Showing papers on "Hartley transform published in 2017"

An open-source full 3D electromagnetic modeler for 1D VTI media in Python: empymod

Abstract: The Python-code empymod computes the 3D electromagnetic field in a layered earth with vertical transverse isotropy by combining and extending two earlier presented algorithms in this journal. The bottleneck in frequency- and time-domain calculations of electromagnetic responses derived in the wavenumber-frequency domain is the transformations from the wavenumber to the space domain and from the frequency to the time domain, the so-called Hankel and Fourier transforms. Three different Hankel transform methods (quadrature, quadrature-with-extrapolation [QWE], and filters) and four different Fourier transform methods (fast Fourier transform [FFT], FFTLog, QWE, and filters) are included in empymod, which allows us to compare these different methods in terms of speed and precision. The best transform in terms of speed and precision depends on the modeled frequencies. Published digital filters for the Hankel transform are very fast and precise for frequencies in the range of controlled-source electromag...

The Intrinsic Structure and Properties of Laplace-Typed Integral Transforms

Abstract: We would like to establish the intrinsic structure and properties of Laplace-typed integral transforms. The methodology of this article is done by a consideration with respect to the common structure of kernels of Laplace-typed integral transform, and -transform, the generalized Laplace-typed integral transform, is proposed with the feature of inclusiveness. The proposed -transform can provide an adequate transform in a number of engineering problems.

Nonlinear optical double image encryption using random-optical vortex in fractional Hartley transform domain

Abstract: This paper proposed an enhanced asymmetric cryptosystem scheme for optical image encryption in the fractional Hartley transform domain. Grayscale and binary images have been encrypted separately using double random phase encoding. Phase masks based on optical vortex and random phase masks have been jointly used in spatial as well as in the Fourier planes. The images to be encrypted are first multiplied by optical vortex and random phase mask and then transformed with direct and inverse fractional Hartley transform for obtaining the encrypted images. The images are recovered from their corresponding encrypted images by using the correct parameters of the fractional Hartley transform and optical vortex, whose digital implementation has been performed using MATLAB 7.6.0 (R2008a). The random phase masks, optical vortex and transform orders associated with the fractional Hartley transform are extra keys that cause difficulty to an unauthorized user. Thus, the proposed asymmetric scheme is more secure as compared to conventional techniques. The efficacy of the proposed asymmetric scheme is verified by computing the mean squared error between recovered and the original images. The sensitivity of the asymmetric scheme is also verified with encryption parameters, noise and occlusion attacks. Numerical simulation results demonstrate the effectiveness and security performance of the proposed system.

A generalization of the Funk–Radon transform

Abstract: The Funk–Radon transform assigns to a function on the two-sphere its mean values along all great circles. We consider the following generalization: we replace the great circles by the small circles being the intersection of the sphere with planes containing a common point inside the sphere. If is the origin, this is just the classical Funk–Radon transform. We find two mappings from the sphere to itself that enable us to represent the generalized Radon transform in terms of the Funk–Radon transform. This representation is utilized to characterize the nullspace and range as well as to prove an inversion formula of the generalized Radon transform.

Envelope detection using generalized analytic signal in 2D QLCT domains

Abstract: The hypercomplex 2D analytic signal has been proposed by several authors with applications in color image processing. The analytic signal enables to extract local features from images. It has the fundamental property of splitting the identity, meaning that it separates qualitative and quantitative information of an image in form of the local phase and the local amplitude. The extension of analytic signal of linear canonical transform domain from 1D to 2D, covering also intrinsic 2D structures, has been proposed. We use this improved concept on envelope detector. The quaternion Fourier transform plays a vital role in the representation of multidimensional signals. The quaternion linear canonical transform (QLCT) is a well-known generalization of the quaternion Fourier transform. Some valuable properties of the two-sided QLCT are studied. Different approaches to the 2D quaternion Hilbert transforms are proposed that allow the calculation of the associated analytic signals, which can suppress the negative frequency components in the QLCT domains. As an application, examples of envelope detection demonstrate the effectiveness of our approach.

