framedesignex.m

Sparse Signal Representation using Overlapping Frames (matlab toolbox)

function F=FrameDesignEx(TestNo,arg1,arg2)
% FrameDesignEx   Here we design an example frame for an AR(1) signal. 
%                 The different steps of the design process are briefly
% explained and done. The steps are:
% 1.  Decide for the frame structure to use, i.e. size of F, and
%     target sparseness factor.
% 2.  Prepare the set training vectors, make X.
%     also these vectors are stored in a mat-file used during frame design
%     see DataFile.m, ex: help DataFile
% 3.  Set the initial frame and store it in FrameFile, see: help FrameFile.
%     The initial values for the frame may be generated in many ways, 
%     for example one of the files SetF03, SetF05, ..., could be used,
%     see help text for these. SetFnn generates the FrameFile. It may be
%     needed to update som of the variables stored in the mat-file.
%     An alternative is to use GenLloyd to find the initial values of F,
%     then we must remember to store the variables in the mat-file.
% 4.  Design the frame using DesignF or DesignFb
% 5.  We may now look at the designed frame and plot training results.
% The frame is now ready to use for sparse representation, for examples see
% SignalExpansion.m, ex: Y=SignalExpansion(5,1,255,'FrameEx2s20',0.25);
% Some frame properties can be found by for example
% [a,b,c,d,e,f,g,Ang]=FrameProperties('FrameEx1s20',[2,3,7,8,9,27,28,29,31,32,33]);
%
% F=FrameDesignEx(TestNo,arg1,arg2);   
% F=FrameDesignEx(1,0.2);   
% F=FrameDesignEx(2,0.2);   
%-----------------------------------------------------------------------------------
% arguments:
%  F          - the designed frame
%  TestNo     - which test or example to do
%           1 - Design a block-oriented 16x32 frame for an AR(1) signal
%           2 - Continue design from TestNo 1, but now change vector selection method
%           3 - Design a general overlapping frame for an AR(1) signal
%           4 - Design an overlapping frame for an AR(1) signal
%  arg1       - for most tests it is target sparseness factor
%-----------------------------------------------------------------------------------

%----------------------------------------------------------------------
% Copyright (c) 2002.  Karl Skretting.  All rights reserved.
% Hogskolen in Stavanger (Stavanger University), Signal Processing Group
% Mail:  [e-mail]   Homepage:  http://www.ux.his.no/~karlsk/
% 
% HISTORY:  dd.mm.yyyy
% Ver. 1.0  03.12.2002  KS: function made 
%----------------------------------------------------------------------

Mfile='FrameDesignEx';
F=[];
DataFile='DataX001';    % the file where the set of training vectors, X, is stored during design
TotIt=250;              % number of iterations to do
Minutes=60*6;           % minutes to use  

if nargin<3; arg2=0; end;
if nargin<2; arg1=0; end;
if nargin<1;
    Message=[Mfile,': wrong number of arguments, see help.'];
    disp(Message);
    return
end;

if (TestNo==1)  
    % step 1.
    N=16;K=32;P=1;
    disp([Mfile,', Test/example ',int2str(TestNo),', ',int2str(N),'x',int2str(K),...
            ' block-oriented frame for AR(1) signal.']);
    if ((arg1>0) & (arg1<1))
        S=arg1;  % target sparseness factor
    else
        S=0.2;     
    end
    % step 2.
    L=4000;     % number of training vectors
    X=filter(1,[1,-0.95],randn(L*N,1));   % AR(1) signal
    X=reshape(X,N,L);     % here we have L vectors (from a training signal) each of lenght N
    Name='AR(1)';
    X_DC=0;X_LP=[];SizeX=[N*L,1];
    ss2=X(:)'*X(:);    
    WWT=[];XWT=[];
    save(DataFile,'Name','X_DC','X_LP','X','SizeX','ss2','S','WWT','XWT');
    % step 3.
    FrameFile=['FrameEx',int2str(TestNo),'s',int2str(round(S*100))];
    % this m-file is the PreProc method used here
    PreProc=struct('Prog1','','Prog2',Mfile,'Method',TestNo,'arg1',arg1,'arg2',arg2,'arg3',[]);
    % now set how vector selection should be done
    VecSel=struct('Prog1','VSblock','arg1','VSfomp2','arg2',5,'arg3',[],'arg4',[],'arg5',[]);
    % generate F and store how initial F is generated
    F=GenLloyd(NormalizeF(X),K,1);
    % clf;PlotF(F,1,0,0,3); % if we want to look at the vectors
    InitialF=struct('Prog1','GenLloyd','arg1','NormalizeF(X)','arg2',K,'arg3',1,'arg4',[],'arg5',[]);
    History=[Mfile,' ',datestr(now),', initialized the frame ',FrameFile,' using',...
             ' N=',int2str(N),' K=',int2str(K),' P=1'];
    History=char(History,'Initial values made by Generalized Lloyd Algorithm.');    
    SNRtot=[];Type='b';Mdat=1;G=[];Dtab=[];Ctab=[];Savg=S;
    SizeF=[N,K,P];Mdim=1;Class='AR(1)';Fbest=F;
    save(FrameFile,'Class','Type','Mdim','F','SizeF','G','Ctab','Dtab',...
       'Fbest','Savg','Mdat','PreProc','VecSel','InitialF','History','SNRtot');
    % step 4, here we use DesignFb
    disp(' ');
    disp([Mfile,': ',datestr(now),' start design of frame ',FrameFile]);
    ErrCode=DesignFb(FrameFile,TotIt,Minutes/(24*60));
    % step 5
    load(FrameFile);
    disp(History);
    figure(1);clf;PlotF(F,1,0,0,3); 
    figure(2);clf;PlotSNR(SNRtot,History); 
    % signal expansion example
    Y=SignalExpansion(5,1,255,FrameFile,0.25);
end

