MATLAB实现隐马尔可夫预测【数学建模、科学计算算法】.zip

function [ESN,PSN,MUN,SIN]=emlht(w,ES,PS,MU,SI,zm) %function [ESN,PSN,MUN,SIN]=emlht(w,ES,PS,MU,SI,zm) % updates LH subband of HMT model once % by tying within scale for each subband. % % Author: H. Choi % Last update : 12/14/1998 % % the data structure of 2-D DWT follows the format used % in the Rice wavelelet matlab toolbox (see README) % % internal variables: % M : no. of mixture densities % P : size of image (PxP pixels) % level : no. of levels of HMT % % Input : % w : data PxP matrix (wavelet transform of an image) % ES : state transition matrix (MxMxPxP) % PS : state probability matrix (MxPxP) % MU : mean matrix (MxPxP) % SI : variance matrix (MxPxP) % zm : type of density functions % zm = 1 : zero mean (do not update MU) % zm = 0 : nonzero mean (update MU) % % Output: % Updated ES PS MU SI in ESN PSN MUN SIN M=size(ES,1); P=size(w,1); level=log2(P); BE=zeros(M,P,P); BEP=zeros(M,P,P); BER=zeros(M,P,P); AL=zeros(M,P,P); P1=zeros(M,P,P); P2=zeros(M,M,P,P); %UP step wtmp = repmat(w,[1 1 M]); wtmp = shiftdim(wtmp,2); si=1; ei=2^(level-1); sj=2^(level-1)+1; ej=P; gtmp = gauss(wtmp,MU,SI); scale = repmat(mean(gtmp,1),[M 1 1]); BE(:,si:ei,sj:ej) = gtmp(:,si:ei,sj:ej)./scale(:,si:ei,sj:ej); %clear MUtmp SItmp; for k=level:-1:2 J=2^(k-1);J2=J*J; si = 1; ei = J; sj = J+1; ej = 2*J; EStmp = reshape(ES(:,:,si:ei,sj:ej),M,M*J2); if M == 2 %%%%%% For M=2 the following is faster BEtmp = zeros(M,M*J2); BEtmp(:,1:M:(M*J2))=reshape(BE(:,si:ei,sj:ej),M,J2); BEtmp(:,2:M:(M*J2))=BEtmp(:,1:M:(M*J2)); else % For general M (not equal to 2) use the following % BEtmp = zeros(M,M*4^(k-1)); for m=1:M BEtmp(:,m:M:(M*4^(k-1)))=reshape(BE(:,si:ei,sj:ej,:),M,4^(k-1)); end; end; BEtmp = reshape(EStmp.*BEtmp,[M M J J]); BEP(:,si:ei,sj:ej) = squeeze(sum(BEtmp,1)); sni = 1; eni = J/2; snj = J/2+1; enj = J; %construct betachild matrix here BCtmp = BEP(:,si:2:ei,sj:2:ej); BCtmp = BCtmp.*BEP(:,si+1:2:ei,sj:2:ej); BCtmp = BCtmp.*BEP(:,si:2:ei,sj+1:2:ej); BCtmp = BCtmp.*BEP(:,si+1:2:ei,sj+1:2:ej); scaletmp = repmat(mean(BCtmp,1),[M 1 1]); scale(:,sni:eni,snj:enj) = scale(:,sni:eni,snj:enj).*scaletmp; BE(:,sni:eni,snj:enj)=gtmp(:,sni:eni,snj:enj)./scale(:,sni:eni,snj:enj).*BCtmp; %construct BE(:,pai(i),paj(j),dindex) matrix Btmp=zeros(M,J,J); Btmp(:,1:2:J,1:2:J)=BE(:,sni:eni,snj:enj); Btmp(:,2:2:J,1:2:J)=BE(:,sni:eni,snj:enj); Btmp(:,1:2:J,2:2:J)=BE(:,sni:eni,snj:enj); Btmp(:,2:2:J,2:2:J)=BE(:,sni:eni,snj:enj); BER(:,si:ei,sj:ej)=Btmp./BEP(:,si:ei,sj:ej); end; clear EStmp BEtmp BCtmp Btmp; %DOWN step %initialize AL(:,1,2) = PS(:,1,2); for k=2:level J = 2^(k-1); J2=J*J; si=1; ei=J; sj=J+1; ej=2*J; sni = 1; eni = J/2; snj = J/2+1; enj = J; Atmp=zeros(M,J,J); Atmp(:,1:2:J,1:2:J)=AL(:,sni:eni,snj:enj); Atmp(:,2:2:J,1:2:J)=AL(:,sni:eni,snj:enj); Atmp(:,1:2:J,2:2:J)=AL(:,sni:eni,snj:enj); Atmp(:,2:2:J,2:2:J)=AL(:,sni:eni,snj:enj); Atmp = repmat(reshape(Atmp.