The Experts below are selected from a list of 22674 Experts worldwide ranked by ideXlab platform

Yuejie Chi - One of the best experts on this subject based on the ideXlab platform.

  • robust spectral compressed sensing via structured matrix completion
    IEEE Transactions on Information Theory, 2014
    Co-Authors: Yuxin Chen, Yuejie Chi
    Abstract:

    This paper explores the problem of spectral compressed sensing, which aims to recover a spectrally sparse signal from a small random subset of its n time domain samples. The signal of interest is assumed to be a superposition of r multidimensional complex sinusoids, while the underlying frequencies can assume any continuous values in the normalized frequency domain. Conventional compressed sensing paradigms suffer from the basis mismatch issue when imposing a discrete dictionary on the Fourier Representation. To address this issue, we develop a novel algorithm, called enhanced matrix completion (EMaC), based on structured matrix completion that does not require prior knowledge of the model order. The algorithm starts by arranging the data into a low-rank enhanced form exhibiting multifold Hankel structure, and then attempts recovery via nuclear norm minimization. Under mild incoherence conditions, EMaC allows perfect recovery as soon as the number of samples exceeds the order of r log 4 n, and is stable against bounded noise. Even if a constant portion of samples are corrupted with arbitrary magnitude, EMaC still allows exact recovery, provided that the sample complexity exceeds the order of r 2 log 3 n. Along the way, our results demonstrate the power of convex relaxation in completing a low-rank multifold Hankel or Toeplitz matrix from minimal observed entries. The performance of our algorithm and its applicability to super resolution are further validated by numerical experiments.

  • Robust spectral compressed sensing via structured matrix completion
    IEEE Transactions on Information Theory, 2014
    Co-Authors: Yuxin Chen, Yuejie Chi
    Abstract:

    The paper explores the problem of \emph{spectral compressed sensing}, which aims to recover a spectrally sparse signal from a small random subset of its $n$ time domain samples. The signal of interest is assumed to be a superposition of $r$ multi-dimensional complex sinusoids, while the underlying frequencies can assume any \emph{continuous} values in the normalized frequency domain. Conventional compressed sensing paradigms suffer from the basis mismatch issue when imposing a discrete dictionary on the Fourier Representation. To address this issue, we develop a novel algorithm, called \emph{Enhanced Matrix Completion (EMaC)}, based on structured matrix completion that does not require prior knowledge of the model order. The algorithm starts by arranging the data into a low-rank enhanced form exhibiting multi-fold Hankel structure, and then attempts recovery via nuclear norm minimization. Under mild incoherence conditions, EMaC allows perfect recovery as soon as the number of samples exceeds the order of $r\log^{4}n$, and is stable against bounded noise. Even if a constant portion of samples are corrupted with arbitrary magnitude, EMaC still allows exact recovery, provided that the sample complexity exceeds the order of $r^{2}\log^{3}n$. Along the way, our results demonstrate the power of convex relaxation in completing a low-rank multi-fold Hankel or Toeplitz matrix from minimal observed entries. The performance of our algorithm and its applicability to super resolution are further validated by numerical experiments.

A Piccolroaz - One of the best experts on this subject based on the ideXlab platform.

  • free and forced wave propagation in a rayleigh beam grid flat bands dirac cones and vibration localization vs isotropization
    International Journal of Solids and Structures, 2019
    Co-Authors: G Bordiga, L Cabras, Davide Bigoni, A Piccolroaz
    Abstract:

    Abstract In-plane wave propagation in a periodic rectangular frame structure, which includes axial and flexural deformation, the latter enhanced with rotational inertia (so-called ‘Rayleigh beams’), is analyzed both with a Floquet-Bloch exact formulation for free oscillations and with a numerical treatment (developed with PML absorbing boundary conditions) for forced vibrations (including Fourier Representation and energy flux evaluations), induced by a concentrated force or moment. A complex interplay is observed between axial and flexural vibrations (not found in the common idealization of out-of-plane motion), giving rise to several forms of vibration localization: ‘X-’, ‘cross-’ and ‘star-’ shaped, and channel propagation. These localizations are triggered by several factors, including rotational inertia and slenderness of the beams and the type of forcing source (concentrated force or moment). Although the considered grid of beams introduces an orthotropy in the mechanical response, a surprising ‘isotropization’ of the vibration is observed at special frequencies. Moreover, rotational inertia is shown to ‘sharpen’ degeneracies related to Dirac cones (which become more pronounced when the aspect ratio of the grid is increased), while the slenderness can be tuned to achieve a perfectly flat band in the dispersion diagram. The obtained results can be exploited in the realization of metamaterials designed to filter waves during propagation.

