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  • 1
    Online Resource
    Online Resource
    Characterizations of Irregular Multigenerator Gabor Frame on Periodic Subsets of ℝ
    Hindawi Limited ; 2012
    In:  Abstract and Applied Analysis Vol. 2012 ( 2012), p. 1-14
    Details
    In: Abstract and Applied Analysis, Hindawi Limited, Vol. 2012 ( 2012), p. 1-14
    Abstract: We consider the multigenerator system { E m b l T n a l φ l , m , n ∈ ℤ , l = 0 , … , r - 1 } for φ 0 , … , φ r - 1 ∈ L 2 ( 𝕊 ) and a 0 , b 0 , … , a r - 1 , b r - 1 〉 0 , where the parameters b 0 , … , b r - 1 〉 0 are not necessary the same. With the help of frame theory, we provide some sufficient or necessary conditions for the system to be a frame for L 2 ( 𝕊 ) . Moreover, we present some characterizations for this system to be a Parseval frame.
    Type of Medium: Online Resource
    ISSN: 1085-3375 , 1687-0409
    URL: Article
    DOI: 10.1155/2012/746823
    Language: English
    Publisher: Hindawi Limited
    Publication Date: 2012
    detail.hit.zdb_id: 2064801-7
    SSG: 17,1
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  • 2
    Online Resource
    Online Resource
    Wigner-Ville Distribution Associated with the Linear Canonical Transform
    Hindawi Limited ; 2012
    In:  Journal of Applied Mathematics Vol. 2012 ( 2012), p. 1-14
    Details
    In: Journal of Applied Mathematics, Hindawi Limited, Vol. 2012 ( 2012), p. 1-14
    Abstract: The linear canonical transform is shown to be one of the most powerful tools for nonstationary signal processing. Based on the properties of the linear canonical transform and the classical Wigner-Ville transform, this paper investigates the Wigner-Ville distribution in the linear canonical transform domain. Firstly, unlike the classical Wigner-Ville transform, a new definition of Wigner-Ville distribution associated with the linear canonical transform is given. Then, the main properties of the newly defined Wigner-Ville transform are investigated in detail. Finally, the applications of the newly defined Wigner-Ville transform in the linear-frequency-modulated signal detection are proposed, and the simulation results are also given to verify the derived theory.
    Type of Medium: Online Resource
    ISSN: 1110-757X , 1687-0042
    URL: Article
    DOI: 10.1155/2012/740161
    Language: English
    Publisher: Hindawi Limited
    Publication Date: 2012
    detail.hit.zdb_id: 2578385-3
    SSG: 17,1
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  • 3
    Online Resource
    Online Resource
    Integral Equation-Wavelet Collocation Method for Geometric Transformation and Application to Image Processing
    Hindawi Limited ; 2014
    In:  Abstract and Applied Analysis Vol. 2014 ( 2014), p. 1-17
    Details
    In: Abstract and Applied Analysis, Hindawi Limited, Vol. 2014 ( 2014), p. 1-17
    Abstract: Geometric (or shape) distortion may occur in the data acquisition phase in information systems, and it can be characterized by geometric transformation model. Once the distorted image is approximated by a certain geometric transformation model, we can apply its inverse transformation to remove the distortion for the geometric restoration. Consequently, finding a mathematical form to approximate the distorted image plays a key role in the restoration. A harmonic transformation cannot be described by any fixed functions in mathematics. In fact, it is represented by partial differential equation (PDE) with boundary conditions. Therefore, to develop an efficient method to solve such a PDE is extremely significant in the geometric restoration. In this paper, a novel wavelet-based method is presented, which consists of three phases. In phase 1, the partial differential equation is converted into boundary integral equation and representation by an indirect method. In phase 2, the boundary integral equation and representation are changed to plane integral equation and representation by boundary measure formula. In phase 3, the plane integral equation and representation are then solved by a method we call wavelet collocation. The performance of our method is evaluated by numerical experiments.
    Type of Medium: Online Resource
    ISSN: 1085-3375 , 1687-0409
    URL: Article
    DOI: 10.1155/2014/798080
    Language: English
    Publisher: Hindawi Limited
    Publication Date: 2014
    detail.hit.zdb_id: 2064801-7
    SSG: 17,1
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  • 4
    Online Resource
    Online Resource
    Endpoint Sobolev regularity of higher order maximal commutators
    Springer Science and Business Media LLC ; 2023
    In:  Banach Journal of Mathematical Analysis Vol. 17, No. 4 ( 2023-10)
    Details
    In: Banach Journal of Mathematical Analysis, Springer Science and Business Media LLC, Vol. 17, No. 4 ( 2023-10)
    Type of Medium: Online Resource
    ISSN: 2662-2033 , 1735-8787
    URL: Article
    DOI: 10.1007/s43037-023-00288-9
    Language: English
    Publisher: Springer Science and Business Media LLC
    Publication Date: 2023
    detail.hit.zdb_id: 2395499-1
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  • 5
    Online Resource
    Online Resource
    Multiple-Model Cardinality Balanced Multitarget Multi-Bernoulli Filter for Tracking Maneuvering Targets
    Hindawi Limited ; 2013
    In:  Journal of Applied Mathematics Vol. 2013 ( 2013), p. 1-16
    Details
    In: Journal of Applied Mathematics, Hindawi Limited, Vol. 2013 ( 2013), p. 1-16
    Abstract: By integrating the cardinality balanced multitarget multi-Bernoulli (CBMeMBer) filter with the interacting multiple models (IMM) algorithm, an MM-CBMeMBer filter is proposed in this paper for tracking multiple maneuvering targets in clutter. The sequential Monte Carlo (SMC) method is used to implement the filter for generic multi-target models and the Gaussian mixture (GM) method is used to implement the filter for linear-Gaussian multi-target models. Then, the extended Kalman (EK) and unscented Kalman filtering approximations for the GM-MM-CBMeMBer filter to accommodate mildly nonlinear models are described briefly. Simulation results are presented to show the effectiveness of the proposed filter.
    Type of Medium: Online Resource
    ISSN: 1110-757X , 1687-0042
    URL: Article
    DOI: 10.1155/2013/727430
    Language: English
    Publisher: Hindawi Limited
    Publication Date: 2013
    detail.hit.zdb_id: 2578385-3
    SSG: 17,1
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