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1、第7期基于改進(jìn)l1范數(shù)最小化組合算法的欠定盲源分離·5·更多電子資料請登錄賽微電子網(wǎng)www.srvee.com基于改進(jìn)l1范數(shù)最小化組合算法的欠定盲源分離付寧彭喜元(哈爾濱工業(yè)大學(xué)自動(dòng)化測試與控制系,哈爾濱150080)摘要:基于稀疏假設(shè),欠定盲源分離問題一般可采用線性規(guī)劃、最短路徑法和組合算法等l1范數(shù)最小化方法進(jìn)行求解,但是這些傳統(tǒng)方法對源信號(hào)的稀疏性要求較高,從而限制了源信號(hào)的估計(jì)精度。為此,本文提出了一種改進(jìn)的l1范數(shù)最小化組合算法.該算法根據(jù)一定閾值找到與最小l1范數(shù)解最接近的若干次優(yōu)解,將這些次優(yōu)解和最小l1范數(shù)解進(jìn)行加權(quán)疊加,并替代最小l1范數(shù)解,作為源信號(hào)的估
2、計(jì)。采用語音信號(hào)的仿真實(shí)驗(yàn)表明,對于觀測信號(hào)個(gè)數(shù)不太小的高維混合情況,該算法的源信號(hào)估計(jì)精度能夠比傳統(tǒng)的l1范數(shù)最小化組合算法提高10%左右。關(guān)鍵詞:欠定盲源分離；稀疏信號(hào)；l1范數(shù)最小化；線性規(guī)劃中圖分類號(hào):TN911 文獻(xiàn)標(biāo)識(shí)碼:A 國家標(biāo)準(zhǔn)學(xué)科分類代碼:510.40Underdeterminedblindsourceseparationbasedonimprovedcombinatorialalgorithmforl1-normminimizationFuNingPengXiyuan(Dept.ofAutomaticTestandControl,HarbinIn
3、stituteofTechnology,Harbin150080,China)Abstract:Underthesparseassumption,theproblemofunderdeterminedblindsourceseparationcanbesolvedbyl1-normminimizationalgorithmssuchasthelinearprogramming,theshortest-pathalgorithm,thecombinatorialalgorithmandsoon.Buttheseconventionalalgorithmsrelyonthehig
4、hsparsenessofthesources,sotherecoveryaccuracyofthesourcesisnothighenough.Toovercomethisdisadvantage,animprovedcombinatorialalgorithmforl1-normminimizationisproposedinthispaper.First,thealgorithmsearchesthesecondbestsolutionswhichareclosetotheminimuml1-normsolutionaccordingtoathreshold,andth
5、entheweightedsumofthesesecondbestsolutionsandtheminimuml1-normsolutionistakenastheestimationofthesources.Theexperimentsofsoundsourcesshowthattherecoveryaccuracyofthesourcescanbeincreasedbyabout10%whenthenumberofmixturesisnottoosmall.Keywords:underdeterminedblindsourceseparation;sparsesignal
6、s;l1-normminimization;linearprogramming第7期基于改進(jìn)l1范數(shù)最小化組合算法的欠定盲源分離·5·1引言近年來,觀測信號(hào)個(gè)數(shù)少于源信號(hào)個(gè)數(shù)的欠定盲源分離(underdeterminedblindsourceseparation,UBSS),已成為盲源分離(blindsourceseparation,BSS)領(lǐng)域的研究熱點(diǎn)[1-7]?？紤]BSS的基本瞬時(shí)線性混合模型,(1)式中:s(t)=[s1(t),s2(t),,sN(t)]T表示N維源信號(hào)向量,x(t)=[x1(t),x2(t),,xM(t)]T表示M維觀測信號(hào)向量,A表示M×N維的混合
7、矩陣,ai是A的列向量,t是離散時(shí)刻,T是觀測信號(hào)點(diǎn)數(shù)。BSS的命題就是,對任何t,根據(jù)已知的x(t),在A未知的條件下求未知的s(t)。當(dāng)M