Optical image encryption in the fractional Hartley domain, using Arnold transform and singular value decomposition

Abstract: A new scheme for image encryption is proposed, using fractional Hartley transform followed by Arnold transform and singular value decomposition in the frequency domain. As the plaintext is an amplitude image, the mask used in the spatial domain is a random phase mask (RPM). The proposed scheme has been validated for grayscale images and is sensitive to the encryption parameters such as order of Arnold transform and fractional orders of the Hartley transform. We have also evaluated the scheme’s resistance to the well-known noise and occlusions attacks.

Sparse representation of two- and three-dimensional images with fractional Fourier, Hartley, linear canonical, and Haar wavelet transforms

Abstract: Fractional Fourier Transform are introduced as sparsifying transforms.Linear Canonical Transforms are introduced as sparsifying transforms.Various approaches for compressing three-dimensional images are suggested. Display Omitted Sparse recovery aims to reconstruct signals that are sparse in a linear transform domain from a heavily underdetermined set of measurements. The success of sparse recovery relies critically on the knowledge of transform domains that give compressible representations of the signal of interest. Here we consider two- and three-dimensional images, and investigate various multi-dimensional transforms in terms of the compressibility of the resultant coefficients. Specifically, we compare the fractional Fourier (FRT) and linear canonical transforms (LCT), which are generalized versions of the Fourier transform (FT), as well as Hartley and simplified fractional Hartley transforms, which differ from corresponding Fourier transforms in that they produce real outputs for real inputs. We also examine a cascade approach to improve transform-domain sparsity, where the Haar wavelet transform is applied following an initial Hartley transform. To compare the various methods, images are recovered from a subset of coefficients in the respective transform domains. The number of coefficients that are retained in the subset are varied systematically to examine the level of signal sparsity in each transform domain. Recovery performance is assessed via the structural similarity index (SSIM) and mean squared error (MSE) in reference to original images. Our analyses show that FRT and LCT transform yield the most sparse representations among the tested transforms as dictated by the improved quality of the recovered images. Furthermore, the cascade approach improves transform-domain sparsity among techniques applied on small image patches.

On E–discretization of tori of compact simple Lie groups. II

Abstract: Ten types of discrete Fourier transforms of Weyl orbit functions are developed. Generalizing one-dimensional cosine, sine, and exponential, each type of the Weyl orbit function represents an exponential symmetrized with respect to a subgroup of the Weyl group. Fundamental domains of even affine and dual even affine Weyl groups, governing the argument and label symmetries of the even orbit functions, are determined. The discrete orthogonality relations are formulated on finite sets of points from the refinements of the dual weight lattices. Explicit counting formulas for the number of points of the discrete transforms are deduced. Real-valued Hartley orbit functions are introduced, and all ten types of the corresponding discrete Hartley transforms are detailed.

Relation between Quaternion Fourier Transform and Quaternion Wigner-Ville Distribution Associated with Linear Canonical Transform

Abstract: The quaternion Wigner-Ville distribution associated with linear canonical transform (QWVD-LCT) is a nontrivial generalization of the quaternion Wigner-Ville distribution to the linear canonical transform (LCT) domain. In the present paper, we establish a fundamental relationship between the QWVD-LCT and the quaternion Fourier transform (QFT). Based on this fact, we provide alternative proof of the well-known properties of the QWVD-LCT such as inversion formula and Moyal formula. We also discuss in detail the relationship among the QWVD-LCT and other generalized transforms. Finally, based on the basic relation between the quaternion ambiguity function associated with the linear canonical transform (QAF-LCT) and the QFT, we present some important properties of the QAF-LCT.

Double random scrambling encoding in the RPMPFrHT domain

Abstract: In this paper, a novel method of digital image encryption based on the reality-preserving multiple parameter fractional Hartley transform (RPMPFrHT) is proposed. Firstly, we define an RPMPFrHT that make sure the output of cryptosystem is real-value. Then, based on random address sequences generated by coupled logistic function, we propose the double random scrambling encoding scheme which scrambled an image in the spatial domain and the RPMPFrHT domain respectively. Our method can encrypt an original image into noise-like picture with real-value which is convenient for storage and transmission. Numerical simulations have been performed and demonstrated that the proposed image encryption method is effective and sensitive to keys. Moreover, some potential attacks have also been performed to verify the robustness of the proposed method.

