Processing radio frequency ultrasound images: a robust method for local spectral features estimation by a spatially constrained parametric approach.

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.

Estimation of formant contours from continuous speech is a difficult problem that has required either elaborate heuristic rules or complex hidden Markov models. Under high noise levels, these methods deteriorate significantly because of the degraded performance of the spectral estimator on which they are based. This paper proposes a method of formant contour estimation using a measure of confidence for the spectral peak estimation. At high noise levels, most spectral estimation techniques result in large variance and increased spurious/missing peaks; however, it is found that a broad distribution of spectral energy can be determined more reliably using filter-bank analysis. This spectral energy distribution is utilized to differentiate regions of high and low signal-to-noise ratio in the spectrum (for white noise corruption), which in turn is used to determine a “confidence measure” for the spectral peak estimation. The addition of this confidence information to the noisy spectral peak data of a speech utterance results in clear segments of the formant contour standing out from the remaining noisy peak data. Using these segments as anchor regions, an algorithm is developed to determine the complete contours, within the constraints of the known speech properties. [Work supported by NSF.]

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.

This research project examines the applicability of novel spectral domain strain estimation algorithms to improve the clinical value of tissue elasticity images. Pathological changes can be frequently correlated to changes in soft tissue stiffness. Despite the fact that many cancers, including those found in the breast and prostate, often manifest themselves as stiff focal lesions, there location and shape can make them difficult, if not impossible, to detect during a palpation-based physical examination. The mechanical properties of tissue cannot be measured directly using any current imaging modality. However, an ultrasound-based technique known as elastography has evolved over the last fifteen years which is capable of estimating relative strain distributions in soft tissue. Under certain conditions, these strain images (elastograms) can give a clear depiction of the underlying tissue stiffness distributions, and thus, can be used as a clinical tool for the detection of pathological lesions. Conventionally elastographic techniques estimate tissue strain by tracking spatial features found in congruent pairs of ultrasonic echo backscattered signals before and after a small, quasistatic compression is applied to the tissue surface via the ultrasound transducer. Although this technique has shown promise from a clinical perspective in detecting both benign and malignant lesions of the breast and prostate, it is sensitive to extraneous motions that ultimately compromise the strain estimation procedure. To alleviate this problem, the applicability of spectral-domain strain estimation algorithms and techniques were examined. Both simulation and experimental (in vitro) results obtained using an elastographic phantom indicate that this approach holds promise to improve the clinical value of the images produced. Also, initial results obtained using a novel elastographic animal model further support the efficacy of spectral-based strain imaging in vivo.

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.

A spectral estimation technique is presented for autoregressive moving-average (ARMA) processes. The technique is based on a parameter estimation technique known as the rec ursive maximum likelihood (RML) method. The recursive spectral estimation algorithm is presented and its asymptotic properties are discussed. Simulation results are presented to illustrate the performance of the estimator for various types of data.

Wavelets are of wide potential use in statistical contexts. The basics of the discrete wavelet transform are reviewed using a filter notation that is useful subsequently in the paper. A ‘stationary wavelet transform’, where the coefficient sequences are not decimated at each stage, is described. Two different approaches to the construction of an inverse of the stationary wavelet transform are set out. The application of the stationary wavelet transform as an exploratory statistical method is discussed, together with its potential use in nonparametric regression. A method of local spectral density estimation is developed. This involves extensions to the wavelet context of standard time series ideas such as the periodogram and spectrum. The technique is illustrated by its application to data sets from astronomy and veterinary anatomy.

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.

A primal-dual method for estimating the spectrum of a complex sequence is provided that minimizes the l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> norm of the complex spectrum for 1<p<2 via solution of the dual problem in complex space. This provides reduced spectral leakage, enhanced spectral resolution, and robustness to missing data samples when compared to the minimum l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> norm spectral estimate. The optimization of the dual problem converges quickly in a small number of gradient search steps, providing solutions to large problems in very short time. Examples are provided that demonstrate the narrow, spiky nature of the spectrum, the reduced spectral leakage, and robustness to unevenly sampled data.

A summary of several modern spectral estimation methods is presented in this tutorial. Most of the methods may be explained in the context of parametric time series modeling. A few methods involve nonparametric treatment. Techniques discussed include classical spectral estimation, autoregressive (maximum entropy), ARMA, Prony, maximum likelihood, Pisarenko, and MUSIC methods. Many of the techniques have fast computational algorithms, making these methods viable for real time applications. The tutorial concludes with a commentary concerning current spectral estimation research.

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.

Four spectral analysis techniques were applied to pulsed Doppler ultrasonic quadrature signals to compare the relative merits of each technique for estimation of flow velocity and Doppler spectra. The four techniques were 1) the fast Fourier transform method, 2) the maximum likelihood method, 3) the Burg autoregressive algorithm, and 4) the modified covariance approach to autoregressive modeling. Both simulated signals and signals obtained from an in vitro flow system were studied. Optimal parameter values (e.g., model orders) were determined for each method, and the effects of signal-to-noise ratio and signal bandwidth were investigated. The modern spectral analysis techniques were shown to be superior to Fourier techniques in most circumstances, provided the model order was chosen appropriately. Robustness considerations tended to recommend the maximum likelihood method for both velocity and spectral estimation. Despite the restrictions of steady laminar flow, the results provide important basic information concerning the applicability of modern spectral analysis techniques to Doppler ultrasonic evaluation of arterial disease.

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 article, we concentrate on spectral estimation techniques that are useful in extracting the features to be used by automatic speech recognition (ASR) system. As an aid to understanding the spectral estimation process for speech signals, we adopt the source filter model of speech production as presented in X. Huang et al. (2001), wherein speech is divided into two broad classes: voiced and unvoiced. Voiced speech is quasi-periodic, consisting of a fundamental frequency corresponding to the pitch of a speaker, as well as its harmonics. Unvoiced speech is stochastic in nature and is best modeled as white noise convolved with an infinite impulse response filter.

: A vast amount of literature exists that concerns itself with spectrum analysis. In particular, the last two decades have seen a great increase of published theoretical work as well as applications of so-called modern spectral estimation techniques based on nontraditional parametric approaches. Many papers dealing with this subject make it difficult even for the initiated to make the connection to his well known and routinely applied methods based on the Fourier Transform when he reads about modeling a random process to obtain a parametric spectrum of the observed data. The report attempts to show the transition from the classical approach of spectral estimation to the basic parametric methods. It also shows the results of these new techniques when applied to short data records and demonstrates their capabilities and limitations.