（计算机应用技术专业论文）核磁共振谱信号参数的rjmcmc估计.pdf

1999nicholson(nmr) nmrnmr nmr nmr nmr ()nmrnmr nmr rjmcmc rjmcmc mcmc abstract abstract the nmr-based metabonomics approach evolved form the pioneering work of nicholson and co-workers in 1999 has become a novel analytical technique. nmr-based metabonomics are closely related to nmr analysis technology. how to extract form the nmr signal of useful information is a critical part of nmr-based metabonomics research. the nmr signal is considered as a time-domain complex free induction decay(fid) signal which is a sum of exponentially damped sinusoidal components. the detection and estimation problem for damped sinusoidal model has received considerable attention over the past two decades, and this has increased since the advent of nmr-based metabonomics, where it is often both laborious and mathematically challenging to identify all the components. after a biological matrix such as urine, blood plasma or a tissue extract as detected by 1h nmr spectroscopy. ideally for this application one would like a method which is fully automated but still capable of resolving as many resonances as possible in a complex biological sample. in this paper, a reversible jump markov chain monte carlo(rjmcmc) algorithm is applied to signal processing of nmr-based metabonomics. first, after modeling the nmr signal according to its physical characteristics, we derived the posteriori probability from the parameters prior probability based on bayesian theory. then we designed and implemented rjmcmc algorithm with the posterior probability as objective function, and the maximum posteriori probability is corresponding to the optimal parameter. finally, we tested and analyzed the algorithm based on simulation and real data. in addition, we proposed a filtering algorithm according to signal feature to filter out the low-frequency interference component in the nmr signal. keyword: metabonomics nuclear magnetic resonance parameter estimation mcmc algorithm 1 1.1 (metabonomics)1 () 1.2 1.2.1 (nuclear magnetic resonancenmr) (zeeman splitting) rjmcmc 2 1h 1.2.2 nmr nicholson1999 1() 2 3 435000)(1020)(100-,200) (2500) 3(expressed sequence tagsest) 4 5 (nmr)(ms) (gcms)(hplc) nmr 1h nmr nmr nmr nmr 1.2.3 nmr nmr1.1 1.1 nmr rjmcmc 4 ph nmrnmr nmr nmr 1000 nmr nmr (hr-mas)hnmr(mrs) nmr nmrm()n() () nmr 5 ( ) (pca)pca (1)(pc) (2)pc(3)pc pc nmrnmr 1.2.4 nmr nmr nmrnmr nmr (pr) nmr nmr reversible jump markov chain monte carlo(rjmcmc) rjmcmc 6 () 1.4 () rjmcmc metropolis-hastings mcmcmcmc mcmc mcmc mcmc 7 mcmc monte carlo monte carlo 2.1(mcmc) 2.1.1 (monte carlo) “” 1 rjmcmc 8 2 () (0,1)() (0,1) 3 2.1.2 :0 t xt s0t 0121 , nn s s ss s 11001111 (|,)(|) tiiititi p xsxsxsxsp xsxs (2-1) :0 t xt mcmc 9 ( , )p i j 11 ( , )(|) tjti p i jp xsxs (2-2) ( )() ntn tp xst j s( ) tt (0)(0)1 0 t+1 i schapman-kolmogrov 11 (1)()(|) ()( , )( ) itititktkt kk tp xsp xsxs p xsp k it (2-3) chapman-kolmogorov pij( , )p i jp ( , )p i jij 1chapman-kolmogorov (1)( )tt p (2-4) chapman-kolmogorov ( )(1)( (2) )(0) t ttptp pp (2-5) n n ij pinj (|) n ijt njti pp xsxs (2-6) n ij p n pij ij n ij p0 xy() i1ii i * *p (2-7) rjmcmc 10 * ( , )( , ) jk p j kp k j (ij) (2-8) ik(2-8)(2-8) p()jppj ()( , )( , )( , ) jijj ii pp i jp j ip j i (2-9) 1 2.1.3 mcmc ( ) x xx k r mcmc(markov chain monte carlo) 22 mcmc monte carlo mcmc mcmc () mcmc mcmc mcmc mcmcmarkovmonte carlo mcmc( ) xmarkov( ) x mcmc mcmc 11 1xmarkov( , )p ( ) x 2x (0) x1markov 1,.n xx 3mn( )f x ( ) 1 1 () n t t m e ff x nm 2-10 ( ) 0 t t x xmarkov ()( ,) b p xbp x x