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Diffusion MRI (dMRI) allows for non-invasive investigation of brain tissue microstructure. By fitting a model to the dMRI signal, various quantitative measures can be derived from the data, such as fractional anisotropy, neurite density and axonal radii maps. We investigate the Fisher Information Matrix (FIM) and uncertainty propagation as a generally applicable method for quantifying the parameter uncertainties in linear and non-linear diffusion MRI models. In direct comparison with Markov Chain Monte Carlo (MCMC) sampling, the FIM produces similar uncertainty estimates at much lower computational cost. Using acquired and simulated data, we then list several characteristics that influence the parameter variances, including data complexity and signal-to-noise ratio. For practical purposes we investigate a possible use of uncertainty estimates in decreasing intra-group variance in group statistics by uncertainty-weighted group estimates. This has potential use cases for detection and suppression of imaging artifacts.
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Imagen de Difusión por Resonancia Magnética , Neuritas , Humanos , Incertidumbre , Imagen de Difusión por Resonancia Magnética/métodos , Cadenas de Markov , AxonesRESUMEN
Hierarchical Temporal Memory (HTM) is an unsupervised algorithm in machine learning. It models several fundamental neocortical computational principles. Spatial Pooler (SP) is one of the main components of the HTM, which continuously encodes streams of binary input from various layers and regions into sparse distributed representations. In this paper, the goal is to evaluate the sparsification in the SP algorithm from the perspective of information theory by the information bottleneck (IB), Cramer-Rao lower bound, and Fisher information matrix. This paper makes two main contributions. First, we introduce a new upper bound for the standard information bottleneck relation, which we refer to as modified-IB in this paper. This measure is used to evaluate the performance of the SP algorithm in different sparsity levels and various amounts of noise. The MNIST, Fashion-MNIST and NYC-Taxi datasets were fed to the SP algorithm separately. The SP algorithm with learning was found to be resistant to noise. Adding up to 40% noise to the input resulted in no discernible change in the output. Using the probabilistic mapping method and Hidden Markov Model, the sparse SP output representation was reconstructed in the input space. In the modified-IB relation, it is numerically calculated that a lower noise level and a higher sparsity level in the SP algorithm lead to a more effective reconstruction and SP with 2% sparsity produces the best results. Our second contribution is to prove mathematically that more sparsity leads to better performance of the SP algorithm. The data distribution was considered the Cauchy distribution, and the Cramer-Rao lower bound was analyzed to estimate SP's output at different sparsity levels.
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Traditional direction-finding systems are based on processing the outputs of multiple spatially separated antennas. The impinging signal Angle-of-Arrival (AOA) is estimated using the relative phase and amplitude of the multiple outputs that are sampled simultaneously. Here, we explore the potential of a single moving antenna to provide useful direction finding of a single transmitter. If the transmitted signal frequency is steady enough during the collection of data, a single antenna can be moved while tracking the phase changes to provide an Angle-of-Arrival measurement. The advantages of a single-antenna sensor include the sensor size, the lack of a need for multiple-receiver synchronization in time and frequency, the lack of mutual antenna coupling, and the cost of the system. However, a single-antenna sensor requires an accurate knowledge of its position during the data collection and it is challenged by transmitter phase instability, signal modulation, and transmitter movement during the measurement integration time. We analyze the performance of the proposed sensor, support the analysis with simulations and finally, present measurements performed by hardware configured to check the validity of the proposed single-antenna sensor.
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The localization of sensors in wireless sensor networks has recently gained considerable attention. The existing location methods are based on a one-spot measurement model. It is difficult to further improve the positioning accuracy of existing location methods based on single-spot measurements. This paper proposes two location methods based on multi-spot measurements to reduce location errors. Because the multi-spot measurements model has more measurement equations than the single-spot measurements model, the proposed methods provide better performance than the traditional location methods using one-spot measurement in terms of the root mean square error (RMSE) and Cramer-Rao lower bound (CRLB). Both closed-form and iterative algorithms are proposed in this paper. The former performs suboptimally with less computational burden, whereas the latter has the highest positioning accuracy in attaining the CRLB. Moreover, a novel CRLB for the proposed multi-spot measurements model is also derived in this paper. A theoretical proof shows that the traditional CRLB in the case of single-spot measurements performs worse than the proposed CRLB in the case of multi-spot measurements. The simulation results show that the proposed methods have a lower RMSE than the traditional location methods.
