The Maximum Entropy Spectrum and the Burg Technique. Technical Report No. 1: Advanced Signal Processing

A neural net algorithm for multidimensional maximum entropy spectrum estimation

HIGH RESOLUTION 2-DIMENSIONAL POWER SPECTRAL ESTIMATION

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.

The autoregressive (AR) spectral estimator is used to make high resolution spectral estimates based on short data records. Measures of a frequency averaged normalized bias and normalized variance of the spectral estimates are introduced. A large number of spectra are generated. Based on the above mentioned measures and visual inspection of the estimates of the generated spectra, the AR and the conventional tapered and transformed (TT) spectral estimates are compared. It is shown that the AR spectral estimator is as stable as that given by its asymptotic variance. It is also shown that the AR spectral estimator is most powerful in estimating narrow spectral peaks with a high signal-to-interference ratio in the signal bandwidth.

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.

Bipolar disorder (BD) has been associated with abnormal reward functioning including pleasure-seeking and impulsivity. Here we sought to clarify whether these changes can be attributed to abnormalities in the neural processing of reward valuation or error prediction. Moreover, we tested whether abnormalities in these processes are associated with familial vulnerability to BD. We obtained functional magnetic resonance imaging data from patients with recently diagnosed BD (n=85), their unaffected first-degree relatives (n=44), and healthy control participants (n=66) while they were performing a monetary card game. We used a region-of-interest approach to test for group differences in the activation of the midbrain, the ventral striatum, and the prefrontal cortex during reward valuation and error prediction. Patients with BD showed decreased prediction error signal in ventrolateral prefrontal cortex and the unaffected relatives showed decreased prediction error signal in the supplementary motor area in comparison to healthy controls. There were no significant group differences in the activation of the ventral striatum during the task. In healthy controls, prediction error signal in dorsal anterior cingulate cortex correlated with an out-of-scanner measure of motor inhibition but this association was absent in patients and relatives. The findings indicate that abnormal reward processing in BD is primarily related to deficits in the engagement of prefrontal regions involved in inhibitory control during error prediction. In contrast, deficient activation in supplementary motor cortex involved in planning of movement emerged as a familial vulnerability to BD.

Spectral estimation often forms the basis for distinguishing and tracking signals of interest in the presence of noise and for extracting information from the received data. The application of Fourier techniques to the problem of estimating the properties of sinusoids in noise dates back as far as Shuster (1898), Fourier spectrum analysis is the basis for almost all spectral-estimation equipment, * including the common sweeping-filter spectrum analyzer, the parallel filter bank, the fast Fourier transform (FFT), the delay-line time compressor (Deltic), and the compressive spectrum analyzer (Microscan). A problem with Fourier spectrum analysis, however, is that it makes implicit assumptions concerning data outside the observation interval and, frequently, these physically unrealistic assumptions reduce the quality of the estimates. During the past decade, two radically different non-Fourier spectral-estimation techniques have emerged — maximum-entropy spectrum analysis (Burg, 1967) and spectral decomposition (Pisarenko, 1973). These techniques offer alternative and often more realistic data models which, in many cases, lead to better estimation performance. This paper reviews the Fourier methods and compares them to the new techniques in terms of signal models assumed by the three basic methods and their ability to distinguish multiple sinusoids in noise.

Error-based learning underlies motor learning, but what specific motor error drives implicit learning, the procedural component of motor skill, is unclear. A typical action consists of a movement and a performance outcome, e.g., grabbing a coffee cup involves a reaching movement and its actual landing of the hand relative to the target cup. While performance error is fundamental for the cognitive component of motor learning, what error, either performance or movement prediction error, underlies implicit motor learning has not been resolved. These two errors are hard to disentangle as the performance outcome is an integral part of the movement. Here we used the classical visuomotor adaptation paradigm, in which people learn to counter visual perturbations by deliberately aiming off the target, to dissociate the performance error from the prediction error. Using a series of behavioral experiments and model comparisons, we revealed that movement prediction error, but not performance error, can parsimoniously explain diverse learning effects. Importantly, despite the perturbation being visual, the movement prediction error is not specified in visual terms, but determined by a perceptual estimate of the hand kinematics. In other words, contrary to the widely-held concept of sensory prediction error, a perceptual prediction error drives implicit motor learning.

