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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;

?屬性????????????大小?????日期????時(shí)間???名稱
-----------?---------??----------?-----??----
?????目錄???????????0??2018-02-03?11:16??BCS?implemented\
?????文件????????5269??2016-09-24?14:10??BCS?implemented\BCSvb.m
?????文件???????65551??2002-12-03?07:45??BCS?implemented\cameraman.pgm
?????文件????????2629??2016-09-24?14:10??BCS?implemented\demo_BCSvb_1d.m
?????文件????????2099??2016-09-24?14:10??BCS?implemented\demo_BCSvb_2d.m
?????文件????????2112??2016-09-24?14:11??BCS?implemented\demo_BCSvb_2d_small.m
?????文件???????65610??2002-12-03?04:04??BCS?implemented\indor2.pgm
?????目錄???????????0??2018-02-03?11:16??compressive?sensing?basic?knowledge\
?????文件??????107698??2012-07-15?11:18??compressive?sensing?basic?knowledge\anziam_pics.pdf
?????文件?????8367240??2012-07-15?11:20??compressive?sensing?basic?knowledge\baraniuk-IMA-CScamera-june07.pdf
?????文件?????1028107??2012-07-15?11:19??compressive?sensing?basic?knowledge\compressed-sensing1.pdf
?????文件??????284802??2012-07-15?11:18??compressive?sensing?basic?knowledge\Compressive_Sensing.pdf
?????文件??????194495??2012-07-15?11:18??compressive?sensing?basic?knowledge\TerryTao.pdf
?????目錄???????????0??2018-01-11?14:09??CS（matlab）\
?????文件???????80896??2013-02-27?13:30??CS（matlab）\分塊壓縮感知程序（matlab）.doc
?????目錄???????????0??2018-02-03?11:17??CS_Examples\
?????文件????????1557??2014-04-27?20:48??CS_Examples\CS_OMP.m
?????文件????????1220??2014-04-27?20:45??CS_Examples\CS_SPGL1.m
?????目錄???????????0??2018-02-03?11:17??CS_Examples\spgl1_1_7\
?????文件????????3861??2009-05-20?19:22??CS_Examples\spgl1_1_7\ChangeLog
?????文件?????????697??2009-05-20?19:22??CS_Examples\spgl1_1_7\Contents.m
?????文件???????26436??2009-05-20?19:22??CS_Examples\spgl1_1_7\COPYING
?????文件?????????184??2009-05-20?19:22??CS_Examples\spgl1_1_7\NormGroupL2_dual.m
?????文件?????????176??2009-05-20?19:22??CS_Examples\spgl1_1_7\NormGroupL2_primal.m
?????文件?????????375??2009-05-20?19:22??CS_Examples\spgl1_1_7\NormGroupL2_project.m
?????文件?????????221??2009-05-20?19:22??CS_Examples\spgl1_1_7\NormL12_dual.m
?????文件?????????209??2009-05-20?19:22??CS_Examples\spgl1_1_7\NormL12_primal.m
?????文件?????????463??2009-05-20?19:22??CS_Examples\spgl1_1_7\NormL12_project.m
?????文件??????????63??2009-05-20?19:22??CS_Examples\spgl1_1_7\NormL1_dual.m
?????文件??????????63??2009-05-20?19:22??CS_Examples\spgl1_1_7\NormL1_primal.m
?????文件?????????227??2009-05-20?19:22??CS_Examples\spgl1_1_7\NormL1_project.m
............此處省略36個(gè)文件信息