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Algoritmos , Simulación por ComputadorRESUMEN
Sensor placement is an important factor that may significantly affect the localization performance of a sensor network. This paper investigates the sensor placement optimization problem in three-dimensional (3D) space for angle of arrival (AOA) target localization with Gaussian priors. We first show that under the A-optimality criterion, the optimization problem can be transferred to be a diagonalizing process on the AOA-based Fisher information matrix (FIM). Secondly, we prove that the FIM follows the invariance property of the 3D rotation, and the Gaussian covariance matrix of the FIM can be diagonalized via 3D rotation. Based on this finding, an optimal sensor placement method using 3D rotation was created for when prior information exists as to the target location. Finally, several simulations were carried out to demonstrate the effectiveness of the proposed method. Compared with the existing methods, the mean squared error (MSE) of the maximum a posteriori (MAP) estimation using the proposed method is lower by at least 25% when the number of sensors is between 3 and 6, while the estimation bias remains very close to zero (smaller than 0.15 m).
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Target localization plays a vital role in ocean sensor networks (OSNs), in which accurate position information is not only a critical need of ocean observation but a necessary condition for the implementation of ocean engineering. Compared with other range-based localization technologies in OSNs, the received signal strength (RSS)-based localization technique has attracted widespread attention due to its low cost and synchronization-free nature. However, maintaining relatively good accuracy in an environment as dynamic and complex as the ocean remains challenging. One of the most damaging factors that degrade the localization accuracy is the uncertainty in transmission power. Besides the equipment loss, the uncertain factors in the fickle ocean environment may result in a significant deviation between the standard rated transmission power and the usable transmission power. The difference between the rated and actual transmission power would lead to an extra error when it comes to the localization in OSNs. In this case, a method that can locate the target without needing prior knowledge of the transmission power is proposed. The method relies on a two-phase procedure in which the location information and the transmission power are jointly estimated. First, the original nonconvex localization problem is transformed into an alternating non-negativity-constrained least square framework with the unknown transmission power (UT-ANLS). Under this framework, a two-stage optimization method based on interior point method (IPM) and majorization-minimization tactic (MMT) is proposed to search for the optimal solution. In the first stage, the barrier function method is used to limit the optimization scope to find an approximate solution to the problem. However, it is infeasible to approach the constraint boundary due to its intrinsic error. Then, in the second stage, the original objective is converted into a surrogate function consisting of a convex quadratic and concave term. The solution obtained by IPM is considered the initial guess of MMT to jointly estimate both the location and transmission power in the iteration. In addition, in order to evaluate the performance of IPM-MM, the Cramer Rao lower bound (CRLB) is derived. Numerical simulation results demonstrate that IPM-MM achieves better performance than the others in different scenarios.
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The imaging performance of clinical positron emission tomography (PET) systems has evolved impressively during the last â¼15 years. A main driver of these improvements has been the introduction of time-of-flight (TOF) detectors with high spatial resolution and detection efficiency, initially based on photomultiplier tubes, later silicon photomultipliers. This review aims to offer insight into the challenges encountered, solutions developed, and lessons learned during this period. Detectors based on fast, bright, inorganic scintillators form the scope of this work, as these are used in essentially all clinical TOF-PET systems today. The improvement of the coincidence resolving time (CRT) requires the optimization of the entire detection chain and a sound understanding of the physics involved facilitates this effort greatly. Therefore, the theory of scintillation detector timing is reviewed first. Once the fundamentals have been set forth, the principal detector components are discussed: the scintillator and the photosensor. The parameters that influence the CRT are examined and the history, state-of-the-art, and ongoing developments are reviewed. Finally, the interplay between these components and the optimization of the overall detector design are considered. Based on the knowledge gained to date, it appears feasible to improve the CRT from the values of 200-400 ps achieved by current state-of-the-art TOF-PET systems to about 100 ps or less, even though this may require the implementation of advanced methods such as time resolution recovery. At the same time, it appears unlikely that a system-level CRT in the order of â¼10 ps can be reached with conventional scintillation detectors. Such a CRT could eliminate the need for conventional tomographic image reconstruction and a search for new approaches to timestamp annihilation photons with ultra-high precision is therefore warranted. While the focus of this review is on timing performance, it attempts to approach the topic from a clinically driven perspective, i.e. bearing in mind that the ultimate goal is to optimize the value of PET in research and (personalized) medicine.
