基于子空間的三階多項(xiàng)式相位信號(hào)快速稀疏分解算法

歐國(guó)建; 蔣清平; 秦長(zhǎng)春

doi:10.11999/JEIT170593

基于子空間的三階多項(xiàng)式相位信號(hào)快速稀疏分解算法

doi: 10.11999/JEIT170593 cstr: 32379.14.JEIT170593

2.
(重慶大學(xué)飛行器測(cè)控與通信教育部重點(diǎn)實(shí)驗(yàn)室重慶 400044)
3.
(重慶電子工程職業(yè)學(xué)院軟件學(xué)院重慶 401331)

基金項(xiàng)目:

重慶市教委科學(xué)技術(shù)研究項(xiàng)目(KJ1602909, KJ1503004)，國(guó)家自然科學(xué)基金(61371164)，重慶電子工程職業(yè)學(xué)院智能機(jī)器技術(shù)研究中心(XJPT201705)

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出版歷程
- 收稿日期: 2017-06-21
- 修回日期: 2017-11-29
- 刊出日期: 2018-03-19

A Fast Sparse Decomposition for Three-order Polynomial Phase Signal Based on Subspace

2.
(Key Laboratory of Aerocraft Tracking Telemetering &
3.
(School of Software, Chongqing College of Electronic Engineering, Chongqing 401331, China)

Funds:

The project of ChongQing municipal education Commission (KJ1602909, KJ1503004), The National Natural Science Foundation of China (61371164), Intelligent Robot Techndogy Research Center of Electronic Engineering (XJPT201705)

摘要

摘要: 針對(duì)稀疏分解冗余字典中原子數(shù)量龐大的缺點(diǎn)，該文提出一種三階多項(xiàng)式相位信號(hào)的快速稀疏分解算法。該算法根據(jù)三階多項(xiàng)式相位信號(hào)的特點(diǎn)，把原有信號(hào)變換成兩個(gè)子空間信號(hào)，并根據(jù)這兩個(gè)子空間信號(hào)構(gòu)建相應(yīng)的冗余字典，然后采用正交匹配追蹤法來(lái)完成其稀疏分解，最后利用稀疏分解原理完成原有信號(hào)的稀疏分解。該算法把原有信號(hào)變換成兩個(gè)不同子空間信號(hào)，構(gòu)建了兩個(gè)不同的冗余字典，對(duì)比采用一個(gè)冗余字典庫(kù)，這種采用兩個(gè)冗余字典的算法大大減少了原子數(shù)量，并且通過(guò)快速傅里葉變換，在一個(gè)冗余字典進(jìn)行稀疏分解時(shí)，同時(shí)找到另一個(gè)冗余字典中的最匹配的原子。因此該算法通過(guò)減少原子數(shù)量和采用快速傅里葉變換大大加快了稀疏分解速度。實(shí)驗(yàn)結(jié)果表明，相比于采用Gabor原子構(gòu)建的冗余字典，采用匹配追蹤算法與遺傳算法及最近提出的基于調(diào)制相關(guān)劃分的快速稀疏分解，它的稀疏分解速度更快，并且具有更好的收斂性。
- 三階多項(xiàng)式相位信號(hào) /
- 子空間 /
- 快速傅里葉變換 /
- 正交匹配追蹤 /
- 稀疏分解
Abstract: In view of the defect for large number of atoms in the over-complete dictionary during sparse decomposition, this paper presents a fast sparse decomposition algorithm for three-order polynomial phase signal based on subspace. According to the characteristic of three-order polynomial phase signal, the original signal is transformed into two subspace signals, then the atoms are structured based on the two subspace signals in the over-complete dictionary, and the two subspace signals are sparsely decomposed by using orthogonal matching pursuit algorithm. Finally, the sparse decomposition for the original signal is completed by using the theory of the sparse decomposition. In the algorithm, three-order polynomial phase signal is transformed into two subspace signals, and two over-complete dictionaries are structured based on the two subspace signals. Compared to one over-complete dictionary, the atoms are reduced enormously by using two over-complete dictionaries in the algorithm, and one matching atom can be obtained in one over-complete dictionary when another matching atom in another over-complete dictionary is obtained by using fast Fourier transform. Therefore the method can sparsely decompose three-order polynomial phase signal with low computational complexity by reducing the atoms and using fast Fourier transform. Simulation results show that the computational efficiency of the proposed method is better than that of using Gabor atoms, genetic algorithm and the algorithm based on modulation correlation partition, and the sparsity is better.
- Three-order Polynomial Phase Signal (PPS) /
- Subspace /
- Fast Fourier Transform (FFT) /
- Orthogonal Matching Pursuit (OMP) /
- Sparse decomposition

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