Reversible data hiding (RDH) is desirable in applications where both the hidden message and the cover image need to be recovered without loss. Among many RDH approaches is prediction-error expansion (PEE), containing two steps: i) prediction of a target pixel value, and ii) embedding according to the value of the prediction error. In general, higher prediction performance leads to larger embedding capacity and/or lower signal distortion. Leveraging on recent advances in graph signal processing (GSP), we pose pixel prediction as a graph-signal restoration problem, and design non-local graph-based prediction schemes where the appropriate edge weights of the underlying graph are computed using a similar patch searched in a semi-local neighborhood. Specifically, for each candidate patch, we first examine eigenvalues of its structure tensor to estimate its local smoothness. If sufficiently smooth, we pose a maximum a posteriori (MAP) problem using either a quadratic Laplacian regularizer or a graph total variation (GTV) term as signal prior. While the MAP problem using the first prior has a closed-form solution, we design an efficient algorithm for the second prior using alternating direction method of multipliers (ADMM) with nested proximal gradient descent. Finally, hidden message will be embedded into the image according to the resulting prediction errors. Experimental results show that with better quality GSP-based prediction, at low capacity the visual quality of the embedded image exceeds state-of-the-art methods noticeably.

Re: Hoffer et al.: Update on intraocular lens power calculation study protocols: the better way to design and report clinical trials (Ophthalmology. 2020; Jul 9 [Epub ahead of print

This paper uses ARMA model to model the prediction error of wind power, and obtains the probability distribution of the prediction error by probability statistical analysis to simulate the uncertainty of wind power. Latin hypercube simulation is used to sample typical wind power prediction errors, and a large number of wind power scenarios are reduced. On this basis, taking into account the power-to-gas, a optimal dispatch model of the integrated power and gas systems(IPGS) is established with the objective of minimizing the operation cost of the system. The CPLEX solver is used to complete the solution of the model. Finally, modified 6-bus power system and 7-node natural gas system are used to construct an IPGS. This paper uses this IPGS to do the simulation test and cases studies. Which verifies the effectiveness of the model, and further reveals the advantages of power-to-gas in promoting wind power absorption and improving system operation economy.

Population pharmacokinetic (PK) model-based Bayesian estimation is widely used for dose individualization, particularly when sample availability is limited. However, its predictive accuracy can be compromised by factors such as misspecified prior information, intra-patient variability, and uncertainties in PK variations. In this study, we developed a hybrid approach that combines machine learning (ML) with population PK-based Bayesian methods to improve the prediction of infliximab concentrations in children with Crohn’s disease. We calculated prediction errors between Bayesian-estimated and observed infliximab concentrations from 292 measurements across 93 patients. Incorporating clinical patient features, we explored various ML algorithms, including linear regression, random forest, support vector regression, neural networks, and XGBoost to correct the Bayesian-based prediction errors. The predictive performance of these ML models was assessed using root mean square error (RMSE) and mean prediction error (MPE) with 5-fold cross-validation. For Bayesian estimation alone, the RMSE and MPE were 4.8 μg/mL and −0.67 μg/mL, respectively. Among the ML algorithms, the XGBoost model demonstrated the best performance, achieving an RMSE of 3.78 ± 0.85 μg/mL and an MPE of −0.03 ± 0.69 μg/mL in 5-fold cross-validation. The ML-corrected Bayesian estimation significantly reduced the absolute prediction error compared to Bayesian estimation alone. This hybrid population PK-ML approach provides a promising framework for improving the predictive performance of Bayesian estimation, with the potential for continuous learning from new clinical data to enhance dose individualization.

