用哈尔小波压缩

  很伤心，用哈尔小波压缩，本来期望变换能够带来很大的压缩效率。自己动过手，才发现自个太幼稚了。原本有两个想法：

  1. 用哈尔小波直接压缩数据，将能变0的通通写成0，减少数据量

  2. 即使不能直接写0，期望在0附近变化的量能够使用zip方式进行压缩。

  花了一天时间进行试验。最后发现：

  1. 哈尔小波压缩数据需要数据品质的降低。一旦大量数据被阀值筛选为0， 则反变化时，就会有大幅度的误差；

  2. 如果保留尽可能多的小数位，则相应的数据序列没有得到压缩，考虑使用zip方式进行压缩，却发现，针对哈尔变换后的数据压缩率比没有经过哈尔变换的数据低很多。。。

  无语，只能说明这个方法不适合我们高精度的应用。看到网上好多二代无损压缩的论文，先去研究下，再看吧。

  这里，把我试验使用的哈尔小波变化程序提供出来。

 

 

#include<iostream>
#include<stdio.h>
#include<fstream>
#include <math.h>

extern "C"
using namespace std;
double A[16];
double Ar[16];

const double range = 10 ;
const double delta = 0.01 ;
const int DoCount = 10;
int count;

void Decomposition(double* source)
{    
    int i ,j;
    double n[16];

    for(i=0;i<DoCount;i++){
        for(j=0;j<16;j++) {
         if(j<8) n[j] = double(source[j*2]+source[j*2+1])/2;
         else n[j] = double(source[(j-8)*2]-source[(j-8)*2+1])/2;
         if(fabs(n[j])<delta) n[j]=0.0;
        }
        
        for(j =0;j<16;j++){
            source[j]    =    n[j];
        }

    for(j=0;j<8;j++) {
         if(j<4) n[j] = double(source[j*2]+source[j*2+1])/2;
         else n[j] = double(source[(j-4)*2]-source[(j-4)*2+1])/2;
         if(fabs(n[j])<delta) n[j]=0.0;
        }
        for(j =0;j<8;j++){
            source[j]    =    n[j];
        }    
    
    for(j=0;j<4;j++) {
         if(j<2) n[j] = double(source[j*2]+source[j*2+1])/2;
         else n[j] = double(source[(j-2)*2]-source[(j-2)*2+1])/2;
         if(fabs(n[j])<delta) n[j]=0.0;
        }
        for(j =0;j<4;j++){
            source[j]    =    n[j];
        }
    
    for(j=0;j<2;j++) {
         if(j<1) n[j] = double(source[j*2]+source[j*2+1])/2;
         else n[j] = double(source[(j-1)*2]-source[(j-1)*2+1])/2;
         if(fabs(n[j])<delta) n[j]=0.0;
        }
        for(j =0;j<2;j++){
            source[j]    =    n[j];
        }
      
      cout<<"Haar变换("<<i<<")后图像样本:"<<endl;
     for(j=0;j<16;j++){
         if(j%8==0&&j!=0)cout<<" ";
         printf("%1f ",source[j]);
     }
     cout<<endl;
      
    }


    return ;
}

void Rebuild(double* source)
{

    int i,j;
    double n[16];
  for(i=0;i<DoCount;i++) {
        n[0] = double(source[0]+source[1]);
        n[1] = double(source[0]-source[1]);
        for(j =0;j<2;j++){
            source[j]    =    n[j];
        }

        n[0] = double(source[0]+source[2]);
        n[1] = double(source[0]-source[2]);
        n[2] = double(source[1]+source[3]);
        n[3] = double(source[1]-source[3]);
        for(j =0;j<4;j++){
            source[j]    =    n[j];
        }    
    
        n[0]=double(source[0]+source[4]);
        n[1]=double(source[0]-source[4]);
        n[2]=double(source[1]+source[5]);
        n[3]=double(source[1]-source[5]);
        n[4]=double(source[2]+source[6]);    
        n[5]=double(source[2]-source[6]);
        n[6]=double(source[3]+source[7]);
        n[7]=double(source[3]-source[7]);
        for(j =0;j<8;j++){
            source[j]    =    n[j];
        }
    
        n[0]=double(source[0]+source[8]);
        n[1]=double(source[0]-source[8]);
        n[2]=double(source[1]+source[9]);
        n[3]=double(source[1]-source[9]);
        n[4]=double(source[2]+source[10]);    
        n[5]=double(source[2]-source[10]);
        n[6]=double(source[3]+source[11]);
        n[7]=double(source[3]-source[11]);
        n[8]=double(source[4]+source[12]);
        n[9]=double(source[4]-source[12]);
        n[10]=double(source[5]+source[13]);
        n[11]=double(source[5]-source[13]);
        n[12]=double(source[6]+source[14]);    
        n[13]=double(source[6]-source[14]);
        n[14]=double(source[7]+source[15]);
        n[15]=double(source[7]-source[15]);
        for(j =0;j<16;j++){
            source[j]    =    n[j];
        }

    
      cout<<"重构("<<i<<")后图像样本:" << endl;
     for(j=0;j<16;j++){
         if(j%8==0&&j!=0)cout<<" ";
         printf("%f ",source[j]);
      }
     cout<<endl;
    }
  return ;

}


int main()
{
    float temp[16];
    int i,j;
  double *source;
  float value = 0;
    for(i=0;i<16;i++){
        value = value + ceil(drand48()*range*1000)/1000;
        temp[i] = value;
    }

    for(i=0;i<16;i++){
      A[i]    =    double(temp[i]);
  }

    cout<<"源图像样本:"<<endl;
    
    for(i=0;i<16;i++){
        if(i%8==0&&i!=0)cout<<" ";
        cout<<temp[i]<<" ";    
    }
    cout<<endl;        
    source = new double[16];
    for(i=0;i<16;i++){
        source[i]    =    A[i];
    }
  /*
    for(count=0;count<4;count++){
        
        source    =    new double*[8];
        for(i=0;i<8;i++){
            source[i]    =    new double[8];
        }
        
        for(i=0;i<8;i++){
            for(j=0;j<8;j++){
                int a = ( (count>=2) ? i+8 : i );
                int b = ((count%2==1) ? j+8 : j);
                source[i][j]    =    A[a][b];
            }
        }
        */
        Decomposition(source);

    for(i=0;i<16;i++){
        Ar[i]    =    source[i];
  }

  Rebuild(source);
        
/*
    cout<<"重构后图像样本:"<    for(count=0;count<4;count++){
        
        double **source;
        source    =    new double*[8];
        for(i=0;i<8;i++){
            source[i]    =    new double[8];
        }
        
        for(i=0;i<8;i++){
            for(j=0;j<8;j++){
                int a = ( (count>=2) ? i+8 : i );
                int b = ((count%2==1) ? j+8 : j);
                source[i][j]    =    Ar[a][b];
            }
        }
        
        

        for(i=0;i<8;i++){
            for(j=0;j<8;j++){
                int a = ( (count>=2) ? i+8 : i );
                int b = ((count%2==1) ? j+8 : j);
                A[a][b]    =    source[i][j];
            }
        }

    }

    for(i=0;i<16;i++){

        if(i%8==0&&i!=0)cout<        for(j=0;j<16;j++){
            
            if(j%8==0&&j!=0)cout<<" ";
            int a=int(A[i][j]+0.5);
            cout<            //printf("%.1f ",A[i][j]);
        }
        cout<    }
    */
    free(source);
    return 1;
}