Showing papers on "Discrete sine transform published in 2012"

Jointly Optimized Spatial Prediction and Block Transform for Video and Image Coding

Abstract: This paper proposes a novel approach to jointly optimize spatial prediction and the choice of the subsequent transform in video and image compression. Under the assumption of a separable first-order Gauss-Markov model for the image signal, it is shown that the optimal Karhunen-Loeve Transform, given available partial boundary information, is well approximated by a close relative of the discrete sine transform (DST), with basis vectors that tend to vanish at the known boundary and maximize energy at the unknown boundary. The overall intraframe coding scheme thus switches between this variant of the DST named asymmetric DST (ADST), and traditional discrete cosine transform (DCT), depending on prediction direction and boundary information. The ADST is first compared with DCT in terms of coding gain under ideal model conditions and is demonstrated to provide significantly improved compression efficiency. The proposed adaptive prediction and transform scheme is then implemented within the H.264/AVC intra-mode framework and is experimentally shown to significantly outperform the standard intra coding mode. As an added benefit, it achieves substantial reduction in blocking artifacts due to the fact that the transform now adapts to the statistics of block edges. An integer version of this ADST is also proposed.

Introduction to Orthogonal Transforms: With Applications in Data Processing and Analysis

Abstract: A systematic, unified treatment of orthogonal transform methods for signal processing, data analysis and communications, this book guides the reader from mathematical theory to problem solving in practice. It examines each transform method in depth, emphasizing the common mathematical principles and essential properties of each method in terms of signal decorrelation and energy compaction. The different forms of Fourier transform, as well as the Laplace, Z-, Walsh–Hadamard, Slant, Haar, Karhunen–Loeve and wavelet transforms, are all covered, with discussion of how each transform method can be applied to real-world experimental problems. Numerous practical examples and end-of-chapter problems, supported by online Matlab and C code and an instructor-only solutions manual, make this an ideal resource for students and practitioners alike.

DCT-like transform for image compression requires 14 additions only

Abstract: A low-complexity 8-point orthogonal approximate discrete cosine transform (DCT) is introduced. The proposed transform requires no multiplications or bit-shift operations. The derived fast algorithm requires only 14 additions, less than any existing DCT approximation. Moreover, in several image compression scenarios, the proposed transform could outperform the well-known signed DCT, as well as state-of the-art algorithms.

Mode-Dependent Transforms for Coding Directional Intra Prediction Residuals

Abstract: The use of mode-dependent transforms for coding directional intra prediction residuals has been previously shown to provide coding gains, but the transform matrices have to be derived from training. In this paper, we derive a set of separable mode-dependent transforms by using a simple separable, directional, and anisotropic image correlation model. Our analysis shows that only one additional transform, the odd type-3 discrete sine transform (ODST-3), is required for the optimal implementation of mode-dependent transforms. In addition, the four-point ODST-3 also has a structure that can be exploited to reduce the operation count of the transform operation. Experimental results show that in terms of coding efficiency, our proposed approach matches or improves upon the performance of a mode-dependent transforms approach that uses transform matrices obtained through training.

Shift-Invariant and Sampling Spaces Associated With the Fractional Fourier Transform Domain

Abstract: Shift-invariant spaces play an important role in sampling theory, multiresolution analysis, and many other areas of signal and image processing. A special class of the shift-invariant spaces is the class of sampling spaces in which functions are determined by their values on a discrete set of points. One of the vital tools used in the study of sampling spaces is the Zak transform. The Zak transform is also related to the Poisson summation formula and a common thread between all these notions is the Fourier transform. In this paper, we extend some of these notions to the fractional Fourier transform (FrFT) domain. First, we introduce two definitions of the discrete fractional Fourier transform and two semi-discrete fractional convolutions associated with them. We employ these definitions to derive necessary and sufficient conditions pertaining to FrFT domain, under which integer shifts of a function form an orthogonal basis or a Riesz basis for a shift-invariant space. We also introduce the fractional Zak transform and derive two different versions of the Poisson summation formula for the FrFT. These extensions are used to obtain new results concerning sampling spaces, to derive the reproducing-kernel for the spaces of fractional band-limited signals, and to obtain a new simple proof of the sampling theorem for signals in that space. Finally, we present an application of our shift-invariant signal model which is linked with the problem of fractional delay filtering.

