基于高度冗余Gabor框架的欠Nyquist采樣系統(tǒng)子空間探測
doi: 10.11999/JEIT150327 cstr: 32379.14.JEIT150327
基金項目:
國家自然科學基金(61372039)
Subspace Detection of Sub-Nyquist Sampling System Based on Highly Redundant Gabor Frames
Funds:
The National Natural Science Foundation of China (61372039)
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摘要: 基于指數(shù)再生窗Gabor框架的欠Nyquist采樣系統(tǒng)對窄脈沖信號完成采樣與重構(gòu)一般情況下效果較好，但是當框架高度冗余時，使用傳統(tǒng)面向系數(shù)域的方法對信號進行子空間探測會面臨失敗或較大誤差。該文采用面向信號域的思想，構(gòu)建了分塊的對偶Gabor字典，并對信號分塊稀疏表示；根據(jù)信號的分塊表示推導了采樣系統(tǒng)的測量矩陣，提出了測量矩陣受字典相干性約束的分塊-相干性；將信號合成模型引入多觀測向量問題，提出基于分塊-閉包的同步正交匹配追蹤算法(SOMPB,F )，用于信號子空間探測。此外還證明了算法的收斂約束條件。仿真結(jié)果表明，所提子空間探測方法相比傳統(tǒng)方法提高了信號重構(gòu)成功率，降低了采樣通道數(shù)，并增強了系統(tǒng)魯棒性。Abstract: The sampling system based on Gabor frames with exponential reproducing windows holds nice performance for short pulses in general cases, but when the frames are highly redundant, the traditional coefficient oriented methods for subspace detection may fail or have large error. Firstly, the signal oriented idea is introduced and the blocked dual Gabor dictionaries are constructed, finishing the block sparse representation. By introducing the blocked dictionaries, the measurement matrix is constructed and the block-coherence restricted by the coherence of the dictionaries is proposed. Consequently, the synthesis model for signal representation is introduced to subspace detection based on Multiple Measurement Vector problem and the Simultaneous Orthogonal Matching Pursuit is proposed based on blocked-closure(SOMPB,F), using for subspace detection. Additionally, the convergence of the algorithm is proved. At last, simulation experiments prove that the new method improves the recovery rate, decreases the channel numbers and enforces the robustness of the sampling system compared with the traditional methods.
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Key words:
- Signal processing /
- Gabor dictionaries /
- Coherence /
- Sub-Nyquist sampling /
- Subspace
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