Non-orthogonal Domain Research Articles

An adaptive steganography insertion technique based on wavelet transform

Over the past few decades, there have been several successful methods developed for steganography. One popular technique is the insertion method, which is favored for its simplicity and ability to hold a reasonable amount of hidden data. This study introduces an adaptive insertion technique based on the two-dimensional discrete Haar filter (2D DHF). The technique involves transforming the cover image into the wavelet domain using 2D DWT and selecting a predetermined number of coefficients to embed the binary secret message. The selection process is carried out by analyzing the cover image in two non-orthogonal domains: 2D discrete cosine transform and 2D DHF. An adaptive algorithm is employed to minimize the impact on the unrepresented parts of the cover image. The algorithm determines the weights of each coefficient in each domain, and coefficients with low weights are chosen for embedding. To evaluate the effectiveness of the proposed approach, samples from the BOSSbase and custom databases are used. The technique’s performance is measured using three metrics: mean squared error (MSE), peak signal-to-noise ratio (PSNR), and structural similarity index (SSIM). Additionally, a visual inspection by humans is conducted to assess the resulting image. The results demonstrate that the proposed approach outperforms recently reported methods in terms of MSE, PSNR, SSIM, and visual quality.

0161 Structural Changes in Mood Domains During Sleep Deprivation and Recovery

Abstract Introduction Mood is known to vary as a function of sleep debt. Mood batteries often measure multiple, non-orthogonal domains. In the present study, the latent structure of the Automated Neuropsychological Assessment Metrics Mood (ANAM-mood) battery was assessed during five different states of alertness. We present a novel scheme to evaluate changes in the structure of such batteries across conditions. It was hypothesized that the structure would change, with the greatest changes manifest during sleep deprivation. Methods The present analyses were conducted on data from a prior sleep deprivation study (n = 25 healthy young adults). We used the identity property of MANOVA. Given correlation matrices Σi and Σj, structural invariance was defined as Σi Σj-1 ≈ I (Identity). MANOVA statistic m was the largest eigenvalue of Σi Σj-1. Resampling was used to generate m-distributions within and between the five different alertness conditions - Rested, Sleep Deprived (SD) days 1 and 2, and Recovery days 1 and 2. In addition, the relative number of mood dimensions was estimated by the odds (via resampling) of two dimensions explaining 80% of the variance of Σi compared to Σj. Results The pairwise MANOVA-statistic revealed significant structural variations across conditions (p< 0.001 for all comparisons). Significant differences included Rested vs SD1 and SD2. Recovery 1 showed the most pronounced differences to all conditions. Recovery 2 was like Recovery 1, but more like Rested than the prior day. The odds ratio of two-dimensions for Recovery 1 was much higher compared to all other conditions (OR: 2.4-245, p< 0.001). Conclusion Individuals respond differently to a mood survey across specific alertness conditions resulting in structural changes to the data. Wakefulness during recovery from severe sleep loss differs most significantly from all states, contrary to our hypothesis. This is important to consider when interpreting mood changes as measured by such batteries (including related Spielberger's State Anxiety Inventory and Beck Depression Inventory-II) during sleep studies. Follow up studies are needed to fully assess such effects and devise methods to account for them. Support (if any) This effort was fully supported by the Department of Defense Military Operational Medicine Research Program (MOMRP).

Two‐stage frequency‐domain oversampling receivers for cyclic prefix orthogonal frequency‐division multiplexing systems

Orthogonal frequency-division multiplexing (OFDM) is a widely adopted technique in most wireless applications. It has been shown that zero padded OFDM (ZP-OFDM) with frequency-domain oversampling (FDO) can exhibit better performance than cyclic prefix OFDM (CP-OFDM) if the whole OFDM symbol is oversampled in the frequency domain. In this study, the authors propose a novel FDO-based scheme for CP-OFDM, which consists of two stages. First, the conventional CP-OFDM receiver is adopted to estimate the transmitted data and channel information. Second, the received symbol is reconstructed to reduce inter-symbol interference and oversampled in the frequency domain. The proposed scheme combines FDO and symbol reconstruction together, which enables the minimum mean square error (MMSE) and zero forcing (ZF) equalisers to exploit the channel information in high-dimensional non-orthogonal subcarrier domain and thus significantly suppress the interference on multipath channels. Simulation results show that the proposed FDO-MMSE CP-OFDM receiver can achieve much better bit error rate performance than the traditional CP-OFDM receiver and is comparable to the ZP-OFDM receiver with FDO.