We consider the problem of using an autoregressive (AR) approximation to estimate the spectral density function and the n × n autocovariance matrix based on stationary data X1, … , Xn. The consistency of the autoregressive spectral density estimator has been proven since the 1970s under a linearity assumption. We extend these ideas to the nonlinear setting, and give an application to estimating the n × n autocovariance matrix. Under mild assumptions on the underlying dependence structure and the order p of the fitted AR(p) model, we are able to show that the autoregressive spectral estimate and the associated AR‐based autocovariance matrix estimator are consistent. We are also able to establish an explicit bound on the rate of convergence of the proposed estimators.

Maintenance strategies such as condition-based maintenance and predictive maintenance of machines have gained importance in industrial automation firms as key concepts in Industry 4.0. As a result, online condition monitoring of electromechanical systems has become a crucial task in many industrial applications. Motor current signature analysis (MCSA) is an interesting noninvasive alternative to vibration analysis for the condition monitoring and fault diagnosis of mechanical systems driven by electric motors. The MCSA approach is based on the premise that faults in the mechanical load driven by the motor manifest as changes in the motor's current behavior. This paper presents a novel data-driven, MCSA-based CM approach that exploits autoregressive (AR) spectral estimation. A multiresolution analysis of the raw motor currents is first performed using the discrete wavelet transform with Daubechies filters, enabling the separation of noise, disturbances, and variable torque effects from the current signals. AR spectral estimation is then applied to selected wavelet details to extract relevant features for fault diagnosis. In particular, a reference AR power spectral density (PSD) is estimated using data collected under healthy conditions. The AR PSD is then continuously or periodically updated with new data frames and compared to the reference PSD through the Symmetric Itakura-Saito spectral distance (SISSD). The SISSD, which serves as the health indicator, has proven capable of detecting fault occurrences through changes in the AR spectrum. The proposed procedure is tested on real data from two different scenarios: (i) an experimental in-house setup where data are collected during the execution of electric cam motion tasks (imbalance faults are emulated); (ii) the Korea Advanced Institute of Science and Technology testbed, whose data set is publicly available (bearing faults are considered). The results demonstrate the effectiveness of the method in both fault detection and isolation. In particular, the proposed health indicator exhibits strong detection capabilities, as its values under fault conditions exceed those under healthy conditions by one order of magnitude.

Purpose: A critical component of real-time MLC tracking is to incorporate motion prediction in order to account for system latency, the time between the occurrence of motion and MLC leaf repositioning, so as to avoid geometric and dosimetric errors. In this work, we address a major limitation of current motion prediction algorithms – estimating the inherent error in prediction in real-time. We propose using an ensemble of real-time predictors to reduce overall prediction error, and provide a quantitative metric to trigger beam holds based on a user-defined error threshold. Methods: An ensemble of eighteen kernel density estimation (KDE)-based estimators was implemented in parallel and deployed on motion traces recorded from ten lung cancer patients. For each trace, the ensemble generated a sequence of predictions for a look-ahead time of 250ms, typical for many real-time systems. Each predictor, and the ensemble as a whole, was evaluated based on their root-mean-square error (RMSE) with respect to the original data, and assigned a beam hold score between 0 (perfect) and 1 to quantify the number of false beam holds and false beam releases. Results: The average execution time of the KDE-ensemble was 16ms, well below the 250ms look-ahead. For all traces, the ensemble produced a lower RMSE and hold score than any of the individual constituent predictors. For the worst-case motion trace, the minimum RMSE(hold score) for individual predictors was 0.912cm(0.340) compared to 0.854cm(0.305) for the KDE-ensemble predictor. The hold score for individual estimators was ∼0.6 when error estimates were not used to assert beam holds. Conclusion: The KDE-ensemble approach results in improved motion prediction. More importantly, it also provides real-time estimations of prediction error, thus addressing a major gap in current motion prediction algorithms. Such error prediction can be utilized to assert beam-holds during MLC tracking, preventing serious geometric and dosimetric errors. Funding for this work was provided by Elekta Limited.