. Meanwhile, in the offshore area, the random effect was very dominant.

FFT-based interface decohesion modelling by a nonlocal interphase

In this paper, two nonlocal approaches to incorporate interface damage in fast Fourier transform (FFT) based spectral methods are analysed. In FFT based methods, the discretisation is generally non-conforming to the interfaces and hence interface elements cannot be used. This limitation is remedied using the interfacial band concept, i.e., an interphase region of a finite thickness is used to capture the response of a physical sharp interface. Mesh dependency due to localisation in the softening interphase is avoided by applying established regularisation strategies, integral based nonlocal averaging or gradient based nonlocal damage, which render the interphase nonlocal. Application of these regularisation techniques within the interphase sub-domain in a one dimensional FFT framework is explored. The effectiveness of both approaches in terms of capturing the physical fracture energy, computational aspects and ease of implementation is evaluated. The integral model is found to give more regularised solutions and thus a better approximation of the fracture energy.

Collision measurements using digital image correlation techniques

In this study, the digital image correlation (DIC) techniques have been used to analyze the motion during the collisions. The spline interpolation along with two dimensional Fast Fourier Transform (FFT) cross correlation has been used in order to increase the accuracy and decrease the computation time of the method respectively. Three different examples have been analyzed: normal impact of a metal rod with a 3D printed polymer flat, oblique impact of a tennis ball with a tennis racket, and oblique impact of a lacrosse ball with a wooden flat. A speckle pattern study has been done to find the optimum pattern for the DIC technique. For the normal impact of the rod, the velocity during the impact have been measured. The normal velocity has been found by the DIC technique. For the oblique impact of the balls, the linear and angular motion have been calculated during the impact. The velocity field on the ball surface has been measured using the DIC technique. The Hough transform method has been used in combination with the measured velocity field to find the velocity of the centroid of the balls. The angular velocity during the impact has been found using the velocity field of the surface of the ball. It has been shown that the DIC technique can be used to measure the motion of colliding objects.

FPGA Implementation of Underwater Image Enhancement using Nonlinear Filtering

Background/Motivation: Optical image captured by autonomous underwater vehicles need to be preprocessed as they suffer from various adversary underwater conditions and require low power devices such as FPGA. Methods/ Statistical Analysis: Underwater image degradation due to non uniform illumination is corrected by non linear filtering and is implemented in FPGA. Two dimensional Fast Fourier Transform (FFT) and its inverse along with logarithmic computation were implemented in FPGA as a part of filter implementation. One dimensional row wise and column wise FFT were computed first and then combined to form two dimensional FFT. Findings: FPGA’s can be used for implementing architectures that require high level parallelism such as image processing algorithms due to its inherent parallelism. Frequency based filtering method which is employed for preprocessing an underwater image successfully provided good histogram compared to the original one. Device utilization for implementing structure was estimated. Novel method of FFT implementation, its inverse and logarithmic computation was used in this work. The method can be applied to digital signal processing applications that can be implemented in FPGA. Application/Improvements: Automation of image preprocessing is required in unmanned underwater vehicles used for cable detection, navigation etc. These vehicles are to be provided with low power devices such as FPGAs for long run in underwater applications.

An efficient space–time based simulation approach of wind velocity field with embedded conditional interpolation for unevenly spaced locations

The classical spectral representation method (SRM) has been extensively used in the simulation of multivariate stationary Gaussian random processes. Due to the application of fast Fourier transform (FFT), the simulation is usually efficient. However, for processes with a large number of simulation points, it becomes necessary to enhance the simulation efficiency. One example is the wind velocity field along a large-span bridge, where hundreds of wind velocity fluctuations are required. In the case of bridges built over a homogeneous terrain such as coastal area or flat plain, the wind velocity field can be modeled as a multivariate homogeneous random process i.e., the auto power spectral densities (PSDs) at evenly-spaced simulation points are same and the cross PSD is a function of separation distance between two simulation points. Furthermore, in some applications, additional simulation points need to be included to a set of uniformly distributed points in order to make the wind velocity field consistent to the structural dynamic analysis requirement.In this paper, a hybrid approach of space–time random-field based SRM and proper orthogonal decomposition (POD)-based interpolation is developed for simulating the above wind velocity process. In this approach, the random-field based SRM is used to simulate the multivariate homogeneous random process composed of a set of uniformly distributed simulation locations while POD-based interpolation is used to conditionally generate the wind velocities at a few unevenly distributed points using the previously simulated wind velocities. The idea of the former is based on transforming the simulation of the homogeneous random process into that of the corresponding space–time random field where the phase angle is assumed to be zero and the coherence function must be an even function in terms of separation distance. Through this procedure, customary requirement for spectral matrix decomposition is eliminated and application of two dimensional FFT can improve the simulation efficiency dramatically. The shortcomings of this method include a slight approximation regarding the simulated sample and the non-ergodicity for the correlation function. The numerical example of a homogeneous wind velocity field along a bridge deck shows that the proposed random field-based method is very efficient in terms of accuracy and efficiency when the number of simulation locations is large and the POD-based interpolation also has good performance.

