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Auto-regressive (AR) spectral estimation technology is proposed to analyze the Brillouin scattering spectrum in Brillouin optical time-domain refelectometry. It shows that AR based method can reliably estimate the Brillouin frequency shift with an accuracy much better than fast Fourier transform (FFT) based methods provided the data length is not too short. It enables about 3 times improvement over FFT at a moderate spatial resolution. [ABSTRACT FROM AUTHOR]

This paper compares the skill of two algorithms that enable real-time estimation of the directional wave spectra exciting a ship from its measured motions. One algorithm consists of a nonlinear optimization of a parametric or non-parametric spectral model and the other is a Kalman filter based observer. Sea trials have been conducted on an oceanographic vessel that was instrumented with a six degree of freedom fiber optic gyro, complemented with a rate gyro, several accelerometers, a dedicated GPS receiver and a bow mounted down-looking wave radar with motion compensation. The two algorithms are applied to the measured data and a discussion is provided on their skill to recover the properties of existing sea states. [ABSTRACT FROM AUTHOR]

Cables are critical force-bearing components of cable-supported structures that greatly influence structure security. The changes in cable forces can reflect the cable service state and provide an important basis for structural health assessment. This paper proposes a method for real-time cable force identification (CFI) to tracking its varying rules. First, a recursive Capon method based on block updating is derived to estimate the amplitude spectrum at each observation moment. Second, determine the natural frequency (and corresponding mode order) in the transformed frequency domain and calculate the cable tension according to related formulas. Proper algorithm optimization and parameter selection are studied to ensure that the calculation cost meets the real-time requirement of CFI. The proposed method is applied to an experimental cable and the cables of a half-through arch bridge for validation. • A block recursive Capon method (BRC) is proposed for real-time spectrum analysis. • An automatic frequency extraction and tracking method based on BRC is developed. • A real-time online cable force identification method is proposed. • The proposed method is verified by experimental and realistic cables. [ABSTRACT FROM AUTHOR]

Sea states are usually the combination of several time-evolving wave systems whereas the classical spectral estimation methods assume stationarity. A method that adapts to the dynamical evolution of the spectral components is proposed to improve both omnidirectional and directional sea wave spectral estimations. In this method, periodograms are computed for each sea state as in the conventional methods, and rather than only smoothing individual periodograms, the overall time-history of periodograms are simultaneously smoothed in frequency and time dimensions. Since a simple two dimensional averaging would not be appropriate because the temporal evolution of the wave systems reflects typical non-stationary behaviors, we use either kriging or adaptive 2D kernel density estimators that allow the taking care of the spectral component frequency–time evolutions. The method is successfully validated on sequences of spectra typical of sea-state conditions in West Africa. The comparison with the simple 2D averaging method and individual periodogram smoothing method shows that the proposed method gives higher effective numbers of degrees of freedom, better estimates of the spectral shape and reliable spectral moments. The method also provides a tool for sea wave spectra interpolation and may thus be used to fill in missing values and improve wave systems tracking for storm identification purposes. [ABSTRACT FROM AUTHOR]

