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Marius Soltane - One of the best experts on this subject based on the ideXlab platform.
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A Test of Correlation in the Random Coefficients of an Autoregressive Process
Mathematical Methods of Statistics, 2018Co-Authors: Frédéric Proïa, Marius SoltaneAbstract:A random coefficient autoregressive process in which the coefficients are correlated is investigated. First we look at the existence of a strictly stationary causal solution, we give the second-order stationarity conditions and the autocorrelation function of the process. Then we study some asymptotic properties of the empirical mean and the usual estimators of the process, such as convergence, asymptotic normality and rates of convergence, supplied with appropriate assumptions on the driving perturbations. Our objective is to get an overview of the influence of correlated coefficients in the Estimation Step through a simple model. In particular, the lack of consistency is shown for the Estimation of the autoregressive parameter when the independence hypothesis in the random coefficients is violated. Finally, a consistent Estimation is given together with a testing procedure for the existence of correlation in the coefficients. While convergence properties rely on ergodicity, we use a martingale approach to reach most of the results.
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A test of correlation in the random coefficients of an autoregressive process
arXiv: Statistics Theory, 2016Co-Authors: Frédéric Proïa, Marius SoltaneAbstract:A random coefficient autoregressive process is deeply investigated in which the coefficients are correlated. First we look at the existence of a strictly stationary causal solution, we give the second-order stationarity conditions and the autocorrelation function of the process. Then we study some asymptotic properties of the empirical mean and the usual estimators of the process, such as convergence, asymptotic normality and rates of convergence, supplied with the appropriate assumptions on the driving perturbations. Our objective is to get an overview of the influence of correlated coefficients in the Estimation Step, through a simple model. In particular, the lack of consistency is shown for the Estimation of the autoregressive parameter when the independence hypothesis is violated in the random coefficients. Finally, a consistent Estimation is given together with a testing procedure for the existence of correlation in the coefficients. While convergence properties rely on the ergodicity, we use a martingale approach to reach most of the results.
C. Tepedelenlioglu - One of the best experts on this subject based on the ideXlab platform.
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direct blind equalizers of multiple fir channels a deterministic approach
IEEE Transactions on Signal Processing, 1999Co-Authors: G.b. Giannakis, C. TepedelenliogluAbstract:Blind equalization of single-input multi-output channels has practical value for inverse problems encountered in communications, sonar, and seismic data processing. Relying on diversity (sufficient number of multiple outputs), we bypass the channel Estimation Step and derive direct blind FIR equalizers of co-prime FIR channels. There are no constraints on the inaccessible input, apart from a minimum persistence of excitation condition; the input can be deterministic or random with unknown color or distribution. At moderate SNR (>20 dB), the resulting algorithms remain operational even with very short data records (<100 samples), which makes them valuable for equalization of rapidly fading multipath channels. Complexity, persistence of excitation order, and mean-square error performance tradeoffs are delineated for equalizers of single-shift (semi-blind), pair, or, multiple shifts estimated separately or simultaneously. Optimum and suboptimum combinations of the equalizers' outputs are also studied. Simulations illustrate the proposed algorithms and compare them with dual deterministic channel identification algorithms.
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Direct blind equalizers of multiple FIR channels: a deterministic approach
Conference Record of The Thirtieth Asilomar Conference on Signals Systems and Computers, 1996Co-Authors: G.b. Giannakis, C. TepedelenliogluAbstract:Relying upon diversity (sufficient number of multiple outputs) we by-pass the channel Estimation Step and derive direct blind FIR equalizers of co-prime FIR channels. There are no constraints on the inaccessible input apart from a minimum persistence of excitation condition; the input can be deterministic or random with unknown color or distribution. Complexity, persistence of excitation order, and mean-square error performance trade-offs are delineated for equalizers of single-shift, pair, or, multiple-shifts estimated separately, or simultaneously. Simulations illustrate the proposed algorithms and compare them with dual channel identification algorithms.
Frédéric Proïa - One of the best experts on this subject based on the ideXlab platform.
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A Test of Correlation in the Random Coefficients of an Autoregressive Process
Mathematical Methods of Statistics, 2018Co-Authors: Frédéric Proïa, Marius SoltaneAbstract:A random coefficient autoregressive process in which the coefficients are correlated is investigated. First we look at the existence of a strictly stationary causal solution, we give the second-order stationarity conditions and the autocorrelation function of the process. Then we study some asymptotic properties of the empirical mean and the usual estimators of the process, such as convergence, asymptotic normality and rates of convergence, supplied with appropriate assumptions on the driving perturbations. Our objective is to get an overview of the influence of correlated coefficients in the Estimation Step through a simple model. In particular, the lack of consistency is shown for the Estimation of the autoregressive parameter when the independence hypothesis in the random coefficients is violated. Finally, a consistent Estimation is given together with a testing procedure for the existence of correlation in the coefficients. While convergence properties rely on ergodicity, we use a martingale approach to reach most of the results.