Fast computing of discrete cosine and sine transforms of types vi and vii

Abstract: This disclosure presents techniques for implementing a fast algorithm for implementing odd-type DCTs and DSTs. The techniques include the computation of an odd-type transform on any real-valued sequence of data (e.g., residual values in a video coding process or a block of pixel values of an image coding process) by mapping the odd-type transform to a discrete Fourier transform (DFT). The techniques include a mapping between the real-valued data sequence to an intermediate sequence to be used as an input to a DFT. Using this intermediate sequence, an odd-type transform may be achieved by calculating a DFT of odd size. Fast algorithms for a DFT may be then be used, and as such, the odd-type transform may be calculated in a fast manner

A Bijective String Sorting Transform

Abstract: Given a string of characters, the Burrows-Wheeler Transform rearranges the characters in it so as to produce another string of the same length which is more amenable to compression techniques such as move to front, run-length encoding, and entropy encoders. We present a variant of the transform which gives rise to similar or better compression value, but, unlike the original, the transform we present is bijective, in that the inverse transformation exists for all strings. Our experiments indicate that using our variant of the transform gives rise to better compression ratio than the original Burrows-Wheeler transform. We also show that both the transform and its inverse can be computed in linear time and consuming linear storage.

Discrete sine transform for multi-scale realized volatility measures

Abstract: In this study we present a new realized volatility estimator based on a combination of the multi-scale regression and discrete sine transform (DST) approaches. Multi-scale estimators similar to that recently proposed by Zhang (2006) can, in fact, be constructed within a simple regression-based approach by exploiting the linear relation existing between the market microstructure bias and the realized volatilities computed at different frequencies. We show how such a powerful multi-scale regression approach can also be applied in the context of the Zhou [Nonlinear Modelling of High Frequency Financial Time Series, pp. 109–123, 1998] or DST orthogonalization of the observed tick-by-tick returns. Providing a natural orthonormal basis decomposition of observed returns, the DST permits the optimal disentanglement of the volatility signal of the underlying price process from the market microstructure noise. The robustness of the DST approach with respect to the more general dependent structure of the microstruct...

Robust Digital image Watermarking Algorithm in DWT-DFT-SVD domain for color images

Abstract: This paper proposes a Digital Watermarking Algorithm using a unique combination of Discrete Wavelet Transform (DWT), Discrete Fourier Transform (DFT) and Singular Value Decomposition (SVD) for secured transmission of data through watermarking digital color images. The singular values obtained from SVD of DWT+DFT transformed watermark is embedded onto the singular values obtained from SVD of DWT+DFT transformed color image. Experimental results show the promising performance of the proposed algorithm for watermarking. Peak Signal to Noise Ratio (PSNR) values for the watermarked image in the range of 65 to 85 dB and maximum correlation of 0.9998 are achieved.

The Wavelet Transform for Image Processing Applications

Abstract: In recent years, the wavelet transform emerged in the field of image/signal processing as an alternative to the well-known Fourier Transform (FT) and its related transforms, namely, the Discrete Cosine Transform (DCT) and the Discrete Sine Transform (DST). In the Fourier theory, a signal (an image is considered as a finite 2-D signal) is expressed as a sum, theoretically infinite, of sines and cosines, making the FT suitable for infinite and periodic signal analysis. For several years, the FT dominated the field of signal processing, however, if it succeeded well in providing the frequency information contained in the analysed signal; it failed to give any information about the occurrence time. This shortcoming, but not the only one, motivated the scientists to scrutinise the transform horizon for a “messiah” transform. The first step in this long research journey was to cut the signal of interest in several parts and then to analyse each part separately. The idea at a first glance seemed to be very promising since it allowed the extraction of time information and the localisation of different frequency components. This approach is known as the Short-Time Fourier Transform (STFT). The fundamental question, which arises here, is how to cut the signal? The best solution to this dilemma was of course to find a fully scalable modulated window in which no signal cutting is needed anymore. This goal was achieved successfully by the use of the wavelet transform.