Purpose: Computed tomography (CT) performance as well as dose and image quality is directly affected by the x-ray spectrum. However, the current assessment approaches of the CT x-ray spectrum require costly measurement equipment and complicated operational procedures, and are often limited to the spectrum corresponding to the center of rotation. In order to address these limitations, the authors propose an angle-dependent estimation technique, where the incident spectra across a wide range of angular trajectories can be estimated accurately with only a single phantom and a single axial scan in the absence of the knowledge of the bowtie filter. Methods: The proposed technique uses a uniform cylindrical phantom, made of ultra-highmolecular- weight polyethylene and positioned in an off-centered geometry. The projection data acquired with an axial scan have a twofold purpose. First, they serve as a reflection of the transmission measurements across different angular trajectories. Second, they are used to reconstruct the cross sectional image of the phantom, which is then utilized to compute the intersection length of each transmission measurement. With each CT detector element recording a range of transmission measurements for a single angular trajectory, the spectrum is estimated for that trajectory. A data conditioning procedure is used to combine information from hundreds of collected transmission measurements to accelerate the estimation speed, to reduce noise, and to improve estimation stability. The proposed spectral estimation technique was validated experimentally using a clinical scanner (Somatom Definition Flash, Siemens Healthcare, Germany) with spectra provided by the manufacturer serving as the comparison standard. Results obtained with the proposed technique were compared against those obtained from a second conventional transmission measurement technique with two materials (i.e., Cu and Al). After validation, the proposed technique was applied to measure spectra from the clinical system across a range of angular trajectories [-15?, 15?] and spectrum settings (80, 100, 120, 140 kVp). Results: At 140 kVp, the proposed technique was comparable to the conventional technique in terms of the mean energy difference (MED, -0.29 keV) and the normalized root mean square difference (NRMSD, 0.84%) from the comparison standard compared to 0.64 keV and 1.56%, respectively, with the conventional technique. The average absolute MEDs and NRMSDs across kVp settings and angular trajectories were less than 0.61 keV and 3.41%, respectively, which indicates a high level of estimation accuracy and stability. Conclusions: An angle-dependent estimation technique of CT x-ray spectra from rotational transmission measurements was proposed. Compared with the conventional technique, the proposed method simplifies the measurement procedures and enables incident spectral estimation for a wide range of angular trajectories. The proposed technique is suitable for rigorous research objectives as well as routine clinical quality control procedures [ABSTRACT FROM AUTHOR]

Nonparametric spectral estimation is a widely used technique in many applications ranging from radar and seismic data analysis to electroencephalography (EEG) and speech processing. Among the techniques that are used to estimate the spectral representation of a system based on finite observations, multitaper spectral estimation has many important optimality properties, but is not as widely used as it possibly could be. We give a brief overview of the standard nonparametric spectral estimation theory and the multitaper spectral estimation, and give two examples from EEG analyses of anesthesia and sleep. [ABSTRACT FROM PUBLISHER]

Background: The discrete Fourier transform (DFT) is often used as a spectral estimator for analysis of complex fractionated atrial electrograms (CFAE) acquired during atrial fibrillation (AF). However, time resolution can be unsatisfactory, as the frequency resolution is proportional to rate/time interval. In this study we compared the DFT to a new spectral estimator with improved time-frequency resolution. Method: Recently, a novel spectral estimator (NSE) based upon signal averaging was derived and implemented computationally. The NSE is similar to the DFT in that both estimators model the autocorrelation function to form the power spectrum. However, as derived in this study, NSE frequency resolution is proportional to rate/period² and thus unlike the DFT, is not directly dependent on the window length. We hypothesized that the NSE would provide improved time resolution while maintaining satisfactory frequency resolution for computation of CFAE spectral parameters. Window lengths of 8 s, 4 s, 2 s, 1 s, and 0.5 s were used for analysis. Two criteria gauged estimator performance. Firstly, a periodic electrogram pattern with phase jitter was embedded in interference. The error in detecting the frequency of the periodic pattern was determined. Secondly, significant differences in spectral parameters for paroxysmal versus persistent AF data, which have known dissimilarities, were determined using the DFT versus NSE methods. The parameters measured were the dominant amplitude, dominant frequency, and mean spectral profile. Results: At all time resolutions, the error in detecting the frequency of the repeating electrogram pattern was less for NSE than for DFT (p < 0.001). The DFT was accurate to 2 s time resolution/0.5 Hz frequency resolution, while the NSE was accurate to 0.5 s time resolution/0.05 Hz frequency resolution. At all time resolutions, significant differences in the dominant amplitude spectral parameter for paroxysmal versus persistent CFAE were greater using NSE than DFT (p < 0.0001). For three of five time resolutions, the NSE had greater significant differences than DFT for discriminating the dominant frequency and mean spectral profile parameters between AF types. Conclusions: The results suggest that the NSE has improved performance versus DFT for measurement of CFAE spectral properties. [ABSTRACT FROM AUTHOR]