Numerical Simulation of Reactive Fluid Flow on Unstructured Meshes

Reactive transport simulation on unstructured meshes can provide fundamental insight into the effect that geometric complexity of geologic structures has on fluid flow and development of reaction fronts. When applied to conditions ranging from ambient to hydrothermal and combined with compressible flow, accounting for geometric complexity provides an advantage for applications such as enhanced geothermal systems, carbon dioxide sequestration, hydrothermal ore formation, and radioactive waste disposal. We introduce CSMP–GEMS, a thermo–hydro and chemical multicomponent reactive transport code based on coupling of the Complex System Modeling Platform (CSMP) transport modeling framework with the GEMS3K chemical speciation solver. GEMS3K features a comprehensive suite of non-ideal activity and equation-of-state models of solution phases (aqueous electrolyte, gas and fluid mixtures, solid solutions). Current features include transient, compressible, single-phase advective and/or dispersive fluid flow, mass transport, heat transport in saturated porous media, and geochemical reactions in subsurface hydrothermal systems. We present two one-dimensional numerical experiments to compare CSMP–GEMS with the reactive transport codes OpenGeoSys–GEM and TOUGHREACT. Each experiment simulates calcite dissolution and dolomite precipitation during advection and hydrodynamic dispersion. One experiment corresponds to an existing isothermal $$(25\,^{\circ }\mathrm{C})$$ benchmark; the second explores the applicability of the codes to non-isothermal problems. We also present a two-dimensional example that illustrates the application of CSMP–GEMS on unstructured meshes that can represent complex geologic relations. The results suggest that all three codes are well suited to predicting fluid circulation, heat transport, and mineral stability within hydrothermal systems relevant to enhanced geothermal systems and carbon dioxide sequestration in deep aquifers. Self-consistent accounting for kinetic processes is a major advantage of TOUGHREACT, but published applications are restricted to orthogonal meshes, potentially limiting the applicability of TOUGHREACT to geometrically less complex natural systems. OpenGeoSys–GEM can operate on unstructured meshes that may include multiple element types, facilitating the examination of non-orthogonal domains. However, due to its reliance on the groundwater equations, OpenGeoSys–GEM may be best suited for application to systems in which flow includes dispersion/diffusion and is not compressible. CSMP–GEMS does not currently calculate reaction kinetics, but may be useful for application to geometrically complex systems.

A Collocated Grid Based Finite Volume Approach for the Visualization of Heat Transport in 2D Complex Geometries

The present study aim in developing an algorithm for the analysis of thermal transport in two dimensional complex domains. The integral form of the governing equations are discretized using the finite - volume method. The resulting governing equations are solved using Gauss- Seidel iterative method. In this study initially a code has been developed to read the mesh of different complex geometries from commercial meshing software. Later the data pertaining to mesh has been given as input to the numerical code developed for the visualization of thermal transport in these complex geometries. The collocated grid approach has been used to solve the non-orthogonal domains. The results obtained is validated and compared with the commercial software Ansys fluent. Temperature contour plots are used for the visualization of thermal transport in considered geometries.

Collocation Trefftz Method for the Heat Conduction Issue in Irregular Domain

Rules for non-orthogonal borders of irregular domain is the thorny issues when using analytical method for solving mathematical and physical equations. On the basis of solution in the form of separated variables, the border of arbitrary shape with non-orthogonal boundary will be separated into a limited number of discrete points, and then direct assignment for the form solution at each of the discrete points on the border according to boundary conditions, at every discrete points on the border can establish an equation. If the number of discrete points on the border is the same with truncated series after retained series, all coefficients of the form solution can be determined and the problem solved. This paper use Laplace equation as an example to illustrate Collocation Trefftz Method can solve certain steady-state heat conduction problems within non-orthogonal border and irregular domain.

Signal restoration via a splitting approach

In the present study, a novel signal restoration method from noisy data samples is presented and is termed as "signal split (SSplit)" approach. The new method utilizes Stein unbiased risk estimate estimator to split the signal, the Lipschitz exponents to identify noise elements and a heuristic approach for the signal reconstruction. However, unlike many noise removal techniques, the present method works only in the non-orthogonal domain. Signal restoration was performed on each individual part by finding the best compromise between the data samples and the smoothing criteria. Statistical results are quite promising and suggest better performance than the conventional shrinkage. Furthermore, the proposed method preserves the energy of the sharp peaks and edges which, is not however, the case for classical shrinkage methods.