dx()( , )p markov mcmcmcmc metropolis1953 hastingsmetropolis-hastings 2.2 mcmc mcmc metropolis-hastings gibbs metropolis-hastingsmetropolis-hastings 2.2.1 1763 20 30 50 rjmcmc 12 1 2 2.1 x( | )p x( )p x ( | )( | ) ( )/( )pxp xpp x 2-11 ( )( | ) ( )p xp xpdxx ( | ) ( )( , )p xpp x mcmc 13 1 2hpd 3 1 2 2.2.2 metropolis-hastings m-h(metropolis-hastings) 29 ( ) x markovm-h ( , )q x y( , )q x y(s ) (a)x( , )q x (b), x ys( , )q x y (c)x( , )q x y ( , )q x y n xim-hn 1nn xx rjmcmc 14 1nij 2 ( ) ( , ) ( , )min 1, ( ) ( , ) y q y x y x x q x y 2-12 ( , )x y=1 1n xj 3 30,1uu( , )ux y 1n xj 1n xi markov ( , )q x y 3 1n xj ( , )x yy (0,1)uu( , )ux y 1n xj 1n xi ( )0 xmarkov(2-12) ( , )q x y=0 y ( )y=0y 1 ()x0 m-h( , )q x yx-y i 20% mcmc 15 2.2 m-h metropolis-hastingsmcmc markov(burn-in period) 1000-1500 markov markov markovmarkov markov markov 2.3 mcmc mcmc mcmcmcmc markov rjmcmc 16 metropolis-hastings metropolis-hastings 17 nmr nmr nmrnmr nmr 3.1 nmr (free induction decay) rjmcmc 3.1.1 nmr ( )yy t0,1,2,1tn n 1 ( )( )( ) k iik i y ta z tt 3-1 2 ( ) ii jtt i z tee 2 i j ii aae 0,1) i i r i a i ar0,1) i i=12kk max k l z l z l z 0,1 u 4(3-7)(3-8) k a 2 k 1 l z1/3n l z 21 1/3n (n) 2 0 () 22 0 0 ()(|) ( ,)min 1, ()(|) n hh nkkkll ll hh nkkkll yid m dyq zz z z yid m dyq zz 3-12 k a 2 k matlab 2 16 22 (,2) hh kkkkk igka d d a 3-13 =2 =10 kk k (0,1) 1k z (3-15) (0,1) rjmcmc 22 (b)(c) 0 () 22 0 1 2 2 0111 ()11 min 1, ()k1 (1) n hh nkkk hh nkkk yid m dy yidmdy 3-14 0 () 22 1 2 0 2 0111 () min 1,(1)(k1) () n hh nkkk hh nkkk yid m dy yidmdy 3-15 (3-12) 3.2.2 rjmcmc rjmcmc 3.1()k20 1000 23 3.1 rjmcmc (3-14)(3-15) rjmcmc 24 3.3 mcmc k mcmc mcmc mcmc 25 4.1 4.1.1 () 26 4.1() 4.2() 4.14.2 4.13() (4.2255) rjmcmc (3-1) 4.1 rjmcmc rjmcmc 26 1 2 4.1.2 11 (,)x y 22 (,)xy(,) nn xy xy 01 ybb x 0 b 1 b 2 01 1 () n i i ybb x 4-1 b0b1 01 () i ybb x i=12n 2 01 1 () n i i ybb x 01 ybb x ( , )x y 11 , nn ii ii xy xy nn 4-2 4.1 (00) 27 d 12 1,2,.,. n ndy yy 4-3 1,2,.,n 12 ,. n y yy 12 ,. n y yy 1(4-3) 1,2,.,n 12 1,2,.,1,2,.,. 1,2,., n ndny yyn 4-4 1,2,.,n1,2,.,n cd () () sum y c d sum tc 4-5 1,2,.,tn 12 ,. n yy yyyt d 4.3 4.4 4.34.4(4-5) rjmcmc 28 4.5 () 4.6 () 4.54.1 4.6 4.6256 rjmcmc rjmcmc 4.2 4.2.1 29 44.1 10 4.1 1 0.3 0.02 1 0 2 0.31 0.05 2 /4 3 0.8 0.08 3 /2 4 0.9 0.03 0.3 /2 4.1 4.7 fft 4.7fft 4.1123 44.11()2() 3()4()12 33 ( 2 =0.01)4.1 rjmcmc 30 4.8 4.9 4.80255 0 4.2.2 max k=5050( 4)20 0110000k (1000)4.10 k 100010000kk4 5k 4.10 k 31 4.1110000k k 4.11 k k4000 40005 k 54 4.210000 4.2 1 0.3 0.3002 1 1.0202 2 0.31 0.3104 2 2.0200 3 0.8 0.7997 3 2.9624 4 0.9 0.8984 0.3 0.3491 4.2 4 4mcmc rjmcmc 32 (2-10) mcmc (2-10) ( 2 =0.1) 4.12 () 4.13 () 4.124.13 2 =0.1 4.84.9 4.14 k 4.15 k 4.14k34.15 9000k4 44.13 33 4 rjmcmc (2-10) 4.34.2 (2-10) rjmcmc rjmcmc rjmcmckk mcmc (2-10) 4.3 1 0.3 0.3007 1 1.2125 2 0.31 0.3076 2 1.2450 3 0.8 0.8007 3 2.8850 4 0.9 0.9019 0.3 0.1487 rjmcmc 34 4.2.3 rjmcmc 128256 nn(n )128 128256 k18128 windowscpu2.8ghzmatlab 1284.5 5000 mcmc rjmcmc 4.3 35 4.4 1 0.1996 0.0015 0.0877 2 0.0801 0.0024 0.1174 rjmcmc4.1 nmr4.5 (0,1) 4.16 4.16+ 4.6(255) 4.4 rjmcmc 36 mcmc 37 mcmc monte carlo mcmarkovmonte carlo(mcmc) mcmc rjmcmc 1 2mcmc rjmcmc 3k rjmcmc rjmcmc 39 41 1 nicholson jk, wilson d. understanding global systems biology: metabonomics and the continuum of metabolismj. natrevdrugdiscov, 2003, 2(8): 668-676. 2 nicholson jk, lindon jc, holmes e. metabonomics: understanding the metabolic responses of living system to pathophysiological stimuli via multivariate 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