Background: The dominant frequency of the Fourier power spectrum is useful to analyze complex fractionated atrial electrograms (CFAE), but spectral resolution is limited and uniform from DC to the Nyquist frequency. Herein the spectral resolution of a recently described and relatively new spectral estimation technique is compared to the Fourier radix-2 implementation. Methods: In 10 paroxysmal and 10 persistent atrial fibrillation patients, 216 CFAE were acquired from the pulmonary vein ostia and left atrial free wall (977 Hz sampling rate, 8192 sample points, 8.4 s duration). With these parameter values, in the physiologic range of 3-10 Hz, two frequency components can theoretically be resolved at 0.24 Hz using Fourier analysis and at 0.10 Hz on average using the new technique. For testing, two closely-spaced periodic components were synthesized from two different CFAE recordings, and combined with two other CFAE recordings magnified 2χ, that served as interference signals. The ability to resolve synthesized frequency components in the range 3-4 Hz, 4-5 Hz,…, 9-10 Hz was determined for 15 trials each (105 total). Results: With the added interference, frequency resolution averaged 0.29 ± 0.22 Hz for Fourier versus 0.16 ± 0.10 Hz for the new method (p < 0.001). The misalignment error of spectral peaks versus actual values was ±0.023 Hz for Fourier and ±0.009 Hz for the new method (p < 0.001). One or both synthesized peaks were lost in the noise floor 13/105 times using Fourier versus 4/105 times using the new method. Conclusions: Within the physiologically relevant frequency range for characterization of CFAE, the new method has approximately twice the spectral resolution of Fourier analysis, there is less error in estimating frequencies, and peaks appear more readily above the noise floor. Theoretically, when interference is not present, to resolve frequency components separated by 0.10 Hz using Fourier analysis would require an 18.2 s sequence duration, versus 8.4 s with the new method. [ABSTRACT FROM AUTHOR]

In the first part of this article, we show that we can recover the coefficient q in the one-dimensional wave equation from a finite number of special lateral measurements. Moreover, if some estimates on the size of q are available, then q can be recovered from a single boundary measurement. In the second part we treat the multidimensional case and show how we can reconstruct the coefficient q from a sequence of boundary measurements taken at one point only. [ABSTRACT FROM AUTHOR]

Abstract: This paper proposes two novel iterative data-adaptive spectral estimation techniques for blood velocity estimation using medical ultrasound scanners. The techniques make no assumption on the sampling pattern of the emissions or the depth samples, allowing for duplex mode transmissions where B-mode images are interleaved with the Doppler emissions. Furthermore, the techniques are shown, using both simplified and more realistic Field II simulations as well as in vivo data, to outperform current state-of-the-art techniques, allowing for accurate estimation of the blood velocity spectrum using only 30% of the transmissions, thereby allowing for the examination of two separate vessel regions while retaining an adequate updating rate of the B-mode images. In addition, the proposed methods also allow for more flexible transmission patterns, as well as exhibit fewer spectral artifacts as compared to earlier techniques. [Copyright &y& Elsevier]

This paper presents a sensitivity analysis of using instantaneous multichannel two-dimensional (2D) imaging to achieve instantaneous 2D imaging spectroscopy. A simulated multiple-filter mosaic was introduced and used to acquire multichannel data which were transformed into spectra. The feasibility of two different transformation approaches (the concrete pseudoinverse approach and a statistical approach) was investigated through extensive experimental tasks. A promising statistical method was identified to be used for accurate estimation of spectra from multichannel data. Comparison between estimated and measured spectra shows that higher estimation accuracy can be achieved when using a larger number of usable multiple-filter combinations in the mosaic. [ABSTRACT FROM AUTHOR]

In this letter, we propose shrinkage-based Capon (S-Capon) and APES (S-APES) spectral estimators by minimizing the mean-square error (MSE) of standard Capon and APES in linear regression framework. The proposed methods are shown to give more accurate spectral estimates but lower resolution than the methods they based on. We combine Capon with the proposed S-Capon and S-APES to overcome the resolution limit of shrinkage-based methods for estimation of both frequency and amplitude of spectral lines. The so-obtained Capon-SCapon and Capon-SAPES spectral estimators, which have about same computational complexity as Capon, are compared with Capon-APES (CAPES) by numerical examples. Simulations show that the Capon-SCapon performs similarly to CAPES in a wide range of signal-to-noise ratio, and the Capon-SAPES always gives more accurate spectral amplitude (less bias and lower MSE) than CAPES. [ABSTRACT FROM AUTHOR]

