# 浅谈压缩感知（十七）：测量矩阵之有限等距常数RIC的计算

## 一、RIC定义：

CS满足条件：S阶RIP性质只要要求0<δS<1就可以了，而RIC是指满足RIP的最小δS。

RIC与特征值的关系：

## 三、MATLAB代码

function y=RIPText(x,t)
% calculete the kth Restricted Isometry Constant of measurement matrix x.
% Modified on March 13th, 2012.
% Reference: Wei Dai, Olgica Milenkovic. Subspace Pursuit for Compressive Sensing
% Signal Reconstruction. IEEE Trans. ona Information Theory. vol.55, no.5,
% 2230-2249. May, 2009
%calculate the Restricted Isomentry Constant of matrix constructed by
%random n columns of the original matrix x.
%created by Li Bo in March 16th, 2011
%Harbin Institute of Technolgy
n=size(x,2);%the numbers of column of original matrix x
Num=1:n;%create a row of numbers from one to n with iterval 1
Com=combntns(Num,t);% all the combination of the selected t columns from total n columns
ma=size(Com,1);% the number of combinations
delta=zeros(1,ma);% a vector used to store the restricted isometry constant candidate
for i=1:ma
b=x(:,Com(i,:));% new matrix constructed by the t selected columns
e=eig(b'*b-eye(t));%calculate all the eigen values of matrix b'*b-eye(t)
delta(i)=(max(abs(e)));%select the largest absolute eigen value as restricted isomentry candidate
end
y=max(delta);% select the largest one as restricted isometry constant

## 四、参考文章

http://blog.csdn.net/jbb0523/article/details/44622819

posted @ 2015-12-29 16:38  AndyJee  阅读(2758)  评论(0编辑  收藏  举报