Telugu Handwritten Isolated Characters Recognition using Two Dimensional Fast Fourier Transform and Support Vector Machine

Research in character recognition is an old application in the area of pattern recognition and has attracted many researchers during the last few decades. Handwritten character recognition (HCR) is of two types namely, Online and Offline. The recognition accuracy for HCR is less than 60% as per the literature survey. Also the non existence of standard database for Indian languages is another reason for motivation of this work. This work describes Offline HCR by extracting features using 2D FFT and using the support vector machines for Telugu documents. The best percentage recognition accuracy for Telugu handwritten characters is 71%.

Modification of a two-dimensional fast Fourier transform algorithm by the analog of the Cooley-Tukey algorithm for a rectangular signal

One-dimensional fast Fourier transform (FFT) is the most popular tool for computing the two-dimensional Fourier transform. As a rule, a standard method of combination of one-dimensional FFTs--the so-called algorithm "by rows and columns" [1]--is used in the literature. In [2, 3], the authors showed how to compute the FFT for a signal with the number of samples 2 s × 2 s with the use of an analog of the Cooley-Tukey algorithm. In the present paper, a two-dimensional analog of the Cooley-Tukey algorithm is constructed for a rectangular signal with the number of samples 2 s × 2 s + l. The number of operations in this algorithm is much less than that in the successive application of a one dimensional FFT by rows and columns. The testing of the algorithm on image-type signals shows that the speed of computation of the FFT by the algorithm proposed is about 1.7 times higher than that of the algorithm by rows and columns.

FFT spectra based matching algorithm for active dynamic thermography

In Active Dynamic thermography (ADT) sequences of consecutive temperature distributions are analyzed. In biomedical applications of ADT, the problems of a patient's movements in front of a thermal camera should be eliminated before data analysis. Complete mechanical stabilization of the patients is impossible due to natural voluntary and involuntary moves caused by the heart action, breathing, etc. This paper presents a simple and efficient thermal image matching method based on the two dimensional Fast Fourier Transform.

Application of FFT transformation for correlation analysis of near field microscopy measurements

The near field microscopy has been a dynamically developing diagnostic method for the last two decades. The number of measurement modes and data it delivers, sometimes make it difficult for interpreting. Thereby one needs sophisticated methods of extraction to get some specific information from the obtained results. Increasing complexity of the instruments as well as a software allows to acquire several signals simultaneously and to process them in a specific way in order to receive a particular result. Two dimensional Fast Fourier Transformation (2D FFT) is one of the most important tools in the picture analysis in near field microscopy. Such tools as finding specific spatial frequencies or noise filtering are very efficient. In the article we present some results of different modes of AFM measurements, where additional signals were acquired during measurements and by performing 2D FFT with the comparison approach, specific results and information were obtained.

Precision geoid determination by spherical FFT in and around the Korean peninsula

This paper deals with the precision geoid determination by a gravimetric solution in and around the Korean peninsula. A number of data files were compiled for this work, containing now more than 69,900 point gravity data on land and ocean areas. The EGM96 global geopotential model to degree 360 was used in order to determine the long wavelength effect of the geoid surface. By applying the remove-restore technique the geoid undulations were determined by combining a geopotential model, mean free-air gravity anomalies and height in a Digital Elevation Model (DEM). Computation involves a spherical approximation to conduct the Stokes’ integration by a two dimensional spherical Fast Fourier Transform (FFT) with 100% zero-padding. A terrain correction was also computed by FFT with a spherical approximation of the Residual Terrain Model (RTM) terrain correction integration. Accuracy estimates are given for absolute geoid undulations using 78 GPS/Leveling stations. The comparative evaluation gives the bias of 0.187 meters and standard deviation of 0.28 meters, respectively. The relative accuracy achieved was of the order of 3.1 ppm for baselines between 10 and 350 kilometers.

Performance of a pipelined ring algorithm for Fast Fourier Transform on transputer arrays

In this paper a pipelined ring algorithm is presented for efficient computation of one and two dimensional Fast Fourier Transform (FFT) on a message passing multiprocessor. The algorithm has been implemented on a transputer based system and experiments reveal that the algorithm is very efficient. A model for analysing the performance of the algorithm is developed from its computation-communication characteristics. Expressions for execution time, speedup and efficiency are obtained and these expressions are validated with experimental results obtained on a four transputer system. The analytical model is then used to estimate the performance of the algorithm for different number of processors, and for different sizes of the input data.

八分木と２段階ＦＦＴによる３次元衝突領域の高速算出

To avoid collisions of two objects such as a workpiece and a tool, computation of collision domain in which the tip of the tool cannot locate is crucial. Collision domain can well be computed by Inverted Template Method using envelope operation. In this paper, a high-speed algorithm is proposed for three dimensional envelope operation by means of convolution operation. From two input domains α and β, an envelope domain γ is quickly computed by three dimensional Fast Fourier Transform (3D-FFT). Because it needs a huge memory capacity to convolute a whole cubic space precisely at one time, octree model is adopted to represent each of whole domains α, β and γ and Double-stage FFT method is established. First, the upper parts of input octree α and β are convoluted to get the rough sketch of the envelope domain γ. Second, pairs of lower subcubes of α and β are convoluted to compute precise 3D bitmaps. Among all the pairs, only the corresponding to boundary leaf cells of the upper γ octree are extracted. Each set of bitmaps for a leaf cell is converted into a suboctree through OR operation and added under the upper tree. Comparison of computing time with a precedent algorithm shows the superiority of Double-stage FFT method.