A multiplication-free digital architecture for 16×16 2-D DCT/DST transform for HEVC

Abstract: The discrete cosine transform (DCT) is widely employed in image and video coding applications due to its high energy compaction. In addition to 4×4 and 8×8 transforms utilized in earlier video coding standards, the proposed HEVC standard suggests the use of larger transform sizes including 16 × 16 and 32×32 transforms in order to obtain higher coding gains. Further, it also proposes the use of non-square transform sizes as well as the use of the discrete sine transform (DST) in certain intra-prediction modes. The decision on the type of transform used in a given prediction scenario is dynamically made, to obtain required compression rates. This motivated the proposed digital VLSI architecture for a multitransform engine capable of computing 16×16 approximate 2-D DCT/DST transform, with null multiplicative complexity. The relationship between DCT-II and DST-II is employed to compute both transforms using the same digital core, leading to reductions in both area and power. Closed-form relationship between the 16×16 transform and arbitrary smaller sized transform is presented, enabling the usability of this architecture to compute transforms of size 4 · 2P × 4 · 2q where 0 ≤ p, q ≤ 2.

The Discrete Yang-Fourier Transforms in Fractal Space

Abstract: The Yang-Fourier transform (YFT) in fractal space is a generation of Fourier transform based on the local fractional calculus. The discrete Yang-Fourier transform (DYFT) is a specific kind of the approximation of discrete transform, used in Yang- Fourier transform in fractal space. This paper points out new standard forms of discrete Yang-Fourier transforms (DYFT) of fractal signals, and both properties and theorems are investigated in detail. Keywords -Fractal, Signal, Discrete, Yang-Fourier transforms

Noise Power Estimation by the Three-Parameter and Four-Parameter Sine-Fit Algorithms

Abstract: This paper analyzes the performance provided by the three-parameter sine-fit (3PSF) and the four-parameter sine-fit (4PSF) algorithms when estimating the noise power of a sine wave corrupted by a white Gaussian noise. In the former case, the frequency parameter is extracted from the available data by using the interpolated discrete Fourier transform (IpDFT) method. The related procedure is called the 3PSF-IpDFT algorithm. Simple expressions for the expected sum-squared fitting and the expected sum-squared residual errors are derived for both the 3PSF and 4PSF algorithms, which agree with previously published results. These expressions show that the sum-squared fitting error of the 4PSF algorithm is smaller than the corresponding value associated with the 3PSF algorithm when the uncertainty of the sine-wave frequency employed by the latter algorithm is greater than the related Cramer-Rao lower bound. From this point of view, the 4PSF algorithm outperforms the 3PSF-IpDFT algorithm. However, since the frequency estimator provided by the IpDFT method is consistent, the sum-squared fitting error associated with both the 3PSF-IpDFT and 4PSF algorithms can be made negligible as compared with the sum-squared residual errors, when the number of analyzed samples is large enough. Moreover, several simulation results show that the 3PSF-IpDFT algorithm requires a much lower computational effort than the 4PSF algorithm. Therefore, it represents the best alternative when estimating the noise power of a sine wave embedded in white noise.

A new transform method in nabla discrete fractional calculus

Abstract: Starting from the definition of the Sumudu transform on a general nabla time scale, we define the generalized nabla discrete Sumudu transform. We obtain the nabla discrete Sumudu transform of Taylor monomials, fractional sums, and differences. We apply this transform to solve some fractional difference equations with initial value problems.

