A DCT Approximation for Image Compression

An orthogonal approximation for the 8-point discrete cosine transform (DCT) is introduced. The proposed transformation matrix contains only zeros and ones; multiplications and bit-shift operations are absent. Close spectral behavior relative to the DCT was adopted as design criterion. The proposed algorithm is superior to the signed discrete cosine transform. It could also outperform state-of-the-art algorithms in low and high image compression scenarios, exhibiting at the same time a comparable computational complexity.Comment: 10 pages, 6 figure

The Arithmetic Cosine Transform: Exact and Approximate Algorithms

In this paper, we introduce a new class of transform method --- the arithmetic cosine transform (ACT). We provide the central mathematical properties of the ACT, necessary in designing efficient and accurate implementations of the new transform method. The key mathematical tools used in the paper come from analytic number theory, in particular the properties of the Riemann zeta function. Additionally, we demonstrate that an exact signal interpolation is achievable for any block-length. Approximate calculations were also considered. The numerical examples provided show the potential of the ACT for various digital signal processing applications.Comment: 17 pages, 3 figure

An Extension of the Dirichlet Density for Sets of Gaussian Integers

Several measures for the density of sets of integers have been proposed, such as the asymptotic density, the Schnirelmann density, and the Dirichlet density. There has been some work in the literature on extending some of these concepts of density to higher dimensional sets of integers. In this work, we propose an extension of the Dirichlet density for sets of Gaussian integers and investigate some of its properties.Comment: 13 pages, 1 figur

Robust Image Watermarking Using Non-Regular Wavelets

An approach to watermarking digital images using non-regular wavelets is advanced. Non-regular transforms spread the energy in the transform domain. The proposed method leads at the same time to increased image quality and increased robustness with respect to lossy compression. The approach provides robust watermarking by suitably creating watermarked messages that have energy compaction and frequency spreading. Our experimental results show that the application of non-regular wavelets, instead of regular ones, can furnish a superior robust watermarking scheme. The generated watermarked data is more immune against non-intentional JPEG and JPEG2000 attacks.Comment: 13 pages, 11 figure

A New Information Theoretical Concept: Information-Weighted Heavy-tailed Distributions

Given an arbitrary continuous probability density function, it is introduced a conjugated probability density, which is defined through the Shannon information associated with its cumulative distribution function. These new densities are computed from a number of standard distributions, including uniform, normal, exponential, Pareto, logistic, Kumaraswamy, Rayleigh, Cauchy, Weibull, and Maxwell-Boltzmann. The case of joint information-weighted probability distribution is assessed. An additive property is derived in the case of independent variables. One-sided and two-sided information-weighting are considered. The asymptotic behavior of the tail of the new distributions is examined. It is proved that all probability densities proposed here define heavy-tailed distributions. It is shown that the weighting of distributions regularly varying with extreme-value index $\alpha > 0$ still results in a regular variation distribution with the same index. This approach can be particularly valuable in applications where the tails of the distribution play a major role.Comment: 21 pages, 7 figure

A Class of DCT Approximations Based on the Feig-Winograd Algorithm

A new class of matrices based on a parametrization of the Feig-Winograd factorization of 8-point DCT is proposed. Such parametrization induces a matrix subspace, which unifies a number of existing methods for DCT approximation. By solving a comprehensive multicriteria optimization problem, we identified several new DCT approximations. Obtained solutions were sought to possess the following properties: (i) low multiplierless computational complexity, (ii) orthogonality or near orthogonality, (iii) low complexity invertibility, and (iv) close proximity and performance to the exact DCT. Proposed approximations were submitted to assessment in terms of proximity to the DCT, coding performance, and suitability for image compression. Considering Pareto efficiency, particular new proposed approximations could outperform various existing methods archived in literature.Comment: 26 pages, 4 figures, 5 tables, fixed arithmetic complexity in Table I

Low-complexity 8-point DCT Approximations Based on Integer Functions

In this paper, we propose a collection of approximations for the 8-point discrete cosine transform (DCT) based on integer functions. Approximations could be systematically obtained and several existing approximations were identified as particular cases. Obtained approximations were compared with the DCT and assessed in the context of JPEG-like image compression.Comment: 21 pages, 4 figures, corrected typo

The Fourier-Like and Hartley-Like Wavelet Analysis Based on Hilbert Transforms

In continuous-time wavelet analysis, most wavelet present some kind of symmetry. Based on the Fourier and Hartley transform kernels, a new wavelet multiresolution analysis is proposed. This approach is based on a pair of orthogonal wavelet functions and is named as the Fourier-Like and Hartley-Like wavelet analysis. A Hilbert transform analysis on the wavelet theory is also included.Comment: 7 pages, 10 figures, Anais do XXII Simp\'osio Brasileiro de Telecomunica\c{c}\~oes, Campinas, 200

An Integer Approximation Method for Discrete Sinusoidal Transforms

Approximate methods have been considered as a means to the evaluation of discrete transforms. In this work, we propose and analyze a class of integer transforms for the discrete Fourier, Hartley, and cosine transforms (DFT, DHT, and DCT), based on simple dyadic rational approximation methods. The introduced method is general, applicable to several block-lengths, whereas existing approaches are usually dedicated to specific transform sizes. The suggested approximate transforms enjoy low multiplicative complexity and the orthogonality property is achievable via matrix polar decomposition. We show that the obtained transforms are competitive with archived methods in literature. New 8-point square wave approximate transforms for the DFT, DHT, and DCT are also introduced as particular cases of the introduced methodology.Comment: 13 pages, 5 figures, 8 table

A Generalized Prefix Construction for OFDM Systems Over Quasi-Static Channels

All practical OFDM systems require a prefix to eliminate inter-symbol interference at the receiver. Cyclic prefix (CP) and zero-padding are well-known prefix construction methods, the former being the most employed technique in practice due to its lower complexity. In this paper we construct an OFDM system with a generalized CP. It is shown that the proposed generalized prefix effectively makes the channel experienced by the packet different from the actual channel. Using an optimization procedure, lower bit error rates can be achieved, outperforming other prefix construction techniques. At the same time the complexity of the technique is comparable to the CP method. The presented simulation results show that the proposed technique not only outperforms the CP method, but is also more robust in the presence of channel estimation errors and mobility. The proposed method is appropriate for practical OFDM systems.Comment: 19 page