Spectrum Analysis: Overview of Classical and High Resolution Spectral Estimation

There have been a significant number of recent papers about hyperspectral imaging, which propose various methods for estimating the number of materials/endmembers in hyperspectral images. This is sometimes called the “intrinsic” dimension (ID) of the image. Estimation of the error variance in each spectral band is a critical first step in ID estimation. The estimated error variances can then be used to preprocess (e.g., whiten) the data, prior to ID estimation. A range of variance estimation methods have been advocated in the literature. We investigate the impact of five variance estimation methods (three using spatial information and two using spectral information) on five ID estimation methods, with the aid of four different, but semirealistic, sets of simulated hyperspectral images. Our findings are as follows: first, for all four sets, the two spectral variance estimation methods significantly outperform the three spatial methods; second, when used with the spectral variance estimation methods, two of the ID estimation methods (called random matrix theory and NWHFC) consistently outperform the other three ID estimation methods; third, the better spectral variance estimation method sometimes gives negative variance estimates; fourth, we introduce a simple correction that guarantees positivity; and fifth, we give a fast algorithm for its computation.

In this paper, we present a new approach to high-resolution spectral characterization of the unknown number of spectral line components embedded in colored noise. The addressed method resolves the spectral analysis problem via intelligent fusing the two spectrum estimation paradigms: (i) the parametric line spectral estimation that employs the modified regularized Prony (MORP) method for multi-harmonic signal characterization and (ii) nonparametric spectral estimation. Two nonparametric high-resolution spectral estimation methods are proposed to be fused with the MORP: the minimum variance (MV) and maximum entropy (ME) techniques. Via aggregation of the developed model-based MORP and model-free MV/ME techniques into the fused MORP-MV/MORP-ME resulting method a substantial improvement of the spectral characterization performances is gained when those are applied to characterization/analysis of the composed distributed scenes that contain noised closely spaced spectral lines to be localized with high resolution and accuracy. The simulation results are presented to illustrate the performance enhancement gained with the proposed fused MORP-MV/MORP-ME method.

We discuss here the use of spectral estimation algorithms for biomedical ultrasound imaging. B-mode ultrasound imagery is based on computing the envelope of acoustic individual radio-frequency (RF) lines. An envelope estimator is thus needed to improve spatial resolution and reduce speckle. There is an analogy between spectral analysis and envelope estimation. Indeed, the signal envelope can be seen as the power spatial density. This study evaluated the potential of high-resolution (HR) spectral estimation techniques in the resolution enhancement of ultrasound images. Several spectral estimation methods were therefore compared using the Monte-Carlo method on a synthetic image for different noise and standard deviation conditions. The paper also illustrates their performance on 20 MHz in-vivo ultrasound imaging of a skin lesion.

Minimum Cross Entropy and Informational Approaches for Spectrum Estimation

PurposeIn order to overcome the uncertainty and improve the accuracy of spectral estimation, this paper aims to establish a grey fuzzy prediction model of soil organic matter content by using grey theory and fuzzy theory.Design/methodology/approachBased on the data of 121 soil samples from Zhangqiu district and Jiyang district of Jinan City, Shandong Province, firstly, the soil spectral data are transformed by spectral transformation methods, and the spectral estimation factors are selected according to the principle of maximum correlation. Then, the generalized greyness of interval grey number is used to modify the estimation factors of modeling samples and test samples to improve the correlation. Finally, the hyper-spectral prediction model of soil organic matter is established by using the fuzzy recognition theory, and the model is optimized by adjusting the fuzzy classification number, and the estimation accuracy of the model is evaluated using the mean relative error and the determination coefficient.FindingsThe results show that the generalized greyness of interval grey number can effectively improve the correlation between soil organic matter content and estimation factors, and the accuracy of the proposed model and test samples are significantly improved, where the determination coefficient R2 = 0.9213 and the mean relative error (MRE) = 6.3630% of 20 test samples. The research shows that the grey fuzzy prediction model proposed in this paper is feasible and effective, and provides a new way for hyper-spectral estimation of soil organic matter content.Practical implicationsThe research shows that the grey fuzzy prediction model proposed in this paper can not only effectively deal with the three types of uncertainties in spectral estimation, but also realize the correction of estimation factors, which is helpful to improve the accuracy of modeling estimation. The research result enriches the theory and method of soil spectral estimation, and it also provides a new idea to deal with the three kinds of uncertainty in the prediction problem by using the three kinds of uncertainty theory.Originality/valueThe paper succeeds in realizing both the grey fuzzy prediction model for hyper-spectral estimating soil organic matter content and effectively dealing with the randomness, fuzziness and grey uncertainty in spectral estimation.

