The Experts below are selected from a list of 36777 Experts worldwide ranked by ideXlab platform
Bertrand David - One of the best experts on this subject based on the ideXlab platform.
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Fast and stable YAST algorithm for principal and minor subspace tracking
IEEE_J_SP, 2008Co-Authors: Roland Badeau, Gael Richard, Bertrand DavidAbstract:This paper presents a new implementation of the YAST algorithm for principal and minor subspace tracking. YAST was initially derived from the Subspace Projection (SP) algorithm by C.E. Davila, which was known for its exceptional convergence rate, compared to other classical principal subspace trackers. The novelty in the YAST algorithm was the lower computational cost (linear if the data correlation matrix satisfies a so-called shift-invariance property), and the extension to minor subspace tracking. However, the original implementation of the YAST algorithm suffered from a numerical stability problem (the subspace weighting matrix slowly loses its Orthonormality). We thus propose in this paper a new implementation of YAST, whose stability is established theoretically and tested via numerical simulations. This algorithm combines all the desired properties for a subspace tracker: remarkably high convergence rate, lowest steady state error, linear complexity, and numerical stability regarding the Orthonormality of the subspace weighting matrix.
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YAST Algorithm for Minor Subspace Tracking
2006Co-Authors: Roland Badeau, Bertrand David, Gael RichardAbstract:This paper introduces a new algorithm for tracking the minor subspace of the correlation matrix associated with time series. This algorithm is shown to have a better convergence rate than existing methods. Moreover, it guarantees the Orthonormality of the subspace weighting matrix at each iteration, and reaches a linear complexity.
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Yet Another Subspace Tracker
2005Co-Authors: Roland Badeau, Bertrand David, Gael RichardAbstract:This paper introduces a new algorithm for tracking the major subspace of the correlationmatrix associated with time series. This algorithm greatly outperforms many well-known subspace trackers in terms of subspace estimation. Moreover, it guarantees the Orthonormality of the subspace weighting matrix at each iteration, and reaches the lowest complexity found in the literature.
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Fast Approximated Power Iteration Subspace Tracking
IEEE Transactions on Signal Processing, 2005Co-Authors: Roland Badeau, Bertrand David, Gael RichardAbstract:This paper introduces a fast implementation of the power iteration method for subspace tracking, based on an approximation less restrictive than the well known projection approximation. This algorithm, referred to as the fast API method, guarantees the Orthonormality of the subspace weighting matrix at each iteration. Moreover, it outperforms many subspace trackers related to the power iteration method, such as PAST, NIC, NP3 and OPAST, while having the same computational complexity. The API method is designed for both exponential windows and sliding windows. Our numerical simulations show that sliding windows offer a faster tracking response to abrupt signal variations.
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sliding window orthonormal past algorithm
International Conference on Acoustics Speech and Signal Processing, 2003Co-Authors: Roland Badeau, Gael Richard, K Abedmeraim, Bertrand DavidAbstract:This paper introduces an orthonormal version of the sliding-window projection approximation subspace tracker (PAST). The new algorithm guarantees the Orthonormality of the signal subspace basis at each iteration. Moreover, it has the same complexity as the original PAST algorithm, and like the more computationally demanding natural power (NP) method, it satisfies a global convergence property, and reaches an excellent tracking performance.
Gael Richard - One of the best experts on this subject based on the ideXlab platform.
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Fast and stable YAST algorithm for principal and minor subspace tracking
IEEE_J_SP, 2008Co-Authors: Roland Badeau, Gael Richard, Bertrand DavidAbstract:This paper presents a new implementation of the YAST algorithm for principal and minor subspace tracking. YAST was initially derived from the Subspace Projection (SP) algorithm by C.E. Davila, which was known for its exceptional convergence rate, compared to other classical principal subspace trackers. The novelty in the YAST algorithm was the lower computational cost (linear if the data correlation matrix satisfies a so-called shift-invariance property), and the extension to minor subspace tracking. However, the original implementation of the YAST algorithm suffered from a numerical stability problem (the subspace weighting matrix slowly loses its Orthonormality). We thus propose in this paper a new implementation of YAST, whose stability is established theoretically and tested via numerical simulations. This algorithm combines all the desired properties for a subspace tracker: remarkably high convergence rate, lowest steady state error, linear complexity, and numerical stability regarding the Orthonormality of the subspace weighting matrix.