Weighted linear prediction (WLP) is a method to compute all-pole models of speech by applying temporal weighting of the square of the residual signal. By using short-time energy (STE) as a weighting function, this algorithm was originally proposed as an improved linear predictive (LP) method based on emphasising those samples that fit the underlying speech production model well. The original formulation of WLP, however, did not guarantee stability of all-pole models. Therefore, the current work revisits the concept of WLP by introducing a modified short-time energy function leading always to stable all-pole models. This new method, stabilised weighted linear prediction (SWLP), is shown to yield all-pole models whose general performance can be adjusted by properly choosing the length of the STE window, a parameter denoted by M. The study compares the performances of SWLP, minimum variance distortionless response (MVDR), and conventional LP in spectral modelling of speech corrupted by additive noise. The comparisons were performed by computing, for each method, the logarithmic spectral differences between the all-pole spectra extracted from clean and noisy speech in different segmental signal-to-noise ratio (SNR) categories. The results showed that the proposed SWLP algorithm was the most robust method against zero-mean Gaussian noise and the robustness was largest for SWLP with a small M-value. These findings were corroborated by a small listening test in which the majority of the listeners assessed the quality of impulse-train-excited SWLP filters, extracted from noisy speech, to be perceptually closer to original clean speech than the corresponding all-pole responses computed by MVDR. Finally, SWLP was compared to other short-time spectral estimation methods (FFT, LP, MVDR) in isolated word recognition experiments. Recognition accuracy obtained by SWLP, in comparison to other short-time spectral estimation methods, improved already at moderate segmental SNR values for sounds corrupted by zero-mean Gaussian noise. For realistic factory noise of low pass characteristics, the SWLP method improved the recognition results at segmental SNR levels below 0dB. [Copyright &y& Elsevier]

Abstract: This paper proposes a high-speed iterative procedure for estimating the ocean wave directional spectrum from vessel motion data. It uses as input data, the measurements from motion sensors that are commonly available on dynamically positioned vessels and which may easily be installed on any ship. Because the necessary sensors are relatively inexpensive or may already be installed, it becomes an ideal solution to provide initial estimates to offline estimation procedures and to give spectral updates under quickly changing weather conditions. The Kalman filtering algorithm, for iterative harmonic detection, and frequency domain vessel response data are used in the estimation procedure. The results and conclusions are still based on synthesized data, but very promising. [Copyright &y& Elsevier]

A signal's spectrum is a representation of the signal in terms of elementary basis functions which facilitates the extraction of desired information. For a temporal signal, the spectrum is one-dimensional and expresses the time-domain signal as a linear combination of sinusoidal basis functions. A space-time signal possesses a multidimensional Fourier transform known as the wavenumber-frequency spectrum, which represents the space-time signal as a weighted summation of monochromatic plane waves. The spatial and temporal frequencies are not separable, as spatial frequency is itself a function of the temporal frequency. Thus, it seems natural to analyze and estimate the spatial and temporal frequency components in tandem. It is therefore surprising that conventional spectral estimation methods focus on either the spatial or temporal dimension, without any regard for the other. Spatial spectral estimation is commonly referred to as source localization, as the direction of the wave number vector is indeed the direction of propagation. Conventional methods analyze a solely spatial aperture without accounting for the temporal structure of the desired signal. Conversely, temporal spectral estimation is performed using a single sensor, and thus the signal aperture is purely temporal. This paper proposes a spatiotemporal framework for spectral estimation based on the linearly constrained minimum variance (LCMV) beamforming method proposed by Frost in 1972. The aperture consists of an array of sensors, each storing a set of previous temporal samples. It is first shown that by taking into account the temporal structure of the desired signal, the ensuing source location estimate is more robust to the effects of noise and reverberation. Unlike conventional localizers, the LCMV steered beam temporally focuses the array onto the desired signal. The desired signal is modeled by an autoregressive (AR) process, and the resulting AR coefficients are embedded in the linear constraints. As a result, the rate of anomalous estimates is significantly reduced as compared to existing techniques. Moreover, it is then demonstrated that by employing multiple sensors and steering the array to the assumed source location, the estimate of the desired signal's temporal spectrum contains a lesser contribution from the unwanted noise and reverberation. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a numerical procedure to estimate the wave spectrum based on measured motions of vessels at zero advance speed. The procedure has an underlying non-parametric formulation which allows for a low constraint on spectral shape estimation. In order to make parameters readily available and provide smooth spectral shape, a parametric form is fitted by using minimization of squared errors between non-parametric and parametric forms. The parametric description is fast even for double peaked spectra due to the use of simplified numerical procedure for a-priori estimation of swell and wind sea spectral properties. [Copyright &y& Elsevier]