传统的周期图检测法是一种近似无偏的估计方法，但存在估计偏差和估计方差相互制约的问题。针对此问题，本文采用多窗谱估计，该方法是基于滤波器组理论改进的周期图检测法，利用多个正交窗进行谱估计，有极佳的能量集中性，能解决谱估计存在较大方差的问题。理论推导及仿真结果证明，基于多窗谱的频谱检测算法是一种低方差、高分辨率的频谱检测方法，能有效实现低信噪比条件下的信号检测，且相比于其他检测算法能达到更好的检测性能。 The traditional periodogram spectral estimation method is an approximately unbiased spectral estimation method, however, with the difficulties of estimated bias and estimated variance dilemmatic. To solve this problem, a kind of accurate non-parametric multitaper method was introduced in this paper which is actually regarded as the improved periodogram spectral estimation method based on filter banks. The multitaper method makes use of multiple orthogonal windows for spectral estimation. By this means, the spectrum is estimated with excellent energy concentration. It can solve the problem of spectral estimation variance. The theoretical derivations and simulations show that the multitaper spectral spectrum detecting algorithm is a low variance and high resolution spectrum detection method, especially for the weak signal detection under strong noise background. It has effective performance and outperforms other spectrum detecting methods in low SNR.

Spectral estimation is a major component in studies aiming at characterizing biological tissues through the analysis of backscattered radio frequency (RF) ultrasonic signals and images. However, conventional spectral estimation techniques yield a well-known trade-off between spatial resolution and variance. The backscattered signals are stochastic by nature, so short-term local analysis results in a high variance of the estimates, which cannot efficiently be reduced through conventional spatial averaging. We address this issue by describing a spectral estimation technique that reduces the variance of the estimates (by smoothing the local estimates in spectrally homogeneous regions) while preserving spectral discontinuities (i.e., the smoothing is not performed across regions with different spectral contents). The proposed approach is set in a Bayesian framework and is based on local autoregressive (AR) estimation, constrained by smoothness priors. These smoothness priors are introduced through a Markov random field in which the associated potential functions are nonquadratic, allowing thereby to preserve discontinuity. The method is validated on simulated RF images and tested on echocardiographic images acquired in vivo. The results are compared to the estimates provided by the conventional Burg technique. These results clearly demonstrate the ability of the proposed approach to improve spectral estimation in terms of variance reduction and discontinuity detection.

We address the problem of efficient resolution, detection and estimation of weak tones in a potentially massive amount of data. Our goal is to produce a relatively small reduced data set characterizing the signals in the environment in time and frequency. The requirements for this problem are that the process must be computationally efficient, high gain and able to resolve signals and efficiently compress the signal information into a form that may be easily displayed and further processed. We base our process on the cross spectral representation we have previously applied to other problems. In selecting this method, we have considered other representations and estimation methods such as the Wigner distribution and Welch's method. We compare our method to these methods. The spectral estimation method we propose is a variation of Welch's method and the cross-power spectral (CPS) estimator which was first applied to signal estimation and detection in the mid 1980's. The CPS algorithm and the method we present here are based on the principles first described by Kodera et al. now frequently called the reassignment principle.

A new spectral reflectance estimation method based on CIE XYZ values under multi‐illuminants was proposed to obtain multi‐spectral images accurately by using digital still cameras. CIE XYZ values under multi‐illuminants were initially predicted from raw RGB responses by using a polynomial model with local training samples. Then, spectral reflectance was constructed from the predicted CIE XYZ values via the pseudo‐inverse method. Experimental results indicated that the new spectral reflectance estimation method significantly outperformed the traditional colorimetric characterization method without requiring extra training samples or greatly increasing computational complexities. © 2016 Wiley Periodicals, Inc. Col Res Appl, 42, 68–77, 2017

In spectral estimation, one has to determine all parameters of an exponential sum for finitely many (noisy) sampled data of this exponential sum. Frequently used methods for spectral estimation are MUSIC (MUltiple SIgnal Classification) and ESPRIT (Estimation of Signal Parameters via Rotational Invariance Technique). For a trigonometric polynomial of large sparsity, we present a new sparse fast Fourier transform by shifted sampling and using MUSIC resp. ESPRIT, where the ESPRIT based method has lower computational cost. Later this technique is extended to a new reconstruction of a multivariate trigonometric polynomial of large sparsity for given (noisy) values sampled on a reconstructing rank-1 lattice. Numerical experiments illustrate the high performance of these procedures.