*BER(:,si:ei,sj:ej),1,M*J2),[M 1]); EStmp = reshape(ES(:,:,si:ei,sj:ej),M,M*J2); ALtmp = reshape(EStmp.*Atmp,[M M J J]); AL(:,si:ei,sj:ej) = squeeze(sum(ALtmp,2)); end; clear Atmp EStmp ALtmp; %compute probabilities for k=2:level J=2^(k-1); J2=J*J; si=1; ei=J; sj=J+1; ej=2*J; sni = 1; eni = J/2; snj = J/2+1; enj = J; temp = repmat(sum(AL(:,si:ei,sj:ej).*BE(:,si:ei,sj:ej), 1),[M 1]); P1(:,si:ei,sj:ej) = AL(:,si:ei,sj:ej).*BE(:,si:ei,sj:ej)./temp; %compute P2 if M == 2 % For M=2 the following may be faster BEtmp = zeros(M,M*J2); BEtmp(:,1:M:(M*J2))=reshape(BE(:,si:ei,sj:ej),M,J2); BEtmp(:,2:M:(M*J2))=BEtmp(:,1:M:(M*J2)); else % For general M (not equal to 2) use the following BEtmp = zeros(M,M*J2); for m=1:M BEtmp(:,m:M:(M*J2))=reshape(BE(:,si:ei,sj:ej,:),M,J2); end; end; BEtmp = reshape(BEtmp,[M M J J]); EStmp = ES(:,:,si:ei,sj:ej); Atmp=zeros(M,J,J); Atmp(:,1:2:J,1:2:J)=AL(:,sni:eni,snj:enj); Atmp(:,2:2:J,1:2:J)=AL(:,sni:eni,snj:enj); Atmp(:,1:2:J,2:2:J)=AL(:,sni:eni,snj:enj); Atmp(:,2:2:J,2:2:J)=AL(:,sni:eni,snj:enj); Atmp = repmat(reshape(Atmp,1,M*J2),[M 1]); Atmp = reshape(Atmp,[M M J J]); BERtmp = repmat(reshape(BER(:,si:ei,sj:ej),1,M*J2),[M 1]); BERtmp = reshape(BERtmp,[M M J J]); temp = repmat(reshape(temp,1,M*J2),[M 1]); temp = reshape(temp, [M M J J]); P2(:,:,si:ei,sj:ej)=BEtmp.*EStmp.*Atmp.*BERtmp./temp; end; P1(:,1,2)=AL(:,1,2).*BE(:,1,2)./repmat(sum(AL(:,1,2).*BE(:,1,2),1),[M 1 1]); clear temp BEtmp EStmp Atmp BERtmp; %PSP=PS; ESP=ES; MUP=MU; SIP=SI; %M step PS(:,1,2)=P1(:,1,2); for k=2:level J=2^(k-1); J2=J*J; si=1; ei=J; sj=J+1; ej=2*J; sni = 1; eni = J/2; snj = J/2+1; enj = J; pstmp = sum(sum(P1(:,si:ei,sj:ej),3),2)/J2; pstmp = pstmp.*(pstmp>1e-4)+1e-4*(pstmp<=1e-4); PS(:,si:ei,sj:ej) = repmat(pstmp,[1 J J]); if zm == 0 % do not update MU if zero mean densities mutmp = sum(sum(wtmp(:,si:ei,sj:ej).*P1(:,si:ei,sj:ej),3),2)/J2; MU(:,si:ei,sj:ej) = repmat(mutmp,[1 J J])./PS(:,si:ei,sj:ej); end; sitmp = sum(sum((wtmp(:,si:ei,sj:ej)-MU(:,si:ei,sj:ej)).^2.*P1(:,si:ei,sj:ej),3),2)/J2; SI(:,si:ei,sj:ej) = repmat(sitmp,[1 J J])./PS(:,si:ei,sj:ej); estmp =sum(sum(P2(:,:,si:ei,sj:ej),4),3)/J2; ptmp = [PS(:,sni,snj)'; PS(:,sni,snj)']; ES(:,:,si:ei,sj:ej)= repmat(estmp,[1 1 J J])./repmat(ptmp,[1 1 J J]); end; %k ESN=ES; PSN=PS; MUN=MU; SIN=SI;