Image Processing Basics - Digital Signal Processing: Fundamentals and Applications - page 741

Now, we show the first row result for the LL2 band in MATLAB as follows:
>> idwt([1 1]/sqrt(2),[ 332.6937 2.4749 ],1)'
ans ¼ 233.5000 237.0000
The recovered LL1 band is shown in the following:

233.5000 237.0000 17.5000 4.0000

248.0000 266.0000 2.0000 12.0000

15.5000 6.0000 3.5000 9.0000

5.0000 6.0000 41.0000 4.0000

Now we are at the level-1 inverse process. For simplicity, the first column result in MATLAB and the completed
results are listed below, respectively.
>> idwt([1 1]/sqrt(2),[ 233.5000 248.0000 15.5000 5.0000],1)'
ans ¼ 176.0696 154.1493 178.8980 171.8269

176.0696 163.3417 14.8492 9.1924

154.1493 171.8269 9.8995 3.5355

178.8980 183.8478 30.4056 11.3137

171.8269 192.3330 27.5772 5.6569

Finally, we perform the inverse of the row transform at level 1. The first row result in MATLAB is listed below:
>> idwt([1 1]/sqrt(2),[ 176.0696 163.3417 14.8492 9.1924],1)'
ans ¼ 114.0000 135.0000 122.0000 109.0000

The final inverse DWT is obtained as

114.0000 135.0000 122.0000 109.0000

102.0000 116.0000 119.0000 124.0000

105.0000 148.0000 138.0000 122.0000

141.0000 102.0000 140.0000 132.0000

Since there is no quantization for each coefficient, we obtain a perfect reconstruction.

Figure 14.42 shows 8-bit grayscale image compression by applying the one-level wavelet trans-
form, in which a 16-tap Daubechies wavelet is used. The wavelet coefficients (each is coded using 8
bits) are shown in Figure 14.42 (b). By discarding the HL, LH, and HH band coefficients, we can
achieve 4:1 compression. The decoded image is displayed in Figure 14.42 ( c). The MATLAB program
is listed in Program 14.4.
Figure 14.43 illustrates two-level wavelet transform and compression results. By discarding the
HL2, LH2, HH2, HL1, LH1, and HH1 subbands, we achieve 16:1 compression. However, as shown in