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Tomografía de Emisión de Positrones , Fotones , Física , Conteo por Cintilación , TecnologíaRESUMEN
We consider measures of nonlinearity (MoNs) of a polynomial curve in two-dimensions (2D), as previously studied in our Fusion 2010 and 2019 ICCAIS papers. Our previous work calculated curvature measures of nonlinearity (MoNs) using (i) extrinsic curvature, (ii) Bates and Watts parameter-effects curvature, and (iii) direct parameter-effects curvature. In this paper, we have introduced the computation and analysis of a number of new MoNs, including Beale's MoN, Linssen's MoN, Li's MoN, and the MoN of Straka, Duník, and SÌimandl. Our results show that all of the MoNs studied follow the same type of variation as a function of the independent variable and the power of the polynomial. Secondly, theoretical analysis and numerical results show that the logarithm of the mean square error (MSE) is an affine function of the logarithm of the MoN for each type of MoN. This implies that, when the MoN increases, the MSE increases. We have presented an up-to-date review of various MoNs in the context of non-linear parameter estimation and non-linear filtering. The MoNs studied here can be used to compute MoN in non-linear filtering problems.
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In this manuscript we derive the Cramér-Rao Lower Bound (CRLB) of the monoexponential diffusion-weighted signal model under a realistic noise assumption, and propose a formulation to obtain optimized sets of b-values that maximize the noise performance of the Apparent Diffusion Coefficient (ADC) maps given a target ADC and a signal-to-noise ratio. Therefore, for various sets of parameters (S0 and ADC), signal-to-noise ratios (SNR) and noise distribution, we computed optimized sets of b-values using CRLB-based analysis in two different ways: (i) through a greedy algorithm where b-values from a pool of candidates were added iteratively to the set, and (ii) through a two b-value search algorithm were all two b-value combinations of the pool of candidates were tested. Further, optimized sets of b-values were computed from synthetic data, phantoms, and in-vivo liver diffusion-weighted imaging (DWI) experiments to validate the CRLB-based analysis. The optimized sets of b-values obtained through the proposed CRLB-based analysis showed good agreement with the optimized sets obtained experimentally from synthetic, phantoms, and in-vivo liver data. The variance of the ADC maps decreased when employing the optimized set of b-values compared to various sets of b-values proposed in the literature for in-vivo liver DWI, although differences of notable magnitude between noise models and optimization strategies were not found. In addition, the higher b-values decreased for lower SNR under the Rician noise distribution. Optimization of the set b-values is critical to maximize the noise performance (i.e., maximize the precision and minimize the variance) of the estimated ADC maps in diffusion-weighted MRI. Hence, the proposed approach may help to optimize and standardize liver diffusion-weighted MRI acquisitions by computing optimized set of b-values for a given set of parameters.
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Imagen de Difusión por Resonancia Magnética/estadística & datos numéricos , Hígado/diagnóstico por imagen , Acetona , Algoritmos , Femenino , Voluntarios Sanos , Humanos , Procesamiento de Imagen Asistido por Computador , Distribución Normal , Fantasmas de Imagen , Reproducibilidad de los Resultados , Relación Señal-Ruido , Adulto JovenRESUMEN
Direct position determination (DPD) is currently a hot topic in wireless localization research as it is more accurate than traditional two-step positioning. However, current DPD algorithms are all based on uniform arrays, which have an insufficient degree of freedom and limited estimation accuracy. To improve the DPD accuracy, this paper introduces a coprime array to the position model of multiple non-circular sources with a moving array. To maximize the advantages of this coprime array, we reconstruct the covariance matrix by vectorization, apply a spatial smoothing technique, and converge the subspace data from each measuring position to establish the cost function. Finally, we obtain the position coordinates of the multiple non-circular sources. The complexity of the proposed method is computed and compared with that of other methods, and the Cramerâ»Rao lower bound of DPD for multiple sources with a moving coprime array, is derived. Theoretical analysis and simulation results show that the proposed algorithm is not only applicable to circular sources, but can also improve the positioning accuracy of non-circular sources. Compared with existing two-step positioning algorithms and DPD algorithms based on uniform linear arrays, the proposed technique offers a significant improvement in positioning accuracy with a slight increase in complexity.
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This paper essentially focuses on parameter estimation of multiple wideband emitting sources with time-varying frequencies, such as two-dimensional (2-D) direction of arrival (DOA) and signal sorting, with a low-cost circular synthetic array (CSA) consisting of only two rotating sensors. Our basic idea is to decompose the received data, which is a superimposition of phase measurements from multiple sources into separated groups and separately estimate the DOA associated with each source. Motivated by joint parameter estimation, we propose to adopt the expectation maximization (EM) algorithm in this paper; our method involves two steps, namely, the expectation-step (E-step) and the maximization (M-step). In the E-step, the correspondence of each signal with its emitting source is found. Then, in the M-step, the maximum-likelihood (ML) estimates of the DOA parameters are obtained. These two steps are iteratively and alternatively executed to jointly determine the DOAs and sort multiple signals. Closed-form DOA estimation formulae are developed by ML estimation based on phase data, which also realize an optimal estimation. Directional ambiguity is also addressed by another ML estimation method based on received complex responses. The Cramer-Rao lower bound is derived for understanding the estimation accuracy and performance comparison. The verification of the proposed method is demonstrated with simulations.
