Showing papers on "Discrete sine transform published in 2017"

Optical multi-image encryption scheme based on discrete cosine transform and nonlinear fractional Mellin transform

Abstract: A new multi-image encryption scheme with an optical implementation based on the nonlinear fractional Mellin transform is proposed, which could avoid the vulnerability of the linear encryption systems and encrypt multiple images simultaneously. In the proposed scheme, the original images are transformed into spectra by the discrete cosine transform, then the spectra are incised and spliced into a composite spectrum, and finally the composite spectrum is performed by the nonlinear fractional Mellin transform to obtain the final encrypted image. After the processing of the fractional Mellin transform, amplitude encoding and phase encoding are adopted. The orders of the fractional Mellin transform are the main keys of this multi-image encryption scheme. Simulation results demonstrate the validity and the security of the proposed scheme.

An Exact and Fast Computation of Discrete Fourier Transform for Polar and Spherical Grid

Abstract: Numerous applied problems of two-dimensional (2-D) and 3-D imaging are formulated in continuous domain. They place great emphasis on obtaining and manipulating the Fourier transform in polar and spherical coordinates. However, the translation of continuum ideas with the discrete sampled data on a Cartesian grid is problematic. There exists no exact and fast solution to the problem of obtaining discrete Fourier transform for polar and spherical grids in the literature. In this paper, we develop exact algorithms to the above problem for 2-D and 3-D, which involve only 1-D equispaced fast Fourier transform with no interpolation or approximation at any stage. The result of the proposed approach leads to a fast solution with very high accuracy. We describe the computational procedure to obtain the solution in both 2-D and 3-D, which includes fast forward and inverse transforms. We find the nested multilevel matrix structure of the inverse process, and we propose a hybrid grid and use a preconditioned conjugate gradient method that exhibits a drastic improvement in the condition number.

Reconstruction of granular railway ballast based on inverse discrete Fourier transform method

Abstract: This paper presents a particle shape characterization and reconstruction method to describe the geometrical information of granular railway ballast. The outline of a real granular particle is segmented and transformed as discrete time domain signals based on Fourier transform method. Then, the discrete Fourier transform algorithm is developed and applied to convert discrete time domain signals into a discrete Fourier spectrum. Meanwhile, the normalized amplitudes are defined as Fourier descriptors, which is found to be applicable to characterize and reconstruct particle contour. Further, the proposed method is validated by comparing the contours of the real particle with that of reconstructed particle. Moreover, the shape indexes of particles Fourier descriptors and reconstruction of ballasted gravel are illustrated and the the results show that the geometrical parameters can be classified as three levels which can represent the geometrical characteristics in terms of macroscopical and microscopic structure. The inverse discrete Fourier transform can quantitatively control the shape of reconstructed particles by controlling the value and distribution of Fourier descriptors, which matchs the three levels of shape indexes. Furthermore, it can be found that a large number of virtual particles with similar geometrical features can be reconstructed using the proposed Fourier descriptors in a rapid and convenient manner, which is beneficial for providing a virtual test sample for the numerical modeling of realistic granular materials.

A Fast Approximation of the Bilateral Filter using the Discrete Fourier Transform

Abstract: The bilateral filter is a popular non-linear smoother that has applications in image processing, computer vision, and computational photography. The novelty of the filter is that a range kernel is used in tandem with a spatial kernel for performing edge-preserving smoothing, where both kernels are usually Gaussian. A direct implementation of the bilateral filter is computationally expensive, and several fast approximations have been proposed to address this problem. In particular, it was recently demonstrated in a series of papers that a fast and accurate approximation of the bilateral filter can be obtained by approximating the Gaussian range kernel using polynomials and trigonometric functions. By adopting some of the ideas from this line of work, we propose a fast algorithm based on the discrete Fourier transform of the samples of the range kernel. We develop a parallel C implementation of the resulting algorithm for Gaussian kernels, and analyze the effect of various extrinsic and intrinsic parameters on the approximation quality and the run time. A key component of the implementation are the recursive Gaussian filters of Deriche and Young.