Steerable Discrete Fourier Transform

Abstract: Directional transforms have recently raised a lot of interest thanks to their numerous applications in signal compression and analysis. In this letter, we introduce a generalization of the discrete Fourier transform (DFT), called steerable DFT (SDFT). Since the DFT is used in numerous fields, it may be of interest in a wide range of applications. Moreover, we also show that the SDFT is highly related to other well-known transforms, such as the Fourier sine and cosine transforms and the Hilbert transforms.

Fractional Riesz–Hilbert-Type Transforms and Associated Monogenic Signals

Abstract: The fractional Hilbert transforms play a significant role in optics and signal processing because they interpolate between the near field and the far field. Mathematically, they interpolate between the identity operator and the Hilbert transform. The higher dimensional analog of the Hilbert transform is the Riesz–Hilbert transform. In this paper, we construct fractional Riesz–Hilbert operators, which also interpolate between the identity operator and the Riesz–Hilbert transform. The fractional Riesz–Hilbert transforms form a semigroup that is generated by the Riesz–Hilbert transforms. Based on the fractional Riesz–Hilbert transform we construct a fractional monogenic signal and generalize the construction of the monogenic signal. Using quaternions instead of complex numbers as eigenvalues of the transform Riesz–Hilbert transform the interpolation path can be generalized and de.pends on the chosen unit quaternion. That leads to the quaternionic fractional Riesz–Hilbert transform and a quaternionic fractional monogenic signal.

Real Time Application of Fourier Transforms

Abstract: In recent days increasing the use of Fourier transform in various applications. The Fourier transform is the simplest among the other transformation method. It is less time consuming, used in power distribution system, mechanical system, industry and wireless network. Mainly in power distribution system the mitigation of power quality disturbance require fast, accuracy and high noise immune method. In the Fourier Transform (FT) area, the advancements of oversampling, computerized sifting and clamor molding are generally received for smothering the quantization commotion. The powerful quantize bits of an ADC are enhanced in view of these techniques. In any case, when preparing the wideband signs for example, linear frequency modulation flag, these strategies can't get viable results, and need high testing rate.

Efficient Real-Fourier Domain-Based Color Shift Keying OFDM Implemented with Hartley Transform for Visible Light Communication System

Abstract: In visible light communication (VLC) system, the color shift keying (CSK) modulation scheme has been employed and combined with orthogonal frequency division multiplexing (OFDM) to improve the spectrum efficiency. However, the traditional fast Fourier transform (FFT) based OFDM module requires the CSK symbols to be Hermitian symmetric, which induces the waste of the bandwidth. In this paper, we propose a real-Fourier domain-based CSK OFDM scheme using the discrete Hartley transform (DHT), which is capable of transforming the real-valued signal to a real-valued signal and removes the requirement of Hermitian symmetry. Hence the spectrum utilization is approximated doubled thanks to removal of the requirement of Hermitian symmetry in conventional FFT-based OFDM systems. Moreover, the theoretical symbol error rate (SER) is evaluated for the asymmetrically-clipped optical OFDM (ACO-OFDM) and the DC-biased optical OFDM (DCO-OFDM) with CSK scheme. We then simulate the performance of CSK modulated DHT- based OFDM system, and the results show that the presented DHT-CSK-OFDM system can provide higher spectral efficiency while maintaining the same error performance as compared with the counterpart FFT-based OFDM systems.

A New Contourlet Transform With Adaptive Directional Partitioning

Abstract: A new image sparse representation tool—adaptive contourlet transform (ACT) is introduced in this letter. Adaptive directional partitioning schemes in ACT can match the arbitrary orientation distribution of natural image, which brings sparser representation. The proposed ACT is based on pseudopolar Fourier transform that has similar geometrical structure to fan filter. This characteristic helps ACT out of the difficulty of designing traditional directional filter bank. Simulation results demonstrate that ACT can provide more efficient image sparse representation compared to contourlet transform.