  • free and forced wave propagation in a rayleigh beam grid flat bands dirac cones and vibration localization vs isotropization
    arXiv: Classical Physics, 2018
    Co-Authors: G Bordiga, L Cabras, Davide Bigoni, A Piccolroaz
    Abstract:

    In-plane wave propagation in a periodic rectangular grid beam structure, which includes rotational inertia (so-called 'Rayleigh beams'), is analyzed both with a Floquet-Bloch exact formulation for free oscillations and with a numerical treatment (developed with PML absorbing boundary conditions) for forced vibrations (including Fourier Representation and energy flux evaluations), induced by a concentrated force or moment. A complex interplay is observed between axial and flexural vibrations (not found in the common idealization of out-of-plane motion), giving rise to several forms of vibration localization: 'X-', 'cross-' and 'star-' shaped, and channel propagation. These localizations are triggered by several factors, including rotational inertia and slenderness of the beams and the type of forcing source (concentrated force or moment). Although the considered grid of beams introduces an orthotropy in the mechanical response, a surprising 'isotropization' of the vibration is observed at special frequencies. Moreover, rotational inertia is shown to 'sharpen' degeneracies related to Dirac cones (which become more pronounced when the aspect ratio of the grid is increased), while the slenderness can be tuned to achieve a perfectly flat band in the dispersion diagram. The obtained results can be exploited in the realization of metamaterials designed to control wave propagation.

Yuxin Chen - One of the best experts on this subject based on the ideXlab platform.

  • robust spectral compressed sensing via structured matrix completion
    IEEE Transactions on Information Theory, 2014
    Co-Authors: Yuxin Chen, Yuejie Chi
    Abstract:

    This paper explores the problem of spectral compressed sensing, which aims to recover a spectrally sparse signal from a small random subset of its n time domain samples. The signal of interest is assumed to be a superposition of r multidimensional complex sinusoids, while the underlying frequencies can assume any continuous values in the normalized frequency domain. Conventional compressed sensing paradigms suffer from the basis mismatch issue when imposing a discrete dictionary on the Fourier Representation. To address this issue, we develop a novel algorithm, called enhanced matrix completion (EMaC), based on structured matrix completion that does not require prior knowledge of the model order. The algorithm starts by arranging the data into a low-rank enhanced form exhibiting multifold Hankel structure, and then attempts recovery via nuclear norm minimization. Under mild incoherence conditions, EMaC allows perfect recovery as soon as the number of samples exceeds the order of r log 4 n, and is stable against bounded noise. Even if a constant portion of samples are corrupted with arbitrary magnitude, EMaC still allows exact recovery, provided that the sample complexity exceeds the order of r 2 log 3 n. Along the way, our results demonstrate the power of convex relaxation in completing a low-rank multifold Hankel or Toeplitz matrix from minimal observed entries. The performance of our algorithm and its applicability to super resolution are further validated by numerical experiments.

  • Robust spectral compressed sensing via structured matrix completion
    IEEE Transactions on Information Theory, 2014
    Co-Authors: Yuxin Chen, Yuejie Chi
    Abstract:

    The paper explores the problem of \emph{spectral compressed sensing}, which aims to recover a spectrally sparse signal from a small random subset of its $n$ time domain samples. The signal of interest is assumed to be a superposition of $r$ multi-dimensional complex sinusoids, while the underlying frequencies can assume any \emph{continuous} values in the normalized frequency domain. Conventional compressed sensing paradigms suffer from the basis mismatch issue when imposing a discrete dictionary on the Fourier Representation. To address this issue, we develop a novel algorithm, called \emph{Enhanced Matrix Completion (EMaC)}, based on structured matrix completion that does not require prior knowledge of the model order. The algorithm starts by arranging the data into a low-rank enhanced form exhibiting multi-fold Hankel structure, and then attempts recovery via nuclear norm minimization. Under mild incoherence conditions, EMaC allows perfect recovery as soon as the number of samples exceeds the order of $r\log^{4}n$, and is stable against bounded noise. Even if a constant portion of samples are corrupted with arbitrary magnitude, EMaC still allows exact recovery, provided that the sample complexity exceeds the order of $r^{2}\log^{3}n$. Along the way, our results demonstrate the power of convex relaxation in completing a low-rank multi-fold Hankel or Toeplitz matrix from minimal observed entries. The performance of our algorithm and its applicability to super resolution are further validated by numerical experiments.