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YAST Algorithm for Minor Subspace Tracking
2006Co-Authors: Roland Badeau, Bertrand David, Gael RichardAbstract:This paper introduces a new algorithm for tracking the minor subspace of the correlation matrix associated with time series. This algorithm is shown to have a better convergence rate than existing methods. Moreover, it guarantees the Orthonormality of the subspace weighting matrix at each iteration, and reaches a linear complexity.
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Yet Another Subspace Tracker
2005Co-Authors: Roland Badeau, Bertrand David, Gael RichardAbstract:This paper introduces a new algorithm for tracking the major subspace of the correlationmatrix associated with time series. This algorithm greatly outperforms many well-known subspace trackers in terms of subspace estimation. Moreover, it guarantees the Orthonormality of the subspace weighting matrix at each iteration, and reaches the lowest complexity found in the literature.
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Fast Approximated Power Iteration Subspace Tracking
IEEE Transactions on Signal Processing, 2005Co-Authors: Roland Badeau, Bertrand David, Gael RichardAbstract:This paper introduces a fast implementation of the power iteration method for subspace tracking, based on an approximation less restrictive than the well known projection approximation. This algorithm, referred to as the fast API method, guarantees the Orthonormality of the subspace weighting matrix at each iteration. Moreover, it outperforms many subspace trackers related to the power iteration method, such as PAST, NIC, NP3 and OPAST, while having the same computational complexity. The API method is designed for both exponential windows and sliding windows. Our numerical simulations show that sliding windows offer a faster tracking response to abrupt signal variations.
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sliding window orthonormal past algorithm
International Conference on Acoustics Speech and Signal Processing, 2003Co-Authors: Roland Badeau, Gael Richard, K Abedmeraim, Bertrand DavidAbstract:This paper introduces an orthonormal version of the sliding-window projection approximation subspace tracker (PAST). The new algorithm guarantees the Orthonormality of the signal subspace basis at each iteration. Moreover, it has the same complexity as the original PAST algorithm, and like the more computationally demanding natural power (NP) method, it satisfies a global convergence property, and reaches an excellent tracking performance.
Roland Badeau - One of the best experts on this subject based on the ideXlab platform.
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Fast and stable YAST algorithm for principal and minor subspace tracking
IEEE_J_SP, 2008Co-Authors: Roland Badeau, Gael Richard, Bertrand DavidAbstract:This paper presents a new implementation of the YAST algorithm for principal and minor subspace tracking. YAST was initially derived from the Subspace Projection (SP) algorithm by C.E. Davila, which was known for its exceptional convergence rate, compared to other classical principal subspace trackers. The novelty in the YAST algorithm was the lower computational cost (linear if the data correlation matrix satisfies a so-called shift-invariance property), and the extension to minor subspace tracking. However, the original implementation of the YAST algorithm suffered from a numerical stability problem (the subspace weighting matrix slowly loses its Orthonormality). We thus propose in this paper a new implementation of YAST, whose stability is established theoretically and tested via numerical simulations. This algorithm combines all the desired properties for a subspace tracker: remarkably high convergence rate, lowest steady state error, linear complexity, and numerical stability regarding the Orthonormality of the subspace weighting matrix.
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YAST Algorithm for Minor Subspace Tracking
2006Co-Authors: Roland Badeau, Bertrand David, Gael RichardAbstract:This paper introduces a new algorithm for tracking the minor subspace of the correlation matrix associated with time series. This algorithm is shown to have a better convergence rate than existing methods. Moreover, it guarantees the Orthonormality of the subspace weighting matrix at each iteration, and reaches a linear complexity.
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Yet Another Subspace Tracker
2005Co-Authors: Roland Badeau, Bertrand David, Gael RichardAbstract:This paper introduces a new algorithm for tracking the major subspace of the correlationmatrix associated with time series. This algorithm greatly outperforms many well-known subspace trackers in terms of subspace estimation. Moreover, it guarantees the Orthonormality of the subspace weighting matrix at each iteration, and reaches the lowest complexity found in the literature.
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Fast Approximated Power Iteration Subspace Tracking
IEEE Transactions on Signal Processing, 2005Co-Authors: Roland Badeau, Bertrand David, Gael RichardAbstract:This paper introduces a fast implementation of the power iteration method for subspace tracking, based on an approximation less restrictive than the well known projection approximation. This algorithm, referred to as the fast API method, guarantees the Orthonormality of the subspace weighting matrix at each iteration. Moreover, it outperforms many subspace trackers related to the power iteration method, such as PAST, NIC, NP3 and OPAST, while having the same computational complexity. The API method is designed for both exponential windows and sliding windows. Our numerical simulations show that sliding windows offer a faster tracking response to abrupt signal variations.
