FastDaubechies2


1   package JSci.maths.wavelet.daubechies2;
2   
3   import JSci.maths.wavelet.FWT;
4   
5   /************************
6   * This is a very fast implementation of the
7   * Fast Wavelet Transform. It uses in-place computations
8   * for less memory usage. Data length should be
9   * a power of 2 a be at least of length 4.
10  * Handles boundaries by assuming periodicity.
11  * Ideal for image processing or processing large
12  * amount of data. Uses floats for more performance.
13  * Safety is minimal, so be careful!
14  * @author Daniel Lemire
15  *************************/
16  public final class FastDaubechies2 extends FWT  {
17    static final private float root3 =  (float)(Math.sqrt(3.0));
18    static final private float normalizer = (float)(Math.pow(2d,-.5d));
19    static final float[] scale = {(1f+(root3))*normalizer/4f,(3f+(root3))*normalizer/4f,(3f+(-1*(root3)))*normalizer/4f,(1f+(-1*(root3)))*normalizer/4f};
20    static final float[] wavelet = {-(1f+(-1*(root3)))*normalizer/4f,(3f+(-1*(root3)))*normalizer/4f,-(3f+(root3))*normalizer/4f,(1f+(root3))*normalizer/4f};
21  
22  
23    public FastDaubechies2() {
24    }
25  
26    public static void transform (float[] v,int last) {
27      float[] ans=new float[last];
28      final int half=last/2;
29      try {
30        for(int k=0;/*k<half*/;k++) {
31            ans[k+half]=v[(2*k+0)]*wavelet[0]+v[(2*k+1)]*wavelet[1]+v[(2*k+2)]*wavelet[2]+v[(2*k+3)]*wavelet[3];
32            ans[k]=v[(2*k+0)]*scale[0]+v[(2*k+1)]*scale[1]+v[(2*k+2)]*scale[2]+v[(2*k+3)]*scale[3];
33        }
34      } catch (IndexOutOfBoundsException   e) {}
35      ans[last-1]=v[last-2]*wavelet[0]+v[last-1]*wavelet[1]+v[0]*wavelet[2]+v[1]*wavelet[3];
36      ans[half-1]=v[last-2]*scale[0]+v[last-1]*scale[1]+v[0]*scale[2]+v[1]*scale[3];
37  
38      System.arraycopy(ans,0,v,0,last);
39    }
40  
41    public void transform (float[] v) {
42      int last;
43      for (last=v.length;last>4;last/=2) {
44        transform(v,last);
45      }
46      if(last!=4)
47        System.err.println("Careful! this should be a power of 2 : "+v.length);
48    }
49  
50    public void invTransform(float[] v) {
51      int last;
52      for (last=4;2*last<=v.length;last*=2) {
53        invTransform(v,last);
54      }
55      if(last!=v.length)
56        System.err.println("Careful! this should be a power of 2 : "+v.length);
57  
58    }
59  
60    public static void invTransform (float[] v, int last) {
61      int ResultingLength=2*last;
62      float[] ans=new float[ResultingLength];
63      try {
64        for(int k=0;/*k<last*/;k++) {
65            ans[(2*k+3)]+=scale[3]*v[k]+wavelet[3]*v[k+last] ;
66            ans[(2*k+2)]+=scale[2]*v[k]+wavelet[2]*v[k+last] ;
67            ans[(2*k+1)]+=scale[1]*v[k]+wavelet[1]*v[k+last] ;
68            ans[(2*k+0)]+=scale[0]*v[k]+wavelet[0]*v[k+last] ;
69        }
70      } catch (IndexOutOfBoundsException   e) {}
71      ans[ResultingLength-2]+=scale[0]*v[last-1]+wavelet[0]*v[ResultingLength-1] ;
72      ans[ResultingLength-1]+=scale[1]*v[last-1]+wavelet[1]*v[ResultingLength-1] ;
73      ans[0]+=scale[2]*v[last-1]+wavelet[2]*v[ResultingLength-1] ;
74      ans[1]+=scale[3]*v[last-1]+wavelet[3]*v[ResultingLength-1] ;
75      System.arraycopy(ans,0,v,0,ans.length);
76    }
77  }
78  
79
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