Jos B T M Roerdink - One of the best experts on this subject based on the ideXlab platform.

  • polyphase decompositions and shift invariant discrete wavelet transforms in the frequency domain
    Signal Processing, 2010
    Co-Authors: Alle Meije Wink, Jos B T M Roerdink
    Abstract:

    Given a signal and its Fourier transform, we derive formulas for its polyphase decomposition in the frequency domain and for the reconstruction from the polyphase Representation back to the Fourier Representation. We present two frequency-domain implementations of the shift-invariant periodic discrete wavelet transform (SI-DWT) and its inverse: one that is based on frequency-domain polyphase decomposition and a more efficient 'direct' implementation, based on a reorganisation of the a trous algorithm. We analyse the computational complexities of both algorithms, and compare them to existing time-domain and frequency domain implementations of the SI-DWT. We experimentally demonstrate the reduction in computation time achieved by the direct frequency domain implementation of the SI-DWT for wavelet filters with non-compact support.

G Bordiga - One of the best experts on this subject based on the ideXlab platform.

  • free and forced wave propagation in a rayleigh beam grid flat bands dirac cones and vibration localization vs isotropization
    International Journal of Solids and Structures, 2019
    Co-Authors: G Bordiga, L Cabras, Davide Bigoni, A Piccolroaz
    Abstract:

    Abstract In-plane wave propagation in a periodic rectangular frame structure, which includes axial and flexural deformation, the latter enhanced with rotational inertia (so-called ‘Rayleigh beams’), is analyzed both with a Floquet-Bloch exact formulation for free oscillations and with a numerical treatment (developed with PML absorbing boundary conditions) for forced vibrations (including Fourier Representation and energy flux evaluations), induced by a concentrated force or moment. A complex interplay is observed between axial and flexural vibrations (not found in the common idealization of out-of-plane motion), giving rise to several forms of vibration localization: ‘X-’, ‘cross-’ and ‘star-’ shaped, and channel propagation. These localizations are triggered by several factors, including rotational inertia and slenderness of the beams and the type of forcing source (concentrated force or moment). Although the considered grid of beams introduces an orthotropy in the mechanical response, a surprising ‘isotropization’ of the vibration is observed at special frequencies. Moreover, rotational inertia is shown to ‘sharpen’ degeneracies related to Dirac cones (which become more pronounced when the aspect ratio of the grid is increased), while the slenderness can be tuned to achieve a perfectly flat band in the dispersion diagram. The obtained results can be exploited in the realization of metamaterials designed to filter waves during propagation.

  • free and forced wave propagation in a rayleigh beam grid flat bands dirac cones and vibration localization vs isotropization
    arXiv: Classical Physics, 2018
    Co-Authors: G Bordiga, L Cabras, Davide Bigoni, A Piccolroaz
    Abstract:

    In-plane wave propagation in a periodic rectangular grid beam structure, which includes rotational inertia (so-called 'Rayleigh beams'), is analyzed both with a Floquet-Bloch exact formulation for free oscillations and with a numerical treatment (developed with PML absorbing boundary conditions) for forced vibrations (including Fourier Representation and energy flux evaluations), induced by a concentrated force or moment. A complex interplay is observed between axial and flexural vibrations (not found in the common idealization of out-of-plane motion), giving rise to several forms of vibration localization: 'X-', 'cross-' and 'star-' shaped, and channel propagation. These localizations are triggered by several factors, including rotational inertia and slenderness of the beams and the type of forcing source (concentrated force or moment). Although the considered grid of beams introduces an orthotropy in the mechanical response, a surprising 'isotropization' of the vibration is observed at special frequencies. Moreover, rotational inertia is shown to 'sharpen' degeneracies related to Dirac cones (which become more pronounced when the aspect ratio of the grid is increased), while the slenderness can be tuned to achieve a perfectly flat band in the dispersion diagram. The obtained results can be exploited in the realization of metamaterials designed to control wave propagation.