Subsignal-based denoising from piecewise linear or constant signal

In the present work, a novel denoising technique for piecewise constant or linear signals is presented termed as signal split. The proposed method separates the sharp edges or transitions from the noise elements by splitting the into different parts. Unlike many noise removal techniques, the method works only in the nonorthogonal domain. The new method utilizes Stein unbiased risk estimate (SURE) to split the signal, Lipschitz exponents to identify noise elements, and a polynomial fitting approach for the sub reconstruction. At the final stage, merging of all parts yield in the fully denoised at a very low computational cost. Statistical results are quite promising and performs better than the conventional shrinkage methods in the case of different types of noise, i.e., speckle, Poisson, and white Gaussian noise. The method has been compared with the state of the art SURE-linear expansion of thresholds denoising technique as well and performs equally well. The method has been extended to the multisplitting approach to identify small edges which are difficult to identify due to the mutual influence of their adjacent strong edges.

Tilted Gaussian beam propagation in inhomogeneous media

The present work is concerned with applying a ray-centered non-orthogonal coordinate system which is a priori matched to linearly-phased localized aperture field distributions. The resulting beam-waveobjects serve as the building blocks for beam-type spectral expansions of aperture fields in 2D inhomogeneous media that are characterized by a generic wave-velocity profile. By applying a rigorous paraxial-asymptotic analysis, a novel parabolic wave equation is obtained and termed "Non-orthogonal domain parabolic equation"--NoDope. Tilted Gaussian beams, which are exact solutions to this equation, match Gaussian aperture distributions over a plane that is tilted with respect to the beam-axes initial directions. A numerical example, which demonstrates the enhanced accuracy of the tilted Gaussian beams over the conventional ones, is presented as well.

Non-Orthogonal Domain Parabolic Equation and Its Tilted Gaussian Beam Solutions

A non-orthogonal coordinate system which is <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> matched to localized initial field distributions for time-harmonic wave propagation is presented. Applying, in addition, a rigorous paraxial-asymptotic approximation, results in a novel parabolic wave equation for beam-type field propagation in 3D homogeneous media. Localized solutions to this equation that exactly match linearly-phased Gaussian aperture distributions are termed tilted Gaussian beams. These beams serve as the building blocks for various beam-type expansion schemes. Application of the scalar waveobjects to electromagnetic field beam-type expansion, as well as reflection and transmission of these waveobjects by planar velocity (dielectric) discontinuity are presented. A numerical example which demonstrates the enhanced accuracy of the tilted Gaussian beams over the conventional ones concludes the paper.

Spectral interpolation in non-orthogonal domains: algorithms and applications

Polynomial spectral methods have become increasingly important in diverse applications such as aeroacoustics, electromagnetics, ocean modeling, seismology, turbulent flows, non-Newtonian flows, non-linear optics, plasma dynamics, and uncertainty quantification. With more emphasis placed in the last 10 years on time-dependent rather than stationary problems, high-order methods, in general, and spectral-based methods, in particular, are potentially more effective than low-order discretizations. New developments in the last few years have addressed issues of complex geometry, finite regularity, fast solvers, multi-resolution, and large-scale simulations. The theme in the present special volume is spectral representations in non-orthogonal domains, specifically in triangles in two-dimensions and tetrahedra in three-dimensions. Multi-dimensional spectral expansions in orthogonal domains (squares or cubes) are based on tensor-products of one-dimensional expansions; for example products of Chebyshev or Legendre polynomials are popular choices. Interpolation is typically based on grid points that are given by the roots of these polynomials (Gauss points) or by the roots of the polynomials’ derivatives (Gauss–Lobatto points, if the end-points are included.) These grid points may also serve as the numerical quadrature points in spectral Galerkin formulations. However, in non-orthogonal domains, tensor-product expansion bases cannot be readily constructed, the best choice of grid points for interpolation or numerical integration is not so obvious. But good progress on both fronts has been made in the last 10 years, setting the foundation for a new generation of spectral and spectral-element methods that can handle truly complex geometries and can deal with error control very effectively. With regards to tensor products, new Jacobi-polynomial representations in conjunction with appropriate transformations have led to tensor-product bases in triangles and tetrahedra. With respect to the best set of grid points, several new algorithms have been proposed that provide excellent approximation properties in triangles and tetrahedra. Wehave collected in this special volumeeleven invited papers by leading researchers in spectralmethods. They are divided in three groups. The first group (1–7) deals with fundamental approximation properties, the second group (8–9) addresses improvements in solution procedures, and the third group (10–11) presents applications.