A New Systolic Array Algorithm and Architecture for the VLSI Implementation of IDST Based on a Pseudo-Band Correlation Structure

Abstract: In this paper a new linear VLSI array architecture for the VLSI implementation of a prime-length 1-D Inverse Discrete Sine Transform (IDST) is proposed. This new design approach uses a ...

Point-Cloud compression using data independent method — A 3D discrete cosine transform approach

Abstract: Point-cloud is a widely used representation for objects and scenes. It generally consists of a large amount of 3D coordinates of points describing reflective surfaces. A subtle problem is that the number of points is usually so large that real-time transmission and efficient storage is not feasible. In this work, we propose to use 3D Discrete Cosine Transform (3D-DCT) to compress these two typical categories of data, namely point-cloud data extracted from objects and environments (i.e. 3D maps). Experimental results show that the proposed method leads to high compression ratio and flexible reconstruction behaviors comparing with other related methods.

Analysis of Simply Supported Rectangular Kirchhoff Plates by the Finite Fourier Sine Transform Method

Abstract: In this work, the boundary value problem of simply supported rectangular Kirchhoff plates subjected to applied transverse loads is solved by the method of finite Fourier sine transform. The finite Fourier sine transform method was adopted as the analytical research tool due to the Dirchlet boundary conditions of the plate problem. Application of the finite Fourier sine transform to the fourth order governing partial differential equation of the Kirchhoff plate problem and the associated boundary conditions simplified the problem to an algebraic problem in the transform domain. The solution is obtained in the plate domain by inversion. The problem was solved for general distributed load p(x, y), point load applied at an arbitrary point on the plate, uniformly distributed patch load over the plate region x0 x  x1, y0 y  y1, and uniformly distributed load over the entire plate. The finite Fourier sine transform solutions obtained in each case were found to be identical solutions obtained with the Navier's double trigonometrical series method as presented in Timoshenko and Woinowsky-Krieger. The finite Fourier sine transform method was found to yield exact solutions to the classical thin plate flexure problem for simply supported edges.

A Low-Complexity Approach to Computation of the Discrete Fractional Fourier Transform

Abstract: This paper proposes an effective approach to the computation of the discrete fractional Fourier transform for an input vector of any length N. This approach uses specific structural properties of the discrete fractional Fourier transformation matrix. Thanks to these properties, the fractional Fourier transformation matrix can be decomposed into a sum of three or two matrices, one of which is a dense matrix, and the rest of the matrix components are sparse matrices. The aforementioned dense matrix has unique structural properties that allow advantageous factorization. This factorization is the main contributor to the reduction in the overall computational complexity of the discrete fractional Fourier transform computation. The remaining calculations do not contribute significantly to the total amount of computation. Thus, the proposed approach allows to reduce the number of arithmetic operations when calculating the discrete fractional Fourier transform.

Multi-Modal Medical Image Fusion using Multi-Resolution Discrete Sine Transform

Abstract: Quick advancement in high innovation and current medical instrumentations, medical imaging has turned into a fundamental part in many applications such as in diagnosis, research and treatment. Images from multimodal imaging devices usually provide complementary and sometime conflicting information. Information from one image may not be adequate to give exact clinical prerequisites to the specialist or doctor. Of-late, Multi-Model medical image fusion playing a challenging role in current research areas. There are many theories and techniques developed to fuse the multimodal images by researchers. In this paper, introducing a new algorithm called as Multi Resolution Discrete Sine Transform which is used for Multi-Model image fusion in medical applications. Performance and evaluation of this algorithm is presented. The main intention of this paper is to apply DST which is easy to understand and demonstrated method to process image fusion techniques. The proposed MDST based image fusion algorithm performance is compared with that of the well-known wavelet based image fusion algorithm. From the results it is observed that the performance of image fusion using MDST is almost similar to that of wavelet based image fusion algorithm. The proposed MDST based image fusion techniques are computationally very simple and it is suitable. The proposed MDST based image fusion algorithms are computationally, exceptionally basic and it is appropriate for real time medical diagnosis applications.

