%%%%%%%%%%%%%?若干頻率正弦疊加信號?隨機欠采樣?壓縮感知恢復（OMP算法）?%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%?國防科學技術大學?楊俊剛?2011.03?%%%%%%%%%%%%%%%%%%%%

clear;

Tend=6;?%?信號持續時間?0-Tend
fs=200;?%?原始波形采樣頻率
tt1=0:1/fs:Tend;?%?原始波形采樣時間點
N=size（tt12）;?%?采樣點數?
f1=13;?%?正弦信號頻率
f2=5;
f3=2;
y1=cos（2*pi*f1*tt1）+cos（2*pi*f2*tt1）+cos（2*pi*f3*tt1）;?%?波形

M=50;??%?隨機欠采樣信號的點數

%%%%%%%%?生成隨機欠采樣位置?%%%%%%%%%%%%%%%%
indexM=fix（rand（1M）*N）;?
indexM=sort（indexM）;
if?（indexM（1）==0）
????indexM（1）=1;
end
?for?kk=1:M-1
?????while（indexM（kk+1）<=indexM（kk））
?????????indexM（kk+1）=indexM（kk+1）+1;
?????end
?end
?%%%%%%%%?生成隨機欠采樣位置?end?%%%%%%%%%%%%%%%%
?
?y2=y1（indexM）;?%?生成欠采樣序列

DCT_Matrix=（dct（eye（N）））.‘;?%?生成稀疏變換矩陣?采用DCT矩陣

Sense=DCT_Matrix（indexM:）;?%?生成對應的測量矩陣

%%%%%%%%?OMP?算法恢復
%%%%%%%%?OMP?start?%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Aug=[];
corelate=zeros（1N）;
rn=y2‘;
PHAI_cs=Sense;
yvec_cs=y2.‘;

K2=4;?%恢復點數
for?kk=1:K2
????corelate=PHAI_cs‘*rn;
????[vapos]=max（abs（corelate））;
????Aug=[AugPHAI_cs（:pos）];
????PHAI_cs（:pos）=zeros（M1）;
????phiy=（（Aug‘）*Aug）^（-1）*Aug‘*yvec_cs;
????rn=yvec_cs-Aug*phiy;
????posarray（kk）=pos;
????waitbar（kk/K2）;
end

recover_x=zeros（N1）;
recover_x（posarray）=phiy;?%?恢復的稀疏變換后的系數
%%%%%%%%OMP?end%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

recover_x1=DCT_Matrix*recover_x;??%?恢復原始信號

figure（1）;plot（（recover_x1））;title（‘恢復信號‘）;
figure（2）;plot（y1）;??title（‘原始信號‘）;
figure（3）;plot（y2）;??title（‘隨機欠采樣信號‘）;

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----
?????目錄???????????0??2014-04-27?20:44??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??2014-04-27?11:46??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
?????目錄???????????0??2014-04-27?11:46??CS_Examples\spgl1_1_7\private\
?????文件????????1561??2009-05-20?19:22??CS_Examples\spgl1_1_7\private\ensure.m
?????文件????????6398??2009-05-20?19:22??CS_Examples\spgl1_1_7\private\heap.c
?????文件????????3660??2009-05-20?19:22??CS_Examples\spgl1_1_7\private\heap.h
?????文件???????11849??2009-05-20?19:22??CS_Examples\spgl1_1_7\private\lsqr.m
?????文件????????2838??2009-05-20?19:22??CS_Examples\spgl1_1_7\private\oneProjector.m
?????文件????????5704??2009-05-20?19:22??CS_Examples\spgl1_1_7\private\oneProjectorCore.c
?????文件????????1485??2009-05-20?19:22??CS_Examples\spgl1_1_7\private\oneProjectorCore.h
?????文件????????4423??2009-05-20?19:22??CS_Examples\spgl1_1_7\private\oneProjectorMex.c
?????文件????????3797??2009-05-20?19:22??CS_Examples\spgl1_1_7\private\oneProjectorMex.m
?????文件???????10390??2009-05-20?19:22??CS_Examples\spgl1_1_7\private\oneProjectorMex.mexglx
?????文件???????17664??2009-05-20?19:22??CS_Examples\spgl1_1_7\private\oneProjectorMex.mexmaci
?????文件????????9216??2009-05-20?19:22??CS_Examples\spgl1_1_7\private\oneProjectorMex.mexw32
?????文件????????2783??2009-05-20?19:22??CS_Examples\spgl1_1_7\README
?????文件???????16195??2009-05-20?19:22??CS_Examples\spgl1_1_7\spgdemo.m
............此處省略8個文件信息