function?[theta?posterior?bound]=BCSvb（Phi?v?hyperpara?niter?tol?plotflag）
%BCSvb:?Bayesian?CS?inversion?implemented?by?variational?Bayes.
%USAGE:?[theta?posterior?bound]=BCSvb（Phi?v?hyperpara?niter?tol?plotflag）
%INPUT?（number?in?[]?means?default?value）:??
%???Phi:?N?x?M?CS?projection?matrix
%???v:?N?x?1?CS?observation
%???hyperpara:?VB?hyperparameters
%???????hyperpara.a0:?scalar?hyperparameter?1?for?noise?precision?[1e-6]
%???????hyperpara.b0:?scalar?hyperparameter?2?for?noise?precision?[1e-6]
%???????hyperpara.c0:?scalar?hyperparameter?1?for?non-zero?coefficients?precision?[1e-6]?
%???????hyperpara.d0:?scalar?hyperparameter?2?for?non-zero?coefficients?precision?[1e-6]?
%???niter:?scalar?maximum?number?of?VB?iterations?[100]
%???tol:?scalar?tolarance?of?relative?change?of?VB?lower?bound?for?two?consecutive?steps?[1e-4]?
%???plotflag:?indicator?one?means?plotting?result?for?each?iteration?zero?means?no?plot?[0]?
%OUTPUT:
%???theta:?M?x?1?mean?of?reconstructed?signal
%???posterior:?hyperparameter?for?posterior?distribution
%???????posterior.MUtheta:?M?x?1?mean?of?inverted?theta?
%???????posterior.VARtheta_diag:?M?x?1?variance?of?inverted?theta?（for?each?coefficient）
%???????posterior.a:?scalar?posterior?hyperparameter?1?for?noise?precision
%???????posterior.b:?scalar?posterior?hyperparameter?2?for?noise?precision
%???????posterior.c:?M?x?1?posterior?hyperparameter?1?for?coefficient?precision
%???????posterior.d:?M?x?1?posterior?hyperparameter?2?for?coefficient?precision
%???bound:?1?x?（number?of?VB?iterations）?VB?lower?bound?for?each?iteration

%--------------------------------------------------------------------------
%?References:
%?S.Ji?Y.Xue?and?L.Carin?“Bayesian?Compressive?Sesning“?（2007）.
%?L.He?and?L.Carin?“Exploiting?Structure?in?Wavelet-based?Bayesian?Compressive?Sensing“?（2008）??
%
%?Lihan?He?ECE?Duke?University
%?Created:?Nov.?21?2008
%?Last?change:?Mar.?3?2009?allowing?[]?for?input?arguments?（using?default?value）
%--------------------------------------------------------------------------

%?---------------------
%?check?input?arguments
%?---------------------

if?nargin<6?plotflag=0;?end
if?nargin<5?tol=1e-4;?end
if?nargin<4?niter=100;?end
if?nargin<3
????hyperpara.a0=1e-6;
????hyperpara.b0=1e-6;
????hyperpara.c0=1e-6;
????hyperpara.d0=1e-6;
end

if?isempty（hyperpara）
????hyperpara.a0=1e-6;
????hyperpara.b0=1e-6;
????hyperpara.c0=1e-6;
????hyperpara.d0=1e-6;
end
if?isempty（niter）?niter=100;?end
if?isempty（tol）?tol=1e-4;?end
if?isempty（plotflag）?plotflag=0;?end

a0=hyperpara.a0;
b0=hyperpara.b0;
c0=hyperpara.c0;
d0=hyperpara.d0;

[NM]?=?size（Phi）;??%?N?-?number?of?CS?measurements;?M?-?sparse?signal?length

%?--------------
%?Initialization
%?--------------

MUtheta=zeros（M1）;
VARtheta_diag=d0/c0*ones（M1）;

c=c0*ones（M1）;
d=d0*ones（M1）;

a=a0;
b=b0;

%---------------
%?precomputation
%---------------
Phi

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----
?????文件????????4812??2009-03-03?15:02??BCSvb.m
?????文件???????65551??2002-12-03?07:45??cameraman.pgm
?????文件????????2215??2009-03-03?15:45??demo_BCSvb_1d.m
?????文件????????1778??2009-03-03?15:46??demo_BCSvb_2d.m
?????文件????????1786??2009-03-03?15:46??demo_BCSvb_2d_small.m
?????文件???????65610??2002-12-03?04:04??indor2.pgm
?????文件?????????564??2009-03-03?16:53??readme.txt