利用FFT實(shí)現(xiàn)基于MP的信號(hào)稀疏分解
MP Based Signal Sparse Decomposition with FFT
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摘要: 該文研究基于Matching Pursuit (MP)方法實(shí)現(xiàn)的信號(hào)稀疏分解算法，通過對(duì)信號(hào)稀疏分解中使用的過完備原子庫(kù)結(jié)構(gòu)特性的分析，提出了一種新的信號(hào)稀疏分解算法。該算法首先通過利用原子庫(kù)的結(jié)構(gòu)特性，很好地處理了稀疏分解過程中計(jì)算量和存儲(chǔ)量之間的關(guān)系。在此基礎(chǔ)上，把信號(hào)稀疏分解中計(jì)算量很大的內(nèi)積運(yùn)算轉(zhuǎn)換成互相關(guān)運(yùn)算，最后用FFT實(shí)現(xiàn)互相關(guān)運(yùn)算，從而大大提高了信號(hào)稀疏分解的速度。算法的有效性為實(shí)驗(yàn)結(jié)果所證實(shí)。
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關(guān)鍵詞:
- 信號(hào)處理;稀疏表示;稀疏分解;Matching Pursuit(MP);FFT
Abstract: In this paper, after study of Matching Pursuit (MP) based signal sparse decomposition, a new sparse decomposition algorithm is presented based on analysis of structure property of the over-complete atom dictionary used in signal sparse decomposition. By making use of the structure property, firstly this new algorithm balances very well computers speed and memory. Then this algorithm converts very time-consuming inner product calculations in sparse decomposition into crosscorrelation calculations that are fast done by FFT. Therefore the new algorithm improves a lot the speed of signal sparse decomposition. Finally the experimental results show that the performance of the proposed algorithm is very good. -
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