Radon transforms and Gegenbauer–Chebyshev integrals, II; examples

Abstract: We transfer the results of Part I related to the modified support theorem and the kernel description of the hyperplane Radon transform to totally geodesic transforms on the sphere and the hyperbolic space, the spherical slice transform, and the spherical mean transform for spheres through the origin. The assumptions for functions are formulated in integral terms and close to minimal.

Fast Fourier transform benchmark on X86 Xeon system for multimedia data processing

Abstract: I benchmarking the well-known Fast Fourier Transforms Library at X86 Xeon E5 2690 v3 system. Fourier transform image processing is an important tool that is used to decompose the image into sine and cosine components. If the input image represented by the equation in the spatial domain, output from the Fourier transform represents the image in the fourier or the frequency domain. Each point represents a particular frequency included in the spatial domain image in the Fourier domain image. Fourier transform is used widely for image analysis, image filtering, image compression and image reconstruction as a wide variety of applications. Fourier transform plays a important role in signal processing, image processing and speech recognition. It has been used in a wide range of sectors. For example, this is often a signal processing, is used in digital signal processing applications, such as voice recognition, image processing. The Discrete Fourier transform is a specific kind of Fourier transform. It maps the sequence over time to sequence over frequencies. If it implemented as a discrete Fourier transform, the time complexity is O (N2). It's actually not a better way to use. Alternatively, the Fast Fourier Transform is possible to easily perform a Discrete Fourier Transform of parallelism with only O (n log n) algorithm. Fast Fourier Transform is widely used in a variety of scientific computing program. If you are using the correct library can improve the performance of the program, without any additional effort. I have a well-known fast Fourier transform library was going to perform a benchmarking on X86 based Intel Xeon E5 2690 systems. In the machine's current Intel Xeon X86 Linux system. I have installed Intel IPP library, FFTW3 Library (West FFT), Kiss -FFT library and the numutils library on Intel X86 Xeon E5 based systems. The benchmark performed at C, and measuring the performance over a range of a transform size. It benchmarks both real and complex transforms in one dimension.

Fourier and Beyond: Invariance Properties of a Family of Integral Transforms

Abstract: The Fourier transform is typically seen as closely related to the additive group of real numbers, its characters and its Haar measure. In this paper, we propose an alternative viewpoint; the Fourier transform can be uniquely characterized by an intertwining relation with dilations and by having a Gaussian as an eigenfunction. This broadens the perspective to an entire family of Fourier-like transforms that are uniquely identified by the same dilation-related property and by having Gaussian-like functions as eigenfunctions. We show that these transforms share many properties with the Fourier transform, particularly unitarity, periodicity and eigenvalues. We also establish short-time analogues of these transforms and show a reconstruction property and an orthogonality relation for the short-time transforms.

Fractional Fourier, Hartley, Cosine and Sine Number-Theoretic Transforms Based on Matrix Functions

Abstract: In this paper, we introduce fractional number-theoretic transforms (FrNTT) based on matrix functions. In contrast to previously proposed FrNTT, our approach does not require the construction of any number-theoretic transform (NTT) eigenvectors set. This allows us to obtain an FrNTT matrix by means of a closed-form expression corresponding to a linear combination of integer powers of the respective NTT matrix. Fractional Fourier, Hartley, cosine and sine number-theoretic transforms are developed. We show that fast algorithms applicable to ordinary NTT can also be used to compute the proposed FrNTT. Furthermore, we investigate the relationship between fractional Fourier and Hartley number-theoretic transforms, and demonstrate the applicability of the proposed FrNTT to a recently introduced image encryption scheme.

A Frequency Domain Neural Network for Fast Image Super-resolution

Abstract: In this paper, we present a frequency domain neural network for image super-resolution. The network employs the convolution theorem so as to cast convolutions in the spatial domain as products in the frequency domain. Moreover, the non-linearity in deep nets, often achieved by a rectifier unit, is here cast as a convolution in the frequency domain. This not only yields a network which is very computationally efficient at testing but also one whose parameters can all be learnt accordingly. The network can be trained using back propagation and is devoid of complex numbers due to the use of the Hartley transform as an alternative to the Fourier transform. Moreover, the network is potentially applicable to other problems elsewhere in computer vision and image processing which are often cast in the frequency domain. We show results on super-resolution and compare against alternatives elsewhere in the literature. In our experiments, our network is one to two orders of magnitude faster than the alternatives with an imperceptible loss of performance.