Abstract: In this study, power quality (PQ) signals are analyzed by using Welch (non-parametric) and autoregressive (parametric) spectral estimation methods. The parameters of the autoregressive (AR) model were estimated by using the Yule–Walker method. PQ spectra were then used to compare the applied spectral estimation methods in terms of their frequency resolution and the effects in determination of spectral components. The variations in the shape of the obtained power spectra were examined in order to detect power system transients. Performance of the proposed methods was evaluated by means of power spectral densities (PSDs). Graphical results comparing the performance of the AR method with that of the Welch technique are given. The results demonstrate superior performance of the AR method over the Welch method. [Copyright &y& Elsevier]

Abstract: It has already been shown that spectral estimation can be improved when applied to subband outputs of an adapted filterbank rather than to the original fullband signal. In the present paper, this procedure is applied jointly to a novel predictive autoregressive (AR) model. The model exploits time-shifting and is therefore referred to as time-shift AR (TS-AR) model. Estimators are proposed for the unknown TS-AR parameters and the spectrum of the observed signal. The TS-AR model yields improved spectrum estimation by taking advantage of the correlation between subseries that arises after decimation. Simulation results on signals with continuous and line spectra that demonstrate the performance of the proposed method are provided. [Copyright &y& Elsevier]

Maximum-likelihood estimation of the parameters of a continuous-time model for irregularly sampled data is very sensitive to initial conditions. Simulations may converge to a good solution if the true parameters are used as starting values for the nonlinear search of the minimum of the negative log likelihood. From realizable starting values, the convergence to a continuous-time model with an accurate spectrum is rare if more than three parameters have to be estimated. A discrete-time spectral estimator that applies a new algorithm for automatic equidistant missing-data analysis to irregularly spaced data is introduced. This requires equidistant resampling of the data. A slotted nearest neighbor (NN) resampling method replaces a true irregular observation time instant by the nearest equidistant resampling time point if and only if the distance to the true time is within half the slot width. It will be shown that this new resampling algorithm with the slotting principle has favorable properties over existing schemes such as NN resampling. A further improvement is obtained by using a slot width that is only a fraction of the resampling time. [ABSTRACT FROM AUTHOR]

