Projection spectral analysis: A unified approach to PCA and ICA with incremental learning

Projection spectral analysis is investigated and refined in this paper, in order to unify principal component analysis and independent component analysis. Singular value decomposition and spectral theorems are applied to nonsymmetric correlation or covariance matrices with multiplicities or singularities, where projections and nilpotents are obtained. Therefore, the suggested approach not only utilizes a sum-product of orthogonal projection operators and real distinct eigenvalues for squared singular values, but also reduces the dimension of correlation or covariance if there are multiple zero eigenvalues. Moreover, incremental learning strategies of projection spectral analysis are also suggested to improve the performance.     

A convex projections method for improved narrow-band interferencerejection in direct-sequence spread-spectrum systems

A method is presented for enhancing the narrow-band interference rejection capability of direct-sequence spread-spectrum systems employing an adaptive notch filter. The method, based on projection onto convex sets, restores that part of the spread-spectrum signal distorted by the filter. Simulation results are presented which show the output bit-error rate (BER) improvement gained by using the signal restoration scheme     

A linear approach to metric circumference computation for digitized convex shapes

Metric measurement of digitized shapes is commonly applied in optical measuring systems.In this letter,three shape-related factors defined by the authors are used in the construction of a multiple linear regression model which is utilized to compute the circumference of the convex shapes in millimeter unit.The model is first built upon the relationship hypothesis and then its adequacy is mathematically validated.The results of applying the developed model to the given number of convex shapes in a finite circumferential length range suggest that,in terms of percent error,the model precision is to satisfaction by being within±4%.The test also shows the model’s robustness against the shape’s orientation anisotropy.     

An adaptive approach to spectral analysis of pattern-reversal visual evoked potentials

A method for spectral analysis of pattern-reversal visual evoked potentials (PRVEP's) is presented that results in spectral peaks of uniform width in the frequency domain for signals with a wide range of time-domain duration. Uniformity of spectral peak width is necessary for accurate comparison of spectra. The desired frequency domain characteristics can be achieved through the application of "tunable" data windows prior to transformation. The Io-sinh (Kaiser), Gaussian, and cosine-taper (Tukey) windows were evaluated as to their ability to produce power spectra with uniform spectral peak width. Objective comparison of power spectra is based on the "spectral parameter," which is a numerical index of power distribution. Application of the method to PRVEP waveforms of normal subjects (N = 20) and to a population of Alzheimer's Disease patients (N = 15) showed the Io-sinh window to be the most effective method, yielding correct classification of all normal and abnormal subjects. The Gaussian window also performed well, with only two misclassifications. Use of the rectangular window resulted in seven misclassifications. The tapered-cosine window was very limited in its applicability, and was about equal in performance to the rectangular window.     

Tomographic image reconstruction using the theory of convex projections

The method of convex projections is applied to reconstruct an image in computer tomography. This appears to the first time that the method has been used to obtain geometry-free reconstruction from ray-sum data. It is shown that a special set of convex projections duplicates the result of the algebraic reconstruction technique (ART). The similarities and differences of these two methods are discussed. It is pointed out that use of a priori information enhances the quality of the results, especially when partial data have been used, in which case ART fails. Simulations and reconstruction of a CT image are also furnished to demonstrate the feasibility of this method.     

A generalized approach to optical low-coherence reflectometryincluding spectral filtering effects

In the interpretation of optical low-coherence reflectometry measurements, the reflectivity of the device under test is in general supposed to be with a slow dependency on optical wavelength. However, recent research aims at investigating strongly wavelength-dependent devices, such as fiber Bragg gratings and semiconductor lasers. In this paper, a general theory including spectral filtering effects is developed. It appears as a generalization of previously reported results only valid under special conditions     

A quantitative analysis approach for cardiac arrhythmia classification using higher order spectral techniques

Ventricular tachyarrhythmias, in particular ventricular fibrillation (VF), are the primary arrhythmic events in the majority of patients suffering from sudden cardiac death. Attention has focused upon these articular rhythms as it is recognized that prompt therapy can lead to a successful outcome. There has been considerable interest in analysis of the surface electrocardiogram (ECG) in VF centred on attempts to understand the pathophysiological processes occurring in sudden cardiac death, predicting the efficacy of therapy, and guiding the use of alternative or adjunct therapies to improve resuscitation success rates. Atrial fibrillation (AF) and ventricular tachycardia (VT) are other types of tachyarrhythmias that constitute a medical challenge. In this paper, a high order spectral analysis technique is suggested for quantitative analysis and classification of cardiac arrhythmias. The algorithm is based upon bispectral analysis techniques. The bispectrum is estimated using an autoregressive model, and the frequency support of the bispectrum is extracted as a quantitative measure to classify atrial and ventricular tachyarrhythmias. Results show a significant difference in the parameter values for different arrhythmias. Moreover, the bicoherency spectrum shows different bicoherency values for normal and tachycardia patients. In particular, the bicoherency indicates that phase coupling decreases as arrhythmia kicks in. The simplicity of the classification parameter and the obtained specificity and sensitivity of the classification scheme reveal the importance of higher order spectral analysis in the classification of life threatening arrhythmias. Further investigations and modification of the classification scheme could inherently improve the results of this technique and predict the instant of arrhythmia change.     