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Localization of a moving target in a dual-frequency radars system has now gained considerable attention. The noncoherent localization approach based on a least squares (LS) estimator has been addressed in the literature. Compared with the LS method, a novel localization method based on a two-step weighted least squares estimator is proposed to increase positioning accuracy for a multi-station dual-frequency radars system in this paper. The effects of signal noise ratio and the number of samples on the performance of range estimation are also analyzed in the paper. Furthermore, both the theoretical variance and Cramer-Rao lower bound (CRLB) are derived. The simulation results verified the proposed method.
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An asynchronous time difference of arrival (ATDOA) positioning system requires no time synchronization among all the anchor and target nodes, which makes it highly practical and can be easily deployed. This paper first presents an ATDOA localization model, and then primarily focuses on two new localization algorithms for the system. The first algorithm is a two-step positioning algorithm that combines semidefinite programming (SDP) with a Taylor series method to achieve global convergence as well as superior estimation accuracy, and the second algorithm is a constrained least-squares method that has the advantage of low complexity and fast convergence while maintaining good performance. In addition, a novel receiver re-selection method is presented to significantly improve estimation accuracy. In this paper, we also derive the Cramer-Rao lower bound (CRLB) of the ATDOA positioning system using a distance-dependent noise variance model, which describes a realistic indoor propagation channel.
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This paper investigates the joint target parameter (delay and Doppler) estimation performance of linear frequency modulation (LFM)-based radar networks in a Rice fading environment. The active radar networks are composed of multiple radar transmitters and multichannel receivers placed on moving platforms. First, the log-likelihood function of the received signal for a Rician target is derived, where the received signal scattered off the target comprises of dominant scatterer (DS) component and weak isotropic scatterers (WIS) components. Then, the analytically closed-form expressions of the Cramer-Rao lower bounds (CRLBs) on the Cartesian coordinates of target position and velocity are calculated, which can be adopted as a performance metric to access the target parameter estimation accuracy for LFM-based radar network systems in a Rice fading environment. It is found that the cumulative Fisher information matrix (FIM) is a linear combination of both DS component and WIS components, and it also demonstrates that the joint CRLB is a function of signal-to-noise ratio (SNR), target's radar cross section (RCS) and transmitted waveform parameters, as well as the relative geometry between the target and the radar network architectures. Finally, numerical results are provided to indicate that the joint target parameter estimation performance of active radar networks can be significantly improved with the exploitation of DS component.
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The localization of a sensor in wireless sensor networks (WSNs) has now gained considerable attention. Since the transmit power and path loss exponent (PLE) are two critical parameters in the received signal strength (RSS) localization technique, many RSS-based location methods, considering the case that both the transmit power and PLE are unknown, have been proposed in the literature. However, these methods require a search process, and cannot give a closed-form solution to sensor localization. In this paper, a novel RSS localization method with a closed-form solution based on a two-step weighted least squares estimator is proposed for the case with the unknown transmit power and uncertainty in PLE. Furthermore, the complete performance analysis of the proposed method is given in the paper. Both the theoretical variance and Cramer-Rao lower bound (CRLB) are derived. The relationships between the deterministic CRLB and the proposed stochastic CRLB are presented. The paper also proves that the proposed method can reach the stochastic CRLB.
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In this paper, we consider the problem of the accuracy of estimating the location and other attributes of a moving single molecule whose trajectory is imaged by fluorescence microscopy. As accuracy in parameter estimation is closely related to the Fisher information matrix, we first give a general expression of the Fisher information matrix for the estimated parameters for a single object moving in three-dimensional (3D) space. Explicit Cramér-Rao lower bound (CRLB) expressions are then obtained from the Fisher information matrix for a single object moving in the two-dimensional (2D) focus plane with the object trajectory being either linear or circular. We also investigate how extraneous noise sources, pixelation, parameters of the detection system and parameters of the trajectory affect the limit of the accuracy. The results obtained in this paper provide insights that enable the experimentalists to optimize their experimental setups for tracking single molecules in order to achieve the best possible accuracy. They are also applicable to the general problem of tracking an object using quantum limited detectors.