It is often advantageous to investigate the relationship between two geophysical data sets in the spectral domain by calculating admittance and coherence functions. While there exist powerful Cartesian windowing techniques to estimate spatially localized (cross-)spectral properties, the inherent sphericity of planetary bodies sometimes necessitates an approach based in spherical coordinates. Direct localized spectral estimates on the sphere can be obtained by tapering, or multiplying the data by a suitable windowing function, and expanding the resultant field in spherical harmonics. The localization of a window in space and its spectral bandlimitation jointly determine the quality of the spatiospectral estimation. Two kinds of axisymmetric windows are here constructed that are ideally suited to this purpose: bandlimited functions that maximize their spatial energy within a cap of angular radius θ0, and spacelimited functions that maximize their spectral power within a spherical harmonic bandwidth L. Both concentration criteria yield an eigenvalue problem that is solved by an orthogonal family of data tapers, and the properties of these windows depend almost entirely upon the space–bandwidth product . The first windows are near perfectly concentrated, and the best-concentrated window approaches a lower bound imposed by a spherical uncertainty principle. In order to make robust localized estimates of the admittance and coherence spectra between two fields on the sphere, we propose a method analogous to Cartesian multitaper spectral analysis that uses our optimally concentrated data tapers. We show that the expectation of localized (cross-)power spectra calculated using our data tapers is nearly unbiased for stochastic processes when the input spectrum is white and when averages are made over all possible realizations of the random variables. In physical situations, only one realization of such a process will be available, but in this case, a weighted average of the spectra obtained using multiple data tapers well approximates the expected spectrum. While developed primarily to solve problems in planetary science, our method has applications in all areas of science that investigate spatiospectral relationships between data fields defined on a sphere. [ABSTRACT FROM AUTHOR]

This paper proposes β-order minimum mean-square error (MMSE) speech enhancement approach for estimating the short time spectral amplitude (STSA) of a speech signal. We analyze the characteristics of the β-order STSA MMSE estimator and the relation between the value of β and the spectral amplitude gain function of the MMSE method. We further investigate the effectiveness of a range of fixed-β values in estimating STSA based on the MMSE criterion, and discuss how the β value could be adapted using the frame signal-to-noise ratio (SNR). The performance of the proposed speech enhancement approach is then evaluated through spectrogram inspection, objective speech distortion measures and subjective listening tests using several types of noise sources from the NOISEX-92 database. Evaluation results show that our approach can achieve a more significant noise reduction and a better spectral estimation of weak speech spectral components from a noisy signal as compared to many existing speech enhancement algorithms. [ABSTRACT FROM AUTHOR]

We describe strategies to accelerate the terminal stage of molecular dynamics (MD)-based relaxation algorithms, where a large fraction of the computational resources are used. First, we analyze the qualitative and quantitative behavior of the QuickMin family of MD relaxation algorithms and explore the influence of spectral properties and dimensionality of the molecular system on the algorithm efficiency. We test two algorithms, the MinMax and Lanczos, for spectral estimation from an MD trajectory, and use this to derive a practical scheme of time step adaptation in MD relaxation algorithms to improve efficiency. We also discuss the implementation aspects. Secondly, we explore the final state refinement acceleration by a combination with the conjugate gradient technique, where the key ingredient is an implicit corrector step. Finally, we test the feasibility of passive Hessian matrix accumulation from an MD trajectory, as another route for final phase acceleration. Our suggestions may be implemented within most MD quench implementations with a few, straightforward lines of code, thus maintaining the appealing simplicity of the MD quench algorithms. In this paper, we also bridge the conceptual gap between the MD quench algorithms inspired from physics and the mathematically rooted line search algorithms. [ABSTRACT FROM AUTHOR]

Time series solutions for spectral analysis in missing data problems use reconstruction of the missing data, or a maximum likelihood approach that analyzes only the available measured data. Maximum likelihood estimation yields the most accurate spectra. An approximate maximum likelihood algorithm is presented that uses only previous observations falling in a finite interval to compute the likelihood, instead of all previous observations. The resulting nonlinear estimation algorithm requires no user-provided initial solution, is suited for order selection, and can give very accurate spectra even if less than 10% of the data remains. [ABSTRACT FROM AUTHOR]

A new approach has been proposed for improving the performance of the Wigner–Ville distribution. This approach is based on signal decomposition and modified magnitude group delay function. Signal decomposition achieved by perfect reconstruction filter bank reduces significantly the existence of crossterms. The Gibbs ripple effect is due to truncation of the Wigner–Ville distribution kernel. The modified magnitude group delay function overcomes this effect without applying any window. Compared to those of Pseudo Wigner–Ville distribution and its versions, the proposed method has significantly improved performance in both time and frequency resolution as there is no time and frequency smoothing. Further, this method obeys better the desirable properties of time–frequency representation and has a better noise immunity. [Copyright &y& Elsevier]

