Structure of nonstationary Gabor frames and their dual systems
نویسندگان
چکیده
منابع مشابه
Nonstationary Gabor Frames
To overcome the limitation induced by the fixed timefrequency resolution over the whole time-frequency plane of Gabor frames, we propose a simple extension of the Gabor theory leading to the construction of frames with timefrequency resolution evolving over time or frequency. We describe the construction of such frames and give the explicit formulation of the canonical dual frame for some condi...
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We present an application of the dual Gabor frames to image processing. Our algorithm is based on finding some dual Gabor frame generators which reconstructs accurately the elements of the underlying Hilbert space. The advantages of these duals constructed by a polynomial of Gabor frame generators are compared with their canonical dual.
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Nonstationary Gabor frames were recently introduced in [2] and represent a natural generalization of classical Gabor frames by allowing for adaptivity of windows and lattice in either time or frequency. In this paper we show a general existence result for this family of frames. We also construct nonstationary Gabor frames with non-compactly supported windows from a related painless nonorthogona...
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Signal analysis with classical Gabor frames leads to a fixed time-frequency resolution over the whole time-frequency plane. To overcome the limitations imposed by this rigidity, we propose an extension of Gabor theory that leads to the construction of frames with time-frequency resolution changing over time or frequency. We describe the construction of the resulting nonstationary Gabor frames a...
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we present an application of the dual gabor frames to image processing. our algorithm is based on finding some dual gabor frame generators which reconstructs accurately the elements of the underlying hilbert space. the advantages of these duals constructed by a polynomial of gabor frame generators are compared with their canonical dual.
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ژورنال
عنوان ژورنال: Applied and Computational Harmonic Analysis
سال: 2014
ISSN: 1063-5203
DOI: 10.1016/j.acha.2014.01.004