Optical OFDM based on the fractional Fourier transform

Abstract: We describe a innovative OFDM scheme based on orthogonal chirped subcarriers, that corresponds to the fractional Fourier transform (FrFT) of the input signal. The FrFT can be electronically implemented with a complexity equivalent to the conventional fast Fourier transform (FFT); on the other hand, the planar device that implements the FrFT in the optical domain is similar to the passive arrayed waveguide grating (AWG) device that performs the FFT. We analyze the spectral efficiency, the peak-to-average power ratio (PAPR) and the frequency offset sensitivity of a FrFT-based optical OFDM system, and make an accurate comparison with the standard FFT-based implementation.

On Sumudu Transform Method in Discrete Fractional Calculus

Abstract: In this paper, starting from the definition of the Sumudu transform on a general time scale, we define the generalized discrete Sumudu transform and present some of its basic properties. We obtain the discrete Sumudu transform of Taylor monomials, fractional sums, and fractional differences. We apply this transform to solve some fractional difference initial value problems.

Video and data processing using even-odd integer transforms

Abstract: Methods, apparatuses and systems for integer transforms, and/or integer transform operations, for transforming data (e.g., residual video data) are disclosed. Included among such methods, apparatuses and systems is an apparatus that may include a processor and memory. The memory may include a set of transform matrices and instructions executable by the processor for transforming data (e.g., residual video data) using any of the set of transform matrices. Each transform matrix of the set of transform matrices may be orthogonal or, alternatively, may be approximately orthogonal and be fully factorizable. Each transform matrix of the set of transform matrices may have a different number of elements. Each element of the respective number of elements is an integer. Differences among norms of basis vectors of each transform matrix satisfy a given threshold, and the basis vectors approximate corresponding basis vectors of a discrete cosine transform (DCT) matrix.

Discrete singular operators and equations in half-space (pp. 84-93)

Abstract: Discrete multidimensional singular integral equations with Calderon–Zygmund kernels are considered in a discrete half-space. The solvability of such equations is studied using the properties of discrete Fourier transform and corresponding properties of Calderon–Zygmund operators.

A New Formulation of the Fast Fractional Fourier Transform

Abstract: By using a spectral approach, we derive a Gaussian-like quadrature of the continuous fractional Fourier transform. The quadrature is obtained from a bilinear form of eigenvectors of the matrix associated to the recurrence equation of the Hermite polynomials. These eigenvectors are discrete approximations of the Hermite functions, which are eigenfunctions of the fractional Fourier transform operator. This new discrete transform is unitary and has a group structure. By using some asymptotic formulas, we rewrite the quadrature in terms of the fast Fourier transform (FFT), yielding a fast discretization of the fractional Fourier transform and its inverse in closed form. We extend the range of the fractional Fourier transform by considering arbitrary complex values inside the unit circle and not only at the boundary. We find that this fast quadrature evaluated at $z=i$ becomes a more accurate version of the FFT and can be used for nonperiodic functions.

Algorithms for transform selection in multiple-transform video compression

Abstract: With a proper transform, an image or motion-compensated residual can be represented quite accurately with a small fraction of the transform coefficients. This is referred to as the energy compaction property. When multiple block transforms are used, selecting the best transform for each block that leads to the best energy compaction is difficult. In this paper, we develop two algorithms to solve this problem. The first algorithm, which is computationally simple, leads to a locally optimal solution. The second algorithm, which is more computationally intensive, gives a globally optimal solution. We discuss the algorithms and their performances. Two-dimensional discrete cosine transform (2-D DCT) and direction-adaptive one-dimensional discrete cosine transforms (1-D DCTs) are used to evaluate the performance of our algorithms. Results obtained are consistent with those from previous research.

