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Huffman编码(哈夫曼编码)的Matlab实现

clear all

fprintf('')

data=imread('cameraman.tif');

data=uint8(data);%读入数据，并将数据限制为uint8

fprintf('Done!\n'孔业礼)

%编码压缩

fprintf('');

[zipped,info]=norm2huff(data);

fprintf('Done!\n')

%解压缩

fprintf('');

unzipped=huff2norm(zipped,info);

fprintf('Done!\n')

%测试是否无失真

isOK=isequal(data(:),unzipped(:))

%显示压缩效果

whos data zipped unzipped

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function [zipped,info]=norm2huff(vector)

if~isa(vector,'uint8'),

error('input argument must be a uint8 vector')

end

2012全国初中数学竞赛

vector=vector(:)';

%将输入向量转换为行向量

f=frequency(vector);

%计算个元素出现的概率

simbols=find(f~=0);

f=f(simbols);%将元素按出现的概率排列

[f,sortindex]=sot(f);

simbols=simbols(sortindex);

太阴历%产生码字 generate the codeword as the 52 bits of a double

len=length(simbols);

simbols_index=num2cell(1:len);

codeword_tmp=cell(len,1);

while length(f)>1,

index1=simbols_index{1};

index2=simbols_index{2};

codeword_tmp(index1)=addnode(codeword_tmp(index1),uint8(0));

codeword_tmp(index2)=addnode(codeword_tmp(index2),uint8(1));

f=[sum(f(1:2)) f(3:end)];

simbols_index=[{[index1 index2]} simbols_index(3:end)];

%将数据重新排列，是两个节点的频率尽量与前一个节点的频率想当

resort data in order to have two nodes with lower frequency as

first to

[f,sortindex]=sort(f);

simbols_index=simbols_index(sortindex);

end

%对应相应的元素与码字

codeword=cell(256:1);

codeword(simbols)=codeword_tmp;

%计算总的字符串长度

len=0;

for index=1:length(vector),

len=len+length(codeword{double(vector(index))+1});

end

%产生01序列

string=repmat(uint8(0),1,len);

pointer=1;

for index=1:length(vector),

code=codeword{double(vector(index))+1};

len=length(code);

string(pointer+(0:len-1))=code;

pointer=pointer+len;

end

%如果需要，加零

len=length(string);

pad=8-mod(len,8);

if pad>0,

string=[string uint8(zeros(1,pad))];

end

%保存实际有用的码字

codeword=codeword(simbols);

codelen=zeros(size(codeword));

weights=2.^(0:23);

maxcodelen=0;

for index 1:length(codeword),

len=length(codeword{index});

if len>maxcodelen,

maxcodelen=len;

end

if len>0,

code=sum(weights(codeword{index}==1));

code=bitset(code,len+1);

codeword{index}=code;

codelen(index)=len;

end

codeword=[codeword{:}]

%计算压缩后的向量

cols=length(string)/8;

string=reshape(string,8,cols);

weights=2.^(0:7);

zipped=uint8(weights*double(string));

%存储一个稀疏矩阵

huffcodes=sparse(1,1);% init sparse matrix

for index=1:numel(codeword),

huffcodes(codeword(index),1)=simbols(index);

end

%产生信息结构体

info.pad=pad;

碳的化学性质info.ratio=cols./length(vector);

info.length=length(vector);

中国红丝带网info.maxcodelen=maxcodelen;

function codeword_new=addnode(codeword_old,item)

codeword_new=cell(size(codeword_old));

for index=1:length(codeword_old),

codeword_new{index}=[item codeword_old{index}];

end

function vector=huff2norm(zipped,info)

%HUFF2NORM Huffman 解码器

%HUFF2NORM(X,INFO)根据信息体结构 info 返回向量 zipped 的解码结果%

%矩阵参数以X(:)形式输入

if~isa(zipped,'uint8'),

error('input argument must be a uint8 vector')

end

%产生01序列

len=length(zipped);

string=repmat(uint8(0),1,len.*8);

bitindex=1:8;

for index+1:len,

string(bitindex+8.*(index-1))=uint8(bitget(zipped(index),bitindex));

end

%调整字符串

string=logical(string(:)');% remove 0 padding

len=length(string);

%解码

weights=2.^(0:51);

vector=repmat(uint8(0),1,info,length);

vectorindex=1;

codeindex=1;

code=0;

for index=1:len,

code=bitset(code,codeindex,string(index));]

codeindex=codeindex+1;

byte=decode(bitset(code,codeindex),info);

if byte>0,%

vector(vectorindex)=byte-1;

codeindex=1;

code=0;

vectorindex=vectorindex+1;

end

function byte=decode(code,info)

byte=info.huffcodes(code);

function f=frequency(vector)

%FREQUENCY 计算元素出现概率

if~isa(vector,'uint8'),

error('input argument must be a uint8 vector')

end

f=repmat(0,1,256);

%扫描向量

len=length(vector);

for index=0:256,%

f(index+1)=sum(vector==uint8(index));

end

%归一化

f=f./len;

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