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Signal sparse decomposition method based on set partitioning of over-complete dictionary

An over-complete dictionary and signal sparse technology, applied in electrical digital data processing, special data processing applications, instruments, etc., can solve the problems of long operation time and prolonged operation time, and achieve the effect of reducing operation time.

Active Publication Date: 2014-08-20
HARBIN INST OF TECH
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Problems solved by technology

[0005] The present invention solves the problem that the calculation time is too long when the signal is decomposed by using the classic MP method and the existing improved method, especially in order to solve the problem that the calculation time will be further reduced when the signal is too long and the dictionary is too large in practical applications. extended question

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  • Signal sparse decomposition method based on set partitioning of over-complete dictionary
  • Signal sparse decomposition method based on set partitioning of over-complete dictionary
  • Signal sparse decomposition method based on set partitioning of over-complete dictionary

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specific Embodiment approach 1

[0018] Specific embodiment one: illustrate this embodiment in conjunction with Fig. 1, a kind of signal sparse decomposition method based on overcomplete dictionary set division, it comprises the following steps:

[0019] Step 1: Establish different over-complete dictionaries D for signals f with different characteristics. When analyzing Gaussian modulation window signals, establish over-complete dictionaries D based on Gaussian modulation signals.

[0020] Step 2: Divide the overcomplete dictionary into several disjoint sub-dictionaries according to the modulation correlation of atoms, so that each sub-dictionary is composed of atoms satisfying the equivalence relationship, that is, atoms with the same modulation characteristics.

[0021] Step 3: Use the matching pursuit algorithm to decompose the signal, divide the over-complete dictionary into several sub-dictionaries, select an atom from each sub-dictionary composed of atoms satisfying the equivalence relationship as a repr...

specific Embodiment approach 2

[0024] Specific implementation mode two: the specific operation steps of step one described in this implementation mode are:

[0025] In the Hilbert space H=L composed of complex functions 2 (R), there are

[0026] | | f | | = ∫ - ∞ + ∞ | f ( t ) | 2 dt + ∞ - - - ( 1 )

[0027] Where f represents the input signal and t represents time.

[0028] In Hilbert space H=L 2 (R) defines a set of vectors D=(g γ ) γ∈Γ is a dictionary with ||g γ ||=1, let g(t) be a continuously differentiable real function, and its high-order infinitesimal is O(1 / (t ...

specific Embodiment approach 3

[0033] Specific implementation mode three: the specific operation steps of step 2 of this embodiment mode are:

[0034] Divide the atoms with the same s and u factors and different v and w factors in the time-frequency parameter index set γ = (s, u, v, w) into a set, let β = (s, u) represent the equivalent sub-dictionary index set, then Γ β ={β i |i=1,2,...}. The sub-dictionary is shown in formula (3)

[0035] D β i = { g γ | γ = ( s , u , v , w ) ∈ Γ , ( s , u ) i β i } - - - ( ...

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Abstract

The invention discloses a signal sparse decomposition method based on set partitioning of an over-complete dictionary and relates to a signal sparse decomposition method. The method is provided in order to solve the problem that when a classic MP method and an existing improvement method are used for decomposing signals, the operation time is too long. According to the method, the over-complete dictionary is subjected to set partitioning by selecting different factors, a huge redundant dictionary is divided into a plurality of sub-dictionaries, appropriate time frequency is selected from the sub-dictionaries through a matching pursuit algorithm to accurately and rapidly decompose signals, signal residuals are decomposed again according to the standard of actual requirements till reconstructed signals conforming to the standard are obtained, and the reconstructed signals can be shown in the form of the sum of the products of all stages of iteration residuals and corresponding matched atoms. The signal sparse decomposition method is applicable to the field of signal sparse decomposition.

Description

technical field [0001] The invention relates to a signal sparse decomposition method based on overcomplete dictionary set division, in particular to a signal decomposition method. Background technique [0002] Signal decomposition and representation are very important in the field of signal processing research. Especially in signal processing and analysis, signal decomposition plays a vital role. In the method of decomposing the signal, the traditional classical method is to project it onto a set of complete orthogonal bases, such as Fourier transform or wavelet transform. [0003] A linear decomposition of a signal on a single basis like a Fourier basis or a wavelet basis, or other basis, is not flexible enough. Some sparse properties of the signal itself are not fully represented. The Fourier base can only represent a signal with good positioning in the time domain to a certain extent, and its positioning in the frequency domain is poor. The wavelet base is not suitabl...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06F19/00H03M7/30
Inventor 杨柱天张立宪吴芝路赵苑珺
Owner HARBIN INST OF TECH
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