Skeletal muscle velocity is a key indicator of neuromuscular function, and monitoring its changes plays important role in tracking the progression of musculoskeletal diseases, injuries, and fatigue. However, existing methods for non-invasive estimation of skeletal muscle velocity primarily use B- mode ultrasound, often with processing methods that are time-consuming or computationally expensive, with varying accuracy based on tissue structure. Here, we propose a spectral Doppler envelope estimation method designed for skeletal muscle measurements. When compared to the modified signal noise slope intersection (MSNSI) method, our method reduces the overall mean absolute error by 13.9% and the mean absolute zero error by 82.1%. We validated our method using a portable ultrasound system on a benchtop setup that mimics the acoustic properties, measurement angles, and velocity patterns of skeletal muscles. Ex vivo and in vivo muscle velocity estimates of parallel and pennate muscles will be compared to those obtained using the MSNSI method and manual tracking of B-Mode images. Our proposed method could enable automated estimation of skeletal muscle velocities during dynamic activities in unconstrained environments, providing new insight into neuromuscular function and movement biomechanics, with potential applications in monitoring fatigue, disease progression, or injury recovery. [Work supported by the National Science Foundation.]

In this work we develop some parameter and spectral estimation methods in Magnetic Resonance Spectroscopy Signals (MRS). We do this with a dual purpose: first, to enable the full estimation process for the constituent parameters of the time-domain msignal: Amplitude, frequency, damping constant and phase. Second, to generate the parameter estimation in the frequency domain in order to evaluate the effect of the application of time domain estimation methods [2].

One of the most widely used methods of spectral estimation in signal and speech processing is linear predictive coding (LPC), LPC has some attractive features, which account for its popularity, including the properties that the resulting modeling filter (i) matches a finite window of n+1 covariance lags, (ii) is rational of degree at most n, and (iii) has stable zeros and poles. The only limiting factor of this methodology is that the modeling filter is "all-pole," i.e., an autoregressive (AR) model. In this paper, we present a systematic description of all autoregressive moving-average (ARMA) models of processes that have properties (i)-(iii) in the context of cepstral analysis and homomorphic filtering. We show that each such an ARMA model determines and is completely determined by its finite windows of cepstral coefficients and covariance lags. We show that these nth-order windows form local coordinates for all ARMA models of degree n and that the pole-zero model can be determined from the windows as the unique minimum of a convex objective function. We refine this optimization method by first noting that the maximum entropy design of an LPC filter is obtained by maximizing the zeroth cepstral coefficient, subject to the constraint (i). More generally, we modify this scheme to a more well-posed optimization problem where the covariance data enter as a constraint and the linear weights of the cepstral coefficients are "positive"-in a sense that a certain pseudo-polynomial is positive-rather succinctly generalizing the maximum entropy method. This new problem is a homomorphic filter generalization of the maximum entropy method. providing a procedure for the design of any stable, minimum-phase modeling filter of degree less or equal to n that interpolates the given covariance window. We present an algorithm for realizing these filters in a lattice-ladder form, given the covariance window and the moving average part of the model, While we also show how to determine the moving average part using cepstral smoothing, one can make use of any good a priori estimate for the system zeros to initialize the algorithm. We conclude the paper with an example of this method, incorporating an example from the literature on ARMA modeling.

A new spectral estimation method is proposed. Since in the least square L/sub 2/ method the obtained estimates are very much affected by the large signal portions, in the proposed method a loss function which assigns large weighting factor for the small residual portions and vice versa is used. The loss function is based on an assumption that the residual signal has an identical and independent t-distribution t( alpha ) with alpha degrees of freedom to achieve accurate and efficient (low standard deviation) estimates. When alpha = infinity , the conventional L/sub 2/ method is obtained. In the calculation, the loss function is modified in a way similar to the autocorrelation method, so that the proposed method can be seen as a generalization of the autocorrelation method. The optimal solution is selected by the Newton-Raphson method. The simulation results show that only a few iterations are needed to reach a stationary point, the stationary point is always a local minimum, and the obtained predictor is stable.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

In this paper we study the spectral properties of an auto-regressive (AR) spectral estimator proposed by Cadzow, which uses a large number of correlations to set up the normal equations. This Set of overdetermined equations is then solved in a least squares sense. The main contribution of this paper is the derivation of asymptotic relationships, i.e., as the number of samples goes to infinity, between the number of correlations used, the model order and the signal-to-noise ratio of the signal, and the characteristics of the resulting spectral estimate when the signal under study is composed of sinusoids in noise. The characteristics studied are the height, bandwidth, and area of the peaks in the estimated spectrum. The method is shown to be a spectral density estimator like the ME method, where spectral areas rather than spectral values should be interpreted as estimates of power. The role of the number of correlations as a signal-to-noise ratio enhancer is discussed. Computer simulations are presented which verify the theoretical results.