Dft-based channel estimation systems and methods

Abstract: DFT-based channel estimation methods and systems are disclosed. One system includes an inverse discrete Fourier transform module, a noise power estimator, a noise filter and a discrete Fourier transform module. The inverse discrete Fourier transform module is configured to determine time domain estimates by applying an inverse discrete Fourier transform to initial channel estimates computed from pilot signals. Additionally, the noise power estimator is configured to estimate noise power by determining and utilizing time domain samples that are within a vicinity of sinc nulls of the time domain estimates. The noise filter is configured to filter noise from the time domain estimates based on the estimated noise power to obtain noise filtered time domain estimates. Further, the discrete Fourier transform module is configured to perform a discrete Fourier transform on the noise filtered time domain estimates to obtain frequency domain channel estimates for channels on which pilot signals are transmitted.

Fast Yang-Fourier Transforms in Fractal Space

Abstract: The Yang-Fourier transform (YFT) in fractal space is a generation of Fourier transform based on the local fractional calculus. The discrete Yang-Fourier transform (DYFT) is a specific kind of the approximation of discrete transform based on the Yang-Fourier transform in fractal space. In the present letter we point out a new fractal model for the algorithm for fast Yang-Fourier transforms of discrete Yang-Fourier transforms. It is shown that the classical fast Fourier transforms is a special example in fractal dimension 1   .

Speech Compression Using Discrete Wavelet Transform and Discrete Cosine Transform

Abstract: Aim of this paper is to explain and implement transform based speech compression techniques. Transform coding is based on compressing signal by removing redundancies present in it. Speech compression (coding) is a technique to transform speech signal into compact format such that speech signal can be transmitted and stored with reduced bandwidth and storage space respectively .Objective of speech compression is to enhance transmission and storage capacity. In this paper Discrete wavelet transform and Discrete cosine transform based speech compression techniques are implemented with Run length encoding, Huffman encoding and Run length encoding followed by Huffman encoding. Reconstructed speech obtained from implementation are compared on the basis of Compression Factor(CF), Signal to noise ratio (SNR), Peak signal to noise ratio (PSNR), Normalized root mean square error (NRMSE), Retained signal energy (RSE). Results shows that Discrete wavelet transform with RUN length encoding followed by Huffman encoding gives higher compression with intelligible reconstructed speech.

A Family of Fast Hadamard–Fourier Transform Algorithms

Abstract: In this letter, we present a family of fast Hadamard-Fourier transform algorithms which combined Walsh Hadamard and discrete Fourier transforms into one single algorithm These family algorithms can be computed in butterfly structure, and have similar sparse matrix factorization in each stage, and have less computation stages than the sum of Walsh Hadamard and discrete Fourier transforms We factorize the algorithms with regular sparse matrices for every stage in radix-R mode, where R is power of 2

An Integral Transform and Its Applications in Parameter Estimation of LFM Signals

Abstract: This paper proposes a new transform called simplified linear canonical transform (SLCT) that provides a new method for parameter estimation of linear frequency-modulated (LFM) chirp signals embedded in additive white Gaussian noise. The proposed transform is a linear transform and has a more succinct form as compared with the fractional Fourier transform (FRFT). The discrete SLCT with fast Fourier transform (FFT) algorithm provides a computationally fast choice for LFM signal detection or parameter estimation. Using SLCT and a clean technique, all the components of Multi-LFM signals can be estimated seriatim. Simulations illustrate that the proposed algorithm is more effective than existing ones.

Real-time motion detection based on Discrete Cosine Transform

Abstract: We present a motion detection algorithm by a change detection filter matrix derived from Discrete Cosine Transform. Recently, a Fourier reconstruction scheme shows good results for motion detection. However, its computational cost is a major drawback. We revisit the problem and achieve two orders of magnitude faster than the previous algorithm with better performance. The proposed algorithm runs at about 800 frames per second for VGA resolution images on a consumer hardware by using only integer matrix multiplication and the symmetric property of the change detection filter matrix. In addition, our algorithm is fundamentally robust to sudden illumination changes because it works based on edge information. We verify our algorithm with challenging datasets that contain strong and sudden illumination changes.