We present a new method for multi-component power spectra estimation in multi-frequency observations of the CMB. Our method is based on matching the cross- and auto-power spectra of observation maps to their expected values. All the component power spectra are estimated, as well as their mixing matrix. Noise power spectra are also estimated. The method has been applied to full-sky Planck simulations containing five components and white noise. The beam smoothing effect is taken into account. [Copyright &y& Elsevier]

The regularized resolvent transform (RRT) has been applied in a novel way to J-resolved spectra. This involves the direct calculation of the 45° projection without constructing the 2D spectrum. The results show a significant resolution enhancement over that obtained by the 45° projection of a 2D Fourier spectrum, even for much larger signals. In particular, RRT is able to resolve peaks that belong to different overlapping multiplets in a very crowded spectral region, where the conventional technique fails for any signal size. The resolving power of this method along with the significantly shorter signals required, make this method a powerful tool in spectral assignment. [Copyright &y& Elsevier]

A new method for processing diffusion ordered spectroscopy (DOSY) data is presented. This method, the regularized resolvent transform (iRRT—the i denoting the adaptation of the method to evaluate the inverse Laplace transform), is better than conventional processing techniques for generating 2D DOSY spectra using data that has poor chemical shift resolution. From the same data, it is possible to use the iRRT to generate 1D subspectra corresponding to different components of the sample mixture; these subspectra compare favorably to 1D spectra of the pure substances. Both the 2D spectra and the 1D subspectra offer a vast improvement over results generated using a conventional processing technique (non-linear least-squares fitting). Consequently, we present the iRRT as a stable and reliable tool for solving the inverse Laplace transform problem present in experiments such as DOSY. [Copyright &y& Elsevier]

The problem of estimating the amplitude spectrum of a signal is of interest in a number of applications ranging from radar imaging to time-series analysis. The so-called adaptive filterbank-based nonparametric spectral estimators have recently received renewed interest as potential solutions to this problem. In essence, the adaptive filterbank methods determine an estimate of the spectrum for a frequency of interest by computing a finite impulse response filter according to a certain criterion and fitting a sinusoid to the filtered data sequence. In this paper, we first analyze the asymptotic estimation accuracy of the amplitude spectrum for various filterbank estimators. Next, we propose a new adaptive filterbank estimator based on a minimum mean square error criterion. Numerical examples indicate that the new estimator can have a better resolution capability than previously known filterbank estimators. [Copyright &y& Elsevier]

In short-time spectral estimation, Sacchi et al. (IEEE Trans. Signal Process. 46(1) (1998) 31) and Ciuciu et al. (IEEE Trans. Signal Process. 49 (2001) 2202) derived new nonlinear spectral estimators defined as minimizers of penalized criteria. The first contributors have introduced separable penalizations for line spectra (LS) recovering, whereas the latter have proposed circular Gibbs–Markov functions for smooth spectra (SS) restoration, and combined both contributions for estimation of “mixed” spectra (MS), i.e., frequency peaks superimposed on a homogeneous background (Ciuciu et al., 2001). Sacchi et al. resorted to the iteratively reweighted least squares (IRLS) algorithm for the minimization stage. Here, we show that IRLS is a block-coordinate descent (BCD) method performing the minimization of a half-quadratic (HQ) energy. The latter, derived from the Geman and Reynolds construction, has the same minimizer as the initial criterion but depends on more variables. After proving that such a construction is not available for Gibbs–Markov penalizations, we extend the pioneering work of Geman and Yang (IEEE Trans. Image Process. 4(7) (1995) 932) that leads to a suitable HQ energy for any kind of penalization encountered in Ciuciu et al. (2001). The BCD algorithm used for minimizing such HQ criteria is actually an original residual steepest descent (RSD) procedure (IEEE Trans. Acoust. Speech Signal Process. ASSP-33(1) (1985) 174) and thus converges in any convex case. A comparison between RSD, IRLS when available, and a pseudo-conjugate gradient algorithm is addressed in any case. [Copyright &y& Elsevier]