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A test of correlation in the random coefficients of an autoregressive process
arXiv: Statistics Theory, 2016Co-Authors: Frédéric Proïa, Marius SoltaneAbstract:A random coefficient autoregressive process is deeply investigated in which the coefficients are correlated. First we look at the existence of a strictly stationary causal solution, we give the second-order stationarity conditions and the autocorrelation function of the process. Then we study some asymptotic properties of the empirical mean and the usual estimators of the process, such as convergence, asymptotic normality and rates of convergence, supplied with the appropriate assumptions on the driving perturbations. Our objective is to get an overview of the influence of correlated coefficients in the Estimation Step, through a simple model. In particular, the lack of consistency is shown for the Estimation of the autoregressive parameter when the independence hypothesis is violated in the random coefficients. Finally, a consistent Estimation is given together with a testing procedure for the existence of correlation in the coefficients. While convergence properties rely on the ergodicity, we use a martingale approach to reach most of the results.
Soosan Beheshti - One of the best experts on this subject based on the ideXlab platform.
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a noiseless code length method nclm to estimate dimensionality of hyperspectral data
International Conference on Acoustics Speech and Signal Processing, 2009Co-Authors: Masoud Farzam, Soosan BeheshtiAbstract:Hyperspectral image analysis has been subjected to many improvements made in past decade. Yet the accurate Estimation of dimensionality is still a challenge. Since dimension Estimation of the Hyperspectral data is the first Step in analysis of an image, the accuracy of analysis results highly depends on the accuracy of the dimension Estimation Step. Mostly, existing methods isolate the process of dimension Estimation and process of denoising which leads to an inaccurate Estimation of constituent components in the signal. In this paper, the problem of estimating the dimensionality of Hyperspectral data using the concept of “noiseless code length” is addressed. In our proposed method, NCLM, a set of nested subsets including the Hyperspectral data is generated first and then an error comparison approach is utilized by estimating the noiseless data error rather than noisy data error used by the existing methods to find the optimum subset. It has been shown that the estimated noiseless error has a minimum that represents the accurate Estimation of the dimensionality of Hyperspectral data. The comparison of NCLM to other methods shows a substantial improvement in Estimation of dimensionality in Hyperspectral imagery.
Daniel Mozos - One of the best experts on this subject based on the ideXlab platform.
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FPGA Implementation of Abundance Estimation for Spectral Unmixing of Hyperspectral Data Using the Image Space Reconstruction Algorithm
IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 2012Co-Authors: Carlos Gonzalez, Javier Resano, Antonio Plaza, Daniel MozosAbstract:One of the most popular and widely used techniques for analyzing remotely sensed hyperspectral data is spectral unmixing, which relies on two stages: (i) identification of pure spectral signatures (endmembers) in the data, and (ii) Estimation of the abundance of each endmember in each (possibly mixed) pixel. Due to the high dimensionality of the hyperspectral data, spectral unmixing is a very time-consuming task. With recent advances in reconfigurable computing, especially using field programmable gate arrays (FPGAs), hyperspectral image processing algorithms can now be accelerated for on-board exploitation using compact hardware components with small size and cost. Although in previous work several efforts have been directed towards FPGA implementation of endmember extraction algorithms, the abundance Estimation Step has received comparatively much less attention. In this work, we develop a parallel FPGA-based design of the image space reconstruction algorithm (ISRA), a technique for solving linear inverse problems with positive constraints that has been used to estimate the abundance of each endmember in each pixel of a hyperspectral image. It is an iterative algorithm that guarantees convergence (after a certain number of iterations) and positive values in the results of the abundances (an important consideration in unmixing applications). Our system includes a direct memory access (DMA) module and implements a pre-fetching technique to hide the latency of the input/output communications. The method has been implemented on a Virtex-4 XC4VFX60 FPGA (a model that is similar to radiation-hardened FPGAs certified for space operation) and tested using real hyperspectral data sets collected by the Airborne Visible Infra-Red Imaging Spectrometer (AVIRIS) over the Cuprite mining district in Nevada and the Jasper Ridge Biological Preserve in California. Experimental results demonstrate that our hardware version can significantly outperform an equivalent software version, thus being able to provide abundance Estimation results in near real-time, which makes our reconfigurable system appealing for on-board hyperspectral data processing.