if (TestNo==2)  
    disp([Mfile,', Test/example ',int2str(TestNo),', continue from TesNo 1 with', ...
            ' block-oriented frame for AR(1) signal.']);
    % step 1.  values are found when framefile is read
    if ((arg1>0) & (arg1<1))
        S=arg1;  % target sparseness factor
    else
        S=0.2;     
    end
    % step 2.  assume that DataFile is the one made by TestNo 1
    % step 3.
    FrameFile=['FrameEx1s',int2str(round(S*100))];
    load(FrameFile);  % load FrameFile from TestNo 1, but store it by another name
    FrameFile=['FrameEx',int2str(TestNo),'s',int2str(round(S*100))];
    History=char(History,[Mfile,' ',datestr(now),', frame was copied to ',FrameFile,'.']);    
    F=Fbest;
    VecSel=struct('Prog1','VSblock','arg1','VSab2','arg2',5,'arg3',0,'arg4',4,'arg5',[]);
    save(FrameFile,'Class','Type','Mdim','F','SizeF','G','Ctab','Dtab',...
       'Fbest','Savg','Mdat','PreProc','VecSel','InitialF','History','SNRtot');
    % step 4, here we use DesignFb
    disp(' ');
    disp([Mfile,': ',datestr(now),' start design of frame ',FrameFile]);
    ErrCode=DesignFb(FrameFile,2*TotIt,Minutes/(24*60));
    % step 5
    load(FrameFile);   % we want to update VecSel.arg3
    VecSel=struct('Prog1','VSblock','arg1','VSab2','arg2',5,'arg3',20,'arg4',4,'arg5',[]);
    save(FrameFile,'Class','Type','Mdim','F','SizeF','G','Ctab','Dtab',...
       'Fbest','Savg','Mdat','PreProc','VecSel','InitialF','History','SNRtot');
    disp(History);
    figure(1);clf;PlotF(F,1,0,0,3); 
    figure(2);clf;PlotSNR(SNRtot,History); 
    % signal expansion example
    Y=SignalExpansion(5,1,255,FrameFile,0.25);
end

if (TestNo==3)  
    % step 1. 
    % we will use F with initial values from FIR filters, SetF05
    FIRspec=[40,8,0,0.05; 40,8,0,0.2; 28,4,0,0.2; 28,4,0,0.4; 12,4,0,0.5; 
             14,2,0.1,0.6; 14,2,0.2,0.7 ];
    disp([Mfile,', Test/example ',int2str(TestNo),', used some FIR filters ',...
            '(SetF05), overlapping frame for AR(1) signal.']);
    if ((arg1>0) & (arg1<1))
        S=arg1;  % target sparseness factor
    else
        S=0.2;     
    end
    % step 3, first part is done now (since N, K and P are needed but only indirectly given)
    FrameFile=['FrameEx',int2str(TestNo),'s',int2str(round(S*100))];
    ErrCode=SetF05(FrameFile,FIRspec,1.000001);
    if ErrCode
        Message=[Mfile,': an error occurred in SetF05.'];
        disp(Message);
        return;
    end
    load(FrameFile);
    [N,K,P]=size(G);
    % step 2.
    L=4000;     % number of training vectors
    X=filter(1,[1,-0.95],randn(L*N,1));   % AR(1) signal
    X=reshape(X,N,L);     % here we have L vectors (from a training signal) each of lenght N
    Name='AR(1)';
    X_DC=0;X_LP=[];SizeX=[N*L,1];
    ss2=X(:)'*X(:);    
    WWT=[];XWT=[];
    save(DataFile,'Name','X_DC','X_LP','X','SizeX','ss2','S','WWT','XWT');
    % step 3.
    % change some of the initial values of the frame which were set by SetF05
    % the PreProc variable contain som useful information
    PreProc=struct('Prog1','','Prog2',Mfile,'Method',TestNo,'arg1',arg1,'arg2',arg2,'arg3',[]);
    % it is important to set an appropriate vector selection method. For overlapping frame and
    % 1D signal it must be VSolap1 and a suitable method (VSab2 or VSfomp2)
    VecSel=struct('Prog1','VSolap1','arg1','VSab2','arg2',10,'arg3',1,'arg4',[],'arg5',[]);
    Savg=S;       % this is important as SetF05 set this to zero.
    Class='AR(1)';  % useful information
    Fbest=F;       
    Mdat=1;   % this is important too, since SetF05 set this to zero.
    save(FrameFile,'Class','Type','Mdim','F','SizeF','G','Ctab','Dtab',...
       'Fbest','Savg','Mdat','PreProc','VecSel','InitialF','History','SNRtot');
    % step 4, here we use DesignF
    disp(' ');
    disp([Mfile,': ',datestr(now),' start design of frame ',FrameFile]);
    ErrCode=DesignF(FrameFile,TotIt,Minutes/(24*60));
    % step 5, display some information on the designed frame
    load(FrameFile);   % we want to update VecSel.arg3
    VecSel=struct('Prog1','VSolap1','arg1','VSab2','arg2',10,'arg3',20,'arg4',[],'arg5',[]);
    save(FrameFile,'Class','Type','Mdim','F','SizeF','G','Ctab','Dtab',...
       'Fbest','Savg','Mdat','PreProc','VecSel','InitialF','History','SNRtot');
    [a,b,c,d,e,f,g,Ang]=FrameProperties(FrameFile,[2,3,7,8,9,27,28,29,31,32,33]);
    [t1,t2]=FrameInfo(FrameFile,1);
    pause;  % note the symmetry in the frame vectors, there is only 85 free variables
    disp(History);
    figure(1);clf;PlotF(BuildFg(F,G),1,0,0,3);   % BuildFg is needed for general frames
    figure(2);clf;PlotSNR(SNRtot,History); 
    % signal expansion example
    Y=SignalExpansion(5,1,255,FrameFile,0.25);
end

