1 简介
奇异值分解是矩阵对角化的有效数值分析工具，被广泛地应用于图像处理领域。假设数字图像A 的大小为 N × N，对其进行奇异值分解，则存在正
2 部分代码
function out=invzigzag(in,num_rows,num_cols)
% Inverse Zig-zag scanning
% This function reorders a 1-D array into a specifiable
% 2-D matrix by implementing the INVERSE ZIG-ZAG SCNANNING procedure.
% IN specifies the input 1-D array or vector
% NUM_ROWS is the number of rows desired in the output matrix
% NUM_COLS is the number of columns desired in the output matrix
% OUT is the resulting inverse zig-zag scanned matrix
% having the same number of elements as vector IN
%
% As an example,
% IN = [1 2 4 7 5 3 6 8 10 11 9 12];
% OUT = INVZIGZAG(IN,4,3)
% OUT=
%1 2 3
%4 5 6
%7 8 9
%10 11 12
tot_elem=length(in);
if nargin>3
error('Too many input arguments');
elseif nargin<3
error('Too few input arguments');
end
% Check if matrix dimensions correspond
if tot_elem~=num_rows*num_cols
error('Matrix dimensions do not coincide');
end
% Initialise the output matrix
out=zeros(num_rows,num_cols);
cur_row=1;cur_col=1;cur_index=1;
% First element
%out(1,1)=in(1);
while cur_index<=tot_elem
if cur_row==1 & mod(cur_row+cur_col,2)==0 & cur_col~=num_cols
out(cur_row,cur_col)=in(cur_index);
cur_col=cur_col+1;%move right at the top
cur_index=cur_index+1;
elseif cur_row==num_rows & mod(cur_row+cur_col,2)~=0 & cur_col~=num_cols
out(cur_row,cur_col)=in(cur_index);
cur_col=cur_col+1;%move right at the bottom
cur_index=cur_index+1;
elseif cur_col==1 & mod(cur_row+cur_col,2)~=0 & cur_row~=num_rows
out(cur_row,cur_col)=in(cur_index);
cur_row=cur_row+1;%move down at the left
cur_index=cur_index+1;
elseif cur_col==num_cols & mod(cur_row+cur_col,2)==0 & cur_row~=num_rows
out(cur_row,cur_col)=in(cur_index);
cur_row=cur_row+1;%move down at the right
cur_index=cur_index+1;
elseif cur_col~=1 & cur_row~=num_rows & mod(cur_row+cur_col,2)~=0
out(cur_row,cur_col)=in(cur_index);
cur_row=cur_row+1;cur_col=cur_col-1;%move diagonally left down
cur_index=cur_index+1;
elseif cur_row~=1 & cur_col~=num_cols & mod(cur_row+cur_col,2)==0
out(cur_row,cur_col)=in(cur_index);
cur_row=cur_row-1;cur_col=cur_col+1;%move diagonally right up
cur_index=cur_index+1;
elseif cur_index==tot_elem%input the bottom right element
out(end)=in(end);%end of the operation
break%terminate the operation
end
end
3 仿真结果
4 参考文献
[1]黄菊. 基于SVD的音频认证水印算法研究[D]. 西南交通大学.
部分理论引用网络文献，若有侵权联系博主删除。
5 MATLAB代码与数据下载地址
见博客主页