Matlab Code for the Discrete Hankel Transform

Abstract: Previous definitions of a Discrete Hankel Transform (DHT) have focused on methods to approximate the continuous Hankel integral transform without regard for the properties of the DHT itself. Recently, the theory of a Discrete Hankel Transform was proposed that follows the same path as the Discrete Fourier/Continuous Fourier transform. This DHT possesses orthogonality properties which lead to invertibility and also possesses the standard set of discrete shift, modulation, multiplication and convolution rules. The proposed DHT can be used to approximate the continuous forward and inverse Hankel transform. This paper describes the matlab code developed for the numerical calculation of this DHT.

The Sliding Windowed Infinite Fourier Transform [Tips & Tricks]

Abstract: The discrete Fourier transform (DFT) is the standard tool for spectral analysis in digital signal processing, typically computed using the fast Fourier transform (FFT). However, for real-time applications that require recalculating the DFT at each sample or over only a subset of the N center frequencies of the DFT, the FFT is far from optimal.

High-level synthesis implementation of HEVC 2-D DCT/DST on FPGA

Abstract: This paper presents the first known high-level synthesis (HLS) implementation of integer discrete cosine transform (DCT) and discrete sine transform (DST) for High Efficiency Video Coding (HEVC). The proposed approach implements these 2-D transforms by two successive 1-D transforms using a well-known row-column and Even-Odd decomposition techniques. Altogether, the proposed architecture is composed of a 4-point DCT/DST unit for the smallest transform blocks (TBs), an 8/16/32-point DCT unit for the other TBs, and a transpose memory for intermediate results. On Arria II FPGA, the low-cost variant of the proposed architecture is able to support encoding of 1080p format at 60 fps and at the cost of 10.0 kALUTs and 216 DSP blocks. The respective figures for the proposed high-speed variant are 2160p at 30 fps with 13.9 kALUTs and 344 DSP blocks. These cost-performance characteristics outperform respective non-HLS approaches on FPGA.

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.

DCT and DST Based Image Compression for 3D Reconstruction

Abstract: This paper introduces a new method for 2D image compression whose quality is demonstrated through accurate 3D reconstruction using structured light techniques and 3D reconstruction from multiple viewpoints. The method is based on two discrete transforms: (1) A one-dimensional Discrete Cosine Transform (DCT) is applied to each row of the image. (2) The output from the previous step is transformed again by a one-dimensional Discrete Sine Transform (DST), which is applied to each column of data generating new sets of high-frequency components followed by quantization of the higher frequencies. The output is then divided into two parts where the low-frequency components are compressed by arithmetic coding and the high frequency ones by an efficient minimization encoding algorithm. At decompression stage, a binary search algorithm is used to recover the original high frequency components. The technique is demonstrated by compressing 2D images up to 99% compression ratio. The decompressed images, which include images with structured light patterns for 3D reconstruction and from multiple viewpoints, are of high perceptual quality yielding accurate 3D reconstruction. Perceptual assessment and objective quality of compression are compared with JPEG and JPEG2000 through 2D and 3D RMSE. Results show that the proposed compression method is superior to both JPEG and JPEG2000 concerning 3D reconstruction, and with equivalent perceptual quality to JPEG2000.

A New Covariance Function and Spatio‐Temporal Prediction (Kriging) for A Stationary Spatio‐Temporal Random Process

Abstract: Consider a stationary spatio-temporal random process Yts;s∈Rd,t∈Z and let Ytsi;i=1,2,…,m;t=1,…,n be a sample from the process. Our object here is to predict, given the sample, Ytso for all t at the location so. To obtain the predictors, we define a sequence of discrete Fourier transforms Jsiωj;i=1,2,…,m using the observed time series. We consider these discrete Fourier transforms as a sample from the complex valued random variable Jsω. Assuming that the discrete Fourier transforms satisfy a complex stochastic partial differential equation of the Laplacian type with a scaling function that is a polynomial in the temporal spectral frequency ω, we obtain, in a closed form, expressions for the second-order spatio-temporal spectrum and the covariance function. The spectral density function obtained corresponds to a non-separable random process. The optimal predictor of the discrete Fourier transform Jsoω is in terms of the covariance functions. The estimation of the parameters of the spatio-temporal covariance function is considered and is based on the recently introduced frequency variogram method. The methods given here can be extended to situations where the observations are corrupted by independent white noise. The methods are illustrated with a real data set.