if (TestNo==4)  
    % step 1. 
    N=8;K=16;P=4;
    disp([Mfile,', Test/example ',int2str(TestNo),', ',int2str(N),'x',int2str(K),...
            'x',int2str(P),' overlapping frame for AR(1) signal.']);
    if ((arg1>0) & (arg1<1))
        S=arg1;  % target sparseness factor
    else
        S=0.2;     
    end
    % step 2.
    L=6000;     % number of training vectors
    X=filter(1,[1,-0.95],randn(L*N,1));   % AR(1) signal
    X=reshape(X,N,L);     
    Name='AR(1)';
    X_DC=0;X_LP=[];SizeX=[N*L,1];
    ss2=X(:)'*X(:);    
    WWT=[];XWT=[];
    save(DataFile,'Name','X_DC','X_LP','X','SizeX','ss2','S','WWT','XWT');
    % step 3
    FrameFile=['FrameEx',int2str(TestNo),'s',int2str(round(S*100))];
    ErrCode=SetF03(FrameFile,[N,K,P],bin2dec('0111011100000011'));
    % here we use vectors from DCT, LOT and ELT
    if ErrCode
        Message=[Mfile,': an error occurred in SetF03.'];
        disp(Message);
        return;
    end
    load(FrameFile);
    % change some of the initial values of the frame which were set by SetF05
    % the PreProc variable contain som useful information
    PreProc=struct('Prog1','','Prog2',Mfile,'Method',TestNo,'arg1',arg1,'arg2',arg2,'arg3',[]);
    % it is important to set an appropriate vector selection method. For overlapping frame and
    % 1D signal it must be VSolap1 and a suitable method (VSab2 or VSfomp2)
    VecSel=struct('Prog1','VSolap1','arg1','VSab2','arg2',12,'arg3',2,'arg4',[],'arg5',[]);
    Savg=S;       % this is important as SetF03 set this to zero.
    Class='AR(1)';  % useful information
    Fbest=F;       
    Mdat=1;   % this is important too, since SetF03 set this to zero.
    save(FrameFile,'Class','Type','Mdim','F','SizeF','G','Ctab','Dtab',...
       'Fbest','Savg','Mdat','PreProc','VecSel','InitialF','History','SNRtot');
    % step 4, here we use DesignF
    disp(' ');
    disp([Mfile,': ',datestr(now),' start design of frame ',FrameFile]);
    ErrCode=DesignF(FrameFile,TotIt,Minutes/(24*60));
    % step 5, display some information on the designed frame
    load(FrameFile);   % we want to update VecSel.arg3
    VecSel=struct('Prog1','VSolap1','arg1','VSab2','arg2',12,'arg3',20,'arg4',[],'arg5',[]);
    save(FrameFile,'Class','Type','Mdim','F','SizeF','G','Ctab','Dtab',...
       'Fbest','Savg','Mdat','PreProc','VecSel','InitialF','History','SNRtot');
    [a,b,c,d,e,f,g,Ang]=FrameProperties(FrameFile,[2,3,7,8,9,27,28,29,31,32,33]);
    [t1,t2]=FrameInfo(FrameFile,1);
    pause;  % note the symmetry in the frame vectors, there is only 85 free variables
    disp(History);
    figure(1);clf;PlotF(F,1,0,0,3);   % BuildFg is needed for general frames
    figure(2);clf;PlotSNR(SNRtot,History); 
    % signal expansion example
    Y=SignalExpansion(5,1,255,FrameFile,0.25);
end

return