A new approach to spectral estimation: a tunable high-resolutionspectral estimator

Traditional maximum entropy spectral estimation determines a power spectrum from covariance estimates. Here, we present a new approach to spectral estimation, which is based on the use of filter banks as a means of obtaining spectral interpolation data. Such data replaces standard covariance estimates. A computational procedure for obtaining suitable pole-zero (ARMA) models from such data is presented. The choice of the zeros (MA-part) of the model is completely arbitrary. By suitable choices of filter bank poles and spectral zeros, the estimator can be tuned to exhibit high resolution in targeted regions of the spectrum     

Real-valued Hankel transform approach to image reconstruction from projections

A Hankel transform relation based on the real-valued Hartley transform and its application in image reconstuction from projections are proposed. In comparison with its counterpart based on the Fourier transform, the proposed method has evident advantages in computational and memory requirements because all operations are performed in the real-number space.<>     

An approach to high-frequency scattering from smooth convex surfaces

A method based on the Galerkin procedure in the transform domain that not only allows accurate solutions for both the farfield and the induced surface current be derived but also provides a convenient accuracy check for the solutions thus obtained is introduced. The total solution is constructed using only the geometrical optics method and a newly introduced synthetic aperture technique well suited for deriving efficient transform solutions forn-dimensional, smooth curved objects using (n - 1)-dimensional transforms. The need for the conventional creeping-wave contribution is obviated in this method.     

A spectral matching approach for parameter and spectral estimationof nonstationary rational processes

The parameter and spectral estimation problems of nonstationary signals are considered. The nonstationary signals are modeled as rational processes with time-varying parameters. The spectral matching approach, which was introduced by Friedlander and Porat (1984), is generalized to the nonstationary case and two new estimators, namely, the time-varying spectral matching estimator (TVSME) and the time-frequency spectral matching estimator (TFSME) are proposed. The proposed methods estimate the parameters of the time-varying rational model by fitting the parametric spectrum expression to an estimated time-frequency distribution of the signal. An approximate statistical analysis is given for both methods along with computer simulation results, illustrating the performance of the proposed estimators     

JPEG2000-coded image error concealment exploiting convex sets projections.

Transmission errors in JPEG2000 can be grouped into three main classes, depending on the affected area: LL, high frequencies at the lower decomposition levels, and high frequencies at the higher decomposition levels. The first type of errors are the most annoying but can be concealed exploiting the signal spatial correlation like in a number of techniques proposed in the past; the second are less annoying but more difficult to address; the latter are often imperceptible. In this paper, we address the problem of concealing the second class or errors when high bit-planes are damaged by proposing a new approach based on the theory of projections onto convex sets. Accordingly, the error effects are masked by iteratively applying two procedures: low-pass (LP) filtering in the spatial domain and restoration of the uncorrupted wavelet coefficients in the transform domain. It has been observed that a uniform LP filtering brought to some undesired side effects that negatively compensated the advantages. This problem has been overcome by applying an adaptive solution, which exploits an edge map to choose the optimal filter mask size. Simulation results demonstrated the efficiency of the proposed approach.     

Control theoretical approach to multivariable spectral factorisation problem

It is shown how with analogy to analogue control theory, that the problem of polynomial-matrix spectral factorisation can be solved using negative feedback. This recursive method is particularly simple to implement compared with other approaches. The algorithm in its basic form requires no matrix inversions or special matrix decompositions.     

An information-theoretic approach to spectral variability,similarity, and discrimination for hyperspectral image analysis

A hyperspectral image can be considered as an image cube where the third dimension is the spectral domain represented by hundreds of spectral wavelengths. As a result, a hyperspectral image pixel is actually a column vector with dimension equal to the number of spectral bands and contains valuable spectral information that can be used to account for pixel variability, similarity and discrimination. We present a new hyperspectral measure, the spectral information measure (SIM), to describe spectral variability and two criteria, spectral information divergence and spectral discriminatory probability for spectral similarity and discrimination, respectively. The spectral information measure is an information-theoretic measure which treats each pixel as a random variable using its spectral signature histogram as the desired probability distribution. Spectral information divergence (SID) compares the similarity between two pixels by measuring the probabilistic discrepancy between two corresponding spectral signatures. The spectral discriminatory probability calculates spectral probabilities of a spectral database (library) relative to a pixel to be identified so as to achieve material identification. In order to compare the discriminatory power of one spectral measure relative to another, a criterion is also introduced for performance evaluation, which is based on the power of discriminating one pixel from another relative to a reference pixel. The experimental results demonstrate that the new hyperspectral measure can characterize spectral variability more effectively than the commonly used spectral angle mapper (SAM)     

Image recovery in computer tomography from partial fan-beam data by convex projections

For the image recovery process the authors use the convex projections method, also known as the method of projections onto convex sets (POCS). Several incomplete-data geometries, including those associated with limited source travel and beam-blocking internal opacities, are considered. To enable the recovery several prior-knowledge constraints including one associated with the directivity of the image vector are used. The overall recovery algorithm can be practically implemented by exploiting the Toeplitz structure of key operators.     