An adaptive technique for accuracy enhancement of vector quantizers in nonorthogonal domains

Recently, novel vector quantization techniques in multiple nonorthogonal domains for both waveform and model-based signal characterization that give an improved qualitative and quantitative signal coding performance as compared to vector quantization in single domain have been reported. In these techniques, vectors are formed either directly from the signal waveform or from the model parameters extracted from the signal. Then, the vectors are represented in multiple nonorthogonal domains. The encoder chooses the domain that best represents the vector according to a predetermined criterion. An iterative codebook enhancement algorithm, applicable to both waveform and model-based vector quantization in nonorthogonal domains is developed and presented in this paper. In this algorithm, each set of codebooks in a given domain is retrained by the vectors that were best represented by that particular set of codebooks in the most recent iteration. The algorithm is applied successfully and extensive simulation results yield considerable performance enhancement of the vector quantization in nonorthogonal domains, for a given bit rate. Sample results are provided which demonstrate the improved performance.

A high-performance linear predictor employing vector quantization in nonorthogonal domains with application to speech

Linear prediction (LP) is a powerful technique for efficient source-system model based representation of signals, such as speech, and video, with useful applications including compression, and recognition. This has been found to be particularly true when vector quantization is used to code the linear predictor coefficients. Recently, signal processing in multiple nonorthogonal domains has been reported that further enhances the efficiency of signal representation. In this contribution, a novel LP model based coding technique is presented where the advantages of multiple nonorthogonal domain representations of the LP coefficients and the prediction residuals are exploited in conjunction with vector quantization to yield considerable LP coding enhancement. The proposed signal coding technique is applied to one of the most commonly used signals, namely, speech. The resulting performance improvement is clearly demonstrated in terms of reconstruction quality for the same bit rate compared to the existing single domain vector quantization techniques.

An implicit pseudo‐spectral multi‐domain method for the simulation of incompressible flows

AbstractA pseudo‐spectral method for the solution of incompressible flow problems based on an iterative solver involving an implicit treatment of linearized convective terms is presented. The method allows the treatment of moderately complex geometries by means of a multi‐domain approach and it is able to cope with non‐constant fluid properties and non‐orthogonal problem domains. In addition, the fully implicit scheme yields improved stability properties as opposed to semi‐implicit schemes commonly employed. Key components of the method are a Chebyshev collocation discretization, a special pressure–correction scheme, and a restarted GMRES method with a preconditioner derived from a fast direct solver. The performance of the proposed method is investigated by considering several numerical examples of different complexity, and also includes comparisons to alternative solution approaches based on finite‐volume discretizations. Copyright © 2003 John Wiley &amp; Sons, Ltd.

Iterative algorithm for design of vector quantisation codebooks in nonorthogonal domains

An iterative algorithm for codebook accuracy enhancement, applicable to both waveform and linear prediction (LP) model-based vector quantisation in nonorthogonal domains, is developed and presented. Sample results are provided which clearly demonstrate the improved performance for the same bit rate.

Efficient code excited linear predictor using redundant vector quantiser representations

A novel linear prediction (LP) model-based coding technique is presented, where the advantages of multiple non-orthogonal domain representations of LP coefficients and the residuals are exploited in conjunction with vector quantisation. The proposed technique is applied to speech signals and the resulting performance improvement is clearly demonstrated in terms of the reconstruction quality.

Non-orthogonal domains in phase space of quantum optics and their relation to fractional Fourier transforms

It is customary to define a phase space such that position and momentum are mutually orthogonal coordinates. Associated with these coordinates, or domains, are the position and momentum operators. Representations of the state vector in these coordinates are related by the Fourier transformation. We consider a continuum of “fractional” domains making arbitrary angles with the position and momentum domains. Representations in these domains are related by the fractional Fourier transformation. We derive transformation, commutation, and uncertainty relations between coordinate multiplication, differentiation, translation, and phase shift operators making arbitrary angles with each other. These results have a simple geometric interpretation in phase space and applications in quantum optics.