1,721,245 research outputs found
On the identifiability of bilinear systems
No full textEstimation of the unknown parameters that characterize a bilinear system is of primary importance in many applications. By introducing a novel concept of the derivative system for a given bilinear system, it is shown that the Fisher information matrix for a data set generated by a bilinear system with additive Gaussian measurement noise can be expressed explicitly in terms of the outputs of its derivative system which is also bilinear. A connection between the identifiability of the unknown parameters and the output reachability of the derivative system is established. For a bilinear system with a piecewise constant input and uniformly sampled output data, a trackable condition is derived for local identifiability.</p
The fisher information matrix for two-dimensional separable-denominator continuous systems
No full textThe Fisher information matrix for two-dimensional separable-denominator contiuous systems was discussed. The Fisher matrix for the Gaussian noisy output data was derived in an explicit form in terms of system parameters. For a uniformly sampled data it was shown that, the information matric can be expressed through the solutions of Lyapunov equations.</p
The CRLB for bilinear systems and its biomedical applications
No full textThe Cramer Rao lower bound (CRLB) provides a lower bound on the covariance matrix of any unbiased estimator of unknown parameters. It is shown in this paper that the CRLB for a data set generated by a bilinear system with additive Gaussian measurement noise can be expressed explicitly in terms of the outputs of its derivative system which is also bilinear. For bilinear systems with piecewise constant inputs the CRLB for uniformly sampled data can be efficiently computed through solving certain Lyapunov equations. The theoretical results are illustrated through an example arising from surface plasmon resonance experiments for the determination of the kinetic parameters of protein-protein interactions.</p
The Cramer-Rao lower bound for bilinear systems
No full textEstimation of the unknown parameters that characterize a bilinear system is of primary importance in many applications. The Cramer-Rao lower bound (CRLB) provides a lower bound on the covariance matrix of any unbiased estimator of unknown parameters. It is widely applied to investigate the limit of the accuracy with which parameters can be estimated from noisy data. Here it is shown that the CRLB for a data set generated by a bilinear system with additive Gaussian measurement noise can be expressed explicitly in terms of the outputs of its derivative system which is also bilinear. A connection between the nonsingularity of the Fisher information matrix and the local identifiability of the unknown parameters is exploited to derive local identifiability conditions of bilinear systems using the concept of the derivative system. It is shown that for bilinear systems with piecewise constant inputs, the CRLB for uniformly sampled data can be efficiently computed through solving a Lyapunov equation. In addition, a novel method is proposed to derive the asymptotic CRLB when the number of acquired data samples approaches infinity. These theoretical results are illustrated through the simulation of surface plasmon resonance experiments for the determination of the kinetic parameters of protein-protein interactions.</p
Calculation of the Fisher information matrix for multidimensional data sets
No full textThis paper shows how the Fisher information matrix of a given two-dimensional (2D) data set can be expressed using the matrices that determine the 2D system that generates the data set. For uniformly sampled data it is shown how the Fisher information matrix can be expressed through the solutions of Lyapunov equations. The novel techniques are demonstrated with an example arising from nuclear magnetic resonance spectroscopy.</p
A state space approach to noise reduction of 3D fluorescent microscopy images
No full textAn algorithm is presented to calculate a state space realization of a 3D image set. It is based on interpreting the image set as the impulse response of a 3D separable system. As an application it is shown how the approximation steps, including balanced model reduction methods, in the algorithm can be used to suppress noise in 3D image sets. The approach was motivated by a practical problem in the analysis of 3D fluorescent microscopy image data of fluorescently labelled cells.</p
Cramer-Rao lower bound for parameter estimation in nonlinear systems
No full textCalculation of the Cramer-Rao lower bound, i.e., the inverse of the Fisher information matrix, for output data sets of a general nonlinear system is a challenging problem and is considered in this letter. It is shown that the Fisher information matrix for a data set generated by a nonlinear system with additive Gaussian measurement noise can be expressed in terms of the outputs of its derivative system that is also a nonlinear system. An example is considered arising from surface plasmon resonance experiments to determine the dynamic parameters of molecular interactions.</p
Achievable Accuracy of parameter estimation for multidimensional NMR experiments
No full textA fundamental issue in NMR spectroscopy is the estimation of parameters such as the Larmor frequencies of nuclei, J coupling constants, and relaxation rates. The Cramer–Rao lower bound provides a method to assess the best achievable accuracy of parameter estimates resulting from an unbiased estimation procedure. We show how the Cramer–Rao lower bound can be calculated for data obtained from multidimensional NMR experiments. The Cramer–Rao lower bound is compared to the variance of parameter estimates for simulated data using a least-squares estimation procedure. It is also shown how our results on the Cramer–Rao lower bound can be used to analyze whether an experimental design can be improved to provide experimental data which can result in parameter estimates with higher accuracy. The concept of nonuniform averaging in the indirect dimension is introduced and studied in connection with nonuniform sampling of the data
Three-dimensional state space realization algorithm: Noise suppression of fluorescence microscopy images and point spread functions
No full textA recently developed algorithm is applied to calculate a state space realization of a 3D microscopy image set. It is based on interpreting the image set as the impulse response of a 3D separable system. As an application it is shown how this algorithm, combined with approximation steps, can be used to suppress noise in 3D experimental point spread functions. The approach was motivated by a well known problem that a noisy point spread function degrades the results of deconvolution algorithms for the restoration of 3D fluorescence microscopy image sets. The proposed approach can also be applied to 3D fluorescence microscopy image sets of cells.</p
Influence of prior knowledge on the accuracy limit of parameter estimation in single-molecule fluorescence microscopy
No full textIn estimation theory, it is known that prior knowledge of parameters can improve the Cramér-Rao lower bound (CRLB). In this paper, we study the influence of prior knowledge on the CRLB of the estimates of the parameters that describe the trajectory of a moving object (single molecule). Since the CRLB is obtained from the inverse of the Fisher information matrix, we present a general expression of the Fisher information matrix in terms of the image function, the object trajectory and the prior knowledge matrix. Applying this expression to an object moving linearly in a two-dimensional (2D) plane with two distinct cases of prior knowledge, explicit CRLB expressions are derived. From these expressions, we show that the improvement in the CRLB of the parameter estimates is dependent on which parameters are known.</p
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