Removal of compression artifacts using projections onto convex setsand line process modeling

We present a new image recovery algorithm to remove, in addition to blocking, ringing artifacts from compressed images and video. This new algorithm is based on the theory of projections onto convex sets (POCS). A new family of directional smoothness constraint sets is defined based on line processes modeling of the image edge structure. The definition of these smoothness sets also takes into account the fact that the visibility of compression artifacts in an image is spatially varying. To overcome the numerical difficulty in computing the projections onto these sets, a divide-and-conquer (DAC) strategy is introduced. According to this strategy, new smoothness sets are derived such that their projections are easier to compute. The effectiveness of the proposed algorithm is demonstrated through numerical experiments using Motion Picture Expert Group based (MPEG-based) coders-decoders (codecs).     

Image restoration by the method of convex projections: part 1 theory

A projection operator onto a closed convex set in Hilbert space is one of the few examples of a nonlinear map that can be defined in simple abstract terms. Moreover, it minimizes distance and is nonexpansive, and therefore shares two of the more important properties of ordinary linear orthogonal projections onto closed linear manifolds. In this paper, we exploit the properties of these operators to develop several iterative algorithms for image restoration from partial data which permit any number of nonlinear constraints of a certain type to be subsumed automatically. Their common conceptual basis is as follows. Every known property of an original image f is envisaged as restricting it to lie in a well-defined closed convex set. Thus, m such properties place f in the intersection E(0) = E(i) of the corresponding closed convex sets E(1),E(2),...EE(m). Given only the projection operators PE(i) onto the individual E(i)'s, i = 1 --> m, we restore f by recursive means. Clearly, in this approach, the realization of the P(i)'s in a Hilbert space setting is one of the major synthesis problems. Section I describes the geometrical significance of the three main theorems in considerable detail, and most of the underlying ideas are illustrated with the aid of simple diagrams. Section II presents rules for the numerical implementation of 11 specific projection operators which are found to occur frequently in many signal-processing applications, and the Appendix contains proofs of all the major results.     

Nonparametric spectral analysis of gapped data via an adaptive filtering approach

We present an algorithm for nonparametric complex spectral analysis of gapped data via an adaptive finite impulse response (FIR) filtering approach, referred to as the gapped-data amplitude and phase estimation (GAPES) algorithm. The incomplete data sequence may contain gaps of various sizes. The GAPES algorithm iterates the following two steps: (1) estimating the adaptive FIR filter and the corresponding complex spectrum via amplitude and phase estimation (APES), a nonparametric adaptive FIR filtering approach, and (2) filling in the gaps via a least-squares APES fitting criterion. The initial condition for the iteration is obtained from the available data segments via APES. Numerical results are presented to demonstrate the effectiveness of the proposed GAPES algorithm.This work was supported in part by the Senior Individual Grant Program of the Swedish Foundation for Strategic Research, AFRL/SNAT, Air Force Research Laboratory, Air Force Material Command, USAF, under grant number F33615-99-1-1507, and the National Science Foundation Grant MIP-9457388. The US Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notice thereon.     

Extended spectral domain approach for analysis of lossy cylindrical dielectric resonators

The spectral domain approach is extended for evaluating both the resonant frequency and Q factor of a lossy cylindrical dielectric resonator operating in TE/sub 0/ modes, taking into account the effects of conducting enclosure and supporting substrate. On the basis of the equivalence principle, the circular electric currents are introduced to simulate the fields inside and outside the cylindrical dielectric sample, which separates the original problems into two auxiliary structures with radially homogeneous multilayered dielectrics. Using the spectral immittance method in conjunction with the point-matching method, the characteristic equations are derived. The present technique has no need to determine the time-consuming, complex higher-order modes. Some typical examples are computed. The numerical results agree well with experimental data available in the literature.<>     

编码孔径光谱成像仪中凸面闪耀光栅的研制

针对一款基于DMD的光谱维编码Offner光谱成像仪对凸面闪耀光栅的性能要求,提出了一种凸面闪耀光栅的宏观-微观一体化优化设计方法,利用三维偏振光追迹算法有机融合了宏观层面的Offner光学系统设计与微观层面的凸面闪耀光栅槽型设计。介绍了编码孔径Offner光谱成像系统的组成和工作原理,并结合系统的使用要求设计了一款平均衍射效率为85.47%的中波红外凸面闪耀光栅。在此基础上,采用超精密单点金刚石车床成功制备了曲率半径为120 mm、周期为99.945 μm、闪耀角为1.1783°、槽深为1.834 μm的凸面闪耀光栅。测试结果表明,在3~5 μm光谱范围内,最大衍射效率为93.46%,平均衍射效率为84.29%,与理论设计值较为吻合,验证了凸面闪耀光栅设计方法的有效性。