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sliding window orthonormal past algorithm
International Conference on Acoustics Speech and Signal Processing, 2003Co-Authors: Roland Badeau, Gael Richard, K Abedmeraim, Bertrand DavidAbstract:This paper introduces an orthonormal version of the sliding-window projection approximation subspace tracker (PAST). The new algorithm guarantees the Orthonormality of the signal subspace basis at each iteration. Moreover, it has the same complexity as the original PAST algorithm, and like the more computationally demanding natural power (NP) method, it satisfies a global convergence property, and reaches an excellent tracking performance.
P.p. Vaidyanathan - One of the best experts on this subject based on the ideXlab platform.
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ISCAS (3) - Iterative algorithm for the design of optimal FIR analysis/synthesis filters for overdecimated filter banks
2004 IEEE International Symposium on Circuits and Systems (IEEE Cat. No.04CH37512), 2004Co-Authors: A. Tkacenko, P.p. VaidyanathanAbstract:Recently, much attention has been given to the design of signal-adapted filter banks, in which the filter banks are designed to optimize a particular objective function, i.e. coding gain or a multiresolution criterion, for a particular class of input signals. If we restrict the analysis/synthesis filters to satisfy an Orthonormality or biorthogonality condition, but put no restrictions on filter orders, then often times it is known how to choose the filters optimally for the objectives mentioned above. However, such filters are often unrealizable infinite order filters. In this paper, we consider the design of optimal analysis/synthesis filters in which the only restriction is that they must be finite impulse response (FIR) filters. We focus here on minimizing the mean squared reconstruction error for overdecimated filter banks. An iterative method to alternately design the analysis and synthesis banks is presented in which the error is monotonic nonincreasing for each iteration. Simulation results provided show the merit of the proposed algorithm.
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ICASSP (3) - Phase linearization of filters in analysis/synthesis filter banks
Proceedings of ICASSP '94. IEEE International Conference on Acoustics Speech and Signal Processing, 1994Co-Authors: T. Chen, P.p. VaidyanathanAbstract:Analysis/synthesis filter banks with perfect reconstruction property have attracted much attention. In some applications, particularly image coding, it is desirable to design filter banks in which the filters have linear phase. We present a method of linearizing the passband phase response of filters in any given filter bank. While linearizing the phase response, this method preserves the magnitude response of the filters, the perfect reconstruction property, and the paraunitary property (Orthonormality). We present the eigen-approach design and the anticausal implementation of this technique. Using this technique, we illustrate the importance of linear phase in subband coding. >
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On orthonormal wavelets and paraunitary filter banks
IEEE Transactions on Signal Processing, 1993Co-Authors: A.k. Soman, P.p. VaidyanathanAbstract:The known result that a binary-tree-structured filter bank with the same paraunitary polyphase matrix on all levels generates an orthonormal basis is generalized to binary trees having different paraunitary matrices on each level. A converse result that every orthonormal wavelet basis can be generated by a tree-structured filter bank having paraunitary polyphase matrices is then proved. The concept of orthonormal bases is extended to generalized (nonbinary) tree structures, and it is seen that a close relationship exists between Orthonormality and paraunitariness. It is proved that a generalized tree structure with paraunitary polyphase matrices produces an orthonormal basis. Since not all phases can be generated by tree-structured filter banks, it is proved that if an orthonormal basis can be generated using a tree structure, it can be generated specifically by a paraunitary tree. >
A Di Piazza - One of the best experts on this subject based on the ideXlab platform.
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completeness and Orthonormality of the volkov states and the volkov propagator in configuration space
Physical Review D, 2018Co-Authors: A Di PiazzaAbstract:Volkov states and Volkov propagator are the basic analytical tools to investigate QED processes occurring in the presence of an intense plane-wave electromagnetic field. In the present paper we provide alternative and relatively simple proofs of the completeness and of the Orthonormality at a fixed time of the Volkov states. Concerning the completeness, we exploit some known properties of the Green's function of the Dirac operator in a plane wave, whereas the Orthonormality of the Volkov states is proved, relying only on a geometric argument based on the Gauss theorem in four dimensions. In relation with the completeness of the Volkov states, we also study some analytical properties of the Green's function of the Dirac operator in a plane wave, which we explicitly prove to coincide with the Volkov propagator in configuration space. In particular, a closed-form expression in terms of modified Bessel functions and Hankel functions is derived by means of the operator technique in a plane wave and different asymptotic forms are determined. Finally, the transformation properties of the Volkov propagator under general gauge transformations and a general gauge-invariant expression of the so-called dressed mass in configuration space are presented.