Poisson Summation Formulae Associated with the Special Affine Fourier Transform and Offset Hilbert Transform

Abstract: This paper investigates the generalized pattern of Poisson summation formulae from the special affine Fourier transform (SAFT) and offset Hilbert transform (OHT) points of view. Several novel summation formulae are derived accordingly. Firstly, the relationship between SAFT (or OHT) and Fourier transform (FT) is obtained. Then, the generalized Poisson sum formulae are obtained based on above relationships. The novel results can be regarded as the generalizations of the classical results in several transform domains such as FT, fractional Fourier transform, and the linear canonical transform.

Scaling and efficient classical simulation of the quantum Fourier transform

Abstract: We provide numerical evidence that the quantum Fourier transform can be efficiently represented in a matrix product operator with a size growing relatively slowly with the number of qubits. Additionally, we numerically show that the tensors in the operator converge to a common tensor as the number of qubits in the transform increases. Together these results imply that the application of the quantum Fourier transform to a matrix product state with n qubits of maximum Schmidt rank χ can be simulated in O(n (log(n))2 χ2) time. We perform such simulations and quantify the error involved in representing the transform as a matrix product operator and simulating the quantum Fourier transform of periodic states.

DSP Real-Time Implementation of an Audio Compression Algorithm by using the Fast Hartley Transform

Abstract: This paper presents a simulation and hardware implementation of a new audio compression scheme based on the fast Hartley transform in combination with a new modified run length encoding. The proposed algorithm consists of analyzing signals with fast Hartley Transform and then thresholding the ob-tained coefficients below a given threshold which are then encoded using a new approach of run length encoding. The thresholded coefficients are, finally, quantized and coded into binary stream. The experimental results show the ability of the fast Hartley transform to compress audio signals. Indeed, it concentrates the signal energy in a few coefficients and demonstrates the ability of the new approach of run length encoding to increase the compression factor. The results of the current work are compared with wavelet based compression by using objective assessments namely CR, SNR, PSNR and NRMSE. This study shows that the fast Hartley transform is more appropriate than wavelets one since it offers a higher compression ratio and a better speech quality. In addition, we have tested the audio compression system on DSP processor TMS320C6416.This test shows that our system fits with the real-time requirements and ensures a low complexity. The perceptual quality is evaluated with the Mean Opinion Score (MOS).

A spiral based image watermarking scheme using Karhunen---Loeve and discrete hartley transforms

Abstract: The main objective of developing the image watermarking technique is satisfying the robustness and the imperceptibility of multimedia protection To achieve this objective, a novel hybrid image watermarking scheme based on Karhunen Loeve transform (KLT) and discrete hartley transform (DHT) and is proposed In the proposed scheme (KL---DHT based watermarking scheme), the original image is divided into blocks using spiral scan, then the DHT is calculated for each block, after that, the KLT is applied for each DHT block The watermark embedding process is carried out during the KLT transformation process In the watermark extracting process, the watermarked image is distorted using several image attacks such as JPEG image compression, image rotation, image resizing, adding noise (Gaussian, impulsive or speckle) or image contrast adjustment using adaptive histogram equalization Furthermore, the proposed scheme is carried out using block by block image scan and the achieved results are compared with those obtained from other watermarking schemes such as discrete cosine transform/singular value decomposition (DCT---SVD) based watermarking scheme, discrete wavelet transform/SVD (DWT---SVD) based watermarking scheme and SVD watermarking in the homomorphic domain watermarking scheme The achieved results proved that, the superiority of the KL---DHT based watermarking scheme with spiral scan compared to other watermarking schemes in the presence of different image attacks

Properties of the fractional (exponential) Radon transform

Abstract: The fractional Radon transform defined, based on the Fourier slice theorem and the fractional Fourier transform, has many potential applications in optics and the pattern-recognition field. Here we study many properties of the fractional Radon transform using existing theory of the regular Radon transform: the inversion formulas, stability estimates, uniqueness and reconstruction for a local data problem, and a range description. Also, we define the fractional exponential Radon transform and present its inversion.