Comparison of Discrete Cosine Transforms (DCT), Discrete Fourier Transforms (DFT), and Discrete Wavelet Transforms (DWT) in Digital Image Watermarking

Abstract: Digital Image Watermarking is used recently to secure the image by embedding another digital image. It is typically used to identify ownership of the copyright of the signal. Frequency domain transformation methods used widely in Digital Image Compression and Digital Image Watermarking. They reduce the weakness of classics digital image watermarking such as Least Significant Bit (LSB) methods which is more noise-tolerant. Popular transformation method used are Two Dimensional Discrete Cosine Transform (2D DCT), Two Dimensional Discrete Fourier Transforms (2D DFT), and Two Dimensional Discrete Wavelet Transform (2D DWT). This paper will show the comparison result of those three transformation method. The experiments are comparison analysis of image watermark quality using Peak Signal to Noise Ratio (PSNR), color converting, image resizing, image optical scanning and the noise-tolerant of the image watermarked by giving Gaussian noise.

Cosine transforms over fields of characteristic 2: Fast computation and application to image encryption

Abstract: In this paper, we introduce a fast algorithm for computing cosine transforms over fields of characteristic 2 (FFCT). Such transforms, which were recently proposed in the literature, are analogous to real-valued discrete cosine transforms in the same sense in which the finite field Fourier transform (FFFT) is analogous to the discrete Fourier transform. The referred algorithm is based on fast algorithms for computing cyclic convolutions over fields of characteristic 2. In particular, we present an algorithm for an 8-point FFCT over GF(2 8 ) and show how such a transform can be used as the basis of an image encryption scheme. We highlight the advantages of this scheme compared to that based on cosine transforms over fields of odd characteristic and perform computer simulations to demonstrate its resistance against the main cryptographic attacks.

PAPR reduction for FBMC/OQAM using hybrid scheme of different Precoding transform and mu-law companding

Abstract: The filter banks multicarrier with offset quadrature amplitude modulation (FBMC/OQAM) is developing multicarrier modulation technique used in the next wireless communication system (5G). FBMC/OQAM supports high data rate and high band width efficiency. However, one of the major drawbacks of FBMC system is high peak to Average Power Ratio (PAPR) of the transmitted signal, which causes serious degradation in performance of the system. Therefore, it is required to use a proper PAPR scheme at the transmitter to reduce the PAPR. In this paper, a hybrid scheme is investigated with the combination of preceding transform technique and Mu Law Companding technique to reduce PAPR in FBMC systems. Moreover, four preceding techniques are examined to find the best Precoding technique which can be used with Mu law commanding. We assessed the discrete Hartley transform (DHT). The discrete cosine transformed (DCT), the Discrete Sine Transform (DST), and the Walsh Hadamard transforms (WHT) which are applied separately with Mu Companding. The numerical results verify that the FBMC systems with all Precoding technique combined with Mu law commanding can improve PAPR performance of the signals greatly with the best results achieved when the combination scheme consists of the DST Precoding and Mu law commanding for both PAPR and BER performance.

A reversible watermarking algorithm for high efficiency video coding

Abstract: In order to eliminate the error propagation causes by embedding watermark in intra frames, a reversible watermarking algorithm without error propagation for high efficiency video coding (HEVC) is proposed. Firstly, it selects the embedding regions in 4×4 luminance prediction unit (PU) to identify whether it is texture block for low bit rate increasing. Then it uses a novel module for eliminating the error propagation, in which the watermark is embedded in 4×4 quantized discrete sine transform (QDST) coefficients blocks. Lastly, the method of sum invariability is used to embed adaptively watermark in the 4×4 QDST coefficient. The simulation results show that the algorithm has little influence on bit rate and can be well eliminate the error propagation.

All Phase Inverse Discrete Sine Biorthogonal Transform and Its Application in Image Coding

Abstract: —To improve the coding performance in JPEG image compression and reduce the computational complexity, this paper proposes a new transform called All Phase Inverse Discrete Sine Biorthogonal Transform (APIDSBT) based on the All Phase Biorthogonal Transform (APBT) and Inverse Discrete Sine Transform (IDST). Similar to Discrete Sine Transform (DST) matrix and Discrete Cosine Transform (DCT) matrix, it can be used in image compression which transforms the image from spatial domain to frequency domain. Compared with other transforms in JPEG-like image compression algorithm, the Peak Signal-to-Noise Ratio (PSNR) and subjective effects of the reconstructed images using the proposed transform and image coding scheme are better at the same bit rates, especially at low bit rates. The advantage is that the quantization process is simpler and the computational complexity is lower.

Comb-assisted real-time Discrete Fourier Transform processor

Abstract: We present a high-speed flexible photonic-assisted Discrete Fourier Transform (DFT) processor based on a dual, phase-locked optical parametric combs. A 25-point DFT at 500 Million-DFT-point per second throughput is achieved relying on slow, 20 MS/s Analog to Digital Converter (ADC).

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.

A novel frequency estimation algorithm based on DFT and second derivative

Abstract: In this paper, a novel frequency estimation algorithm based on discrete Fourier transform (DFT) and second derivative is proposed. The proposed algorithm consists of three stages, namely, DFT, second derivative, and frequency estimation. First, the input signal is decomposed using DFT into two orthogonal components, the real and imaginary parts. In other words, the signal is filtered with cosine and sine filters. Secondly, the second derivatives of the two orthogonal components are obtained by numerical approximation. Because this step can cause an error, the central difference approximation for five-point second derivative is used for error reduction. Finally, the two orthogonal components and their second derivatives are combined to estimate the power frequency considering a zero-crossing problem and the gains of finite impulse response (FIR) filters. The performance of the proposed algorithm is evaluated considering frequency changes when generating the test signals. Besides, a dynamic conditio...

Single Bin Sliding Discrete Fourier Transform

Abstract: The conventional method for spectrum analysis is the discrete Fourier transform (DFT), usually implemented using a fast Fourier transform (FFT) algorithm. However, certain applications require an online spectrum analysis only on a subset ofM frequencies of an N-point DFT ðM < NÞ. In such cases, the use of single-bin sliding DFT (Sb-SDFT) is preferred over the direct application of FFT. The purpose of this chapter is to provide a concise overview of the Sb-SDFT algorithms, analyze their performance, and highlight advantages and limitations. Finally, a technique to mitigate the spectral leakage effect, which arises when using the Sb-SDFT in nonstationary conditions, is presented.

High-level synthesized 2-D IDCT/IDST implementation for HEVC codecs on FPGA

Abstract: This paper presents efficient inverse discrete cosine transform (IDCT) and inverse discrete sine transform (IDST) implementations for High Efficiency Video Coding (HEVC). The proposal makes use of high-level synthesis (HLS) to implement a complete HEVC 2-D IDCT/IDST architecture directly from the C code of a well-known Even-Odd decomposition algorithm. The final architecture includes a 4-point IDCT/IDST unit for the smallest transform blocks (TB), an 8/16/32-point IDCT unit for the other TBs, and a transpose memory for intermediate results. On Arria II FPGA, it supports real-time (60 fps) HEVC decoding of up to 2160p format with 12.4 kALUTs and 344 DSP blocks. Compared with the other existing HLS approach, the proposed solution is almost 5 times faster and is able to utilize available FPGA resources better.