## 3 Results and Discussion
### Results for AT&T Face Dataset
#### 3.1.2 Results for Different Wavelet Families  
The experiments in Table 3 used the default settings of employing _haar_ with one level of decomposition for MRA-DWT/IDWT and _db2_ with five levels of decomposition for DWT/IDWT-IF and the mean-mean rule of image fusion. The following investigation shows the results of varying the wavelet family for MRA-DWT/IDWT. It is worth noting that different wavelet filters in the wavelet family for MRA-DWT/IDWT have effects when the process starts to decompose an image into sub-bands and when the process starts to reconstruct features from image fusion into one enhanced reconstructed image.  
Different wavelet families for MRA-DWT/IDWT show different characteristics of low- and high-pass filters. The explanation is as follows [58]: wavelet Haar, with only one vanishing moment (_haar_), is not smooth and has anti-symmetry; Daubechies wavelet, with only two vanishing moments (_db2_) for the wavelet function, is not considered smooth and does not have symmetry characteristics; Symlet, with two vanishing moments (_sym2_), is also not considered smooth and has near symmetry characteristics; biorthogonal (_bior nr.nd_) has exact symmetry and is considered smooth only if the wavelet order is large. In the abbreviation, _nr_ is the number of vanishing moments inside the reconstruction filter, and _nd_ is the number of vanishing moments inside the decomposition filter. In this research, we employed _bior 1.3, bior 2.2, bior 2.6, bior 3.3_, and _bior 3.7_.  
Figure 8a and Figure 8b display the results of using _haar_, _db2_, _sym2_, _bior 1.3, bior 2.2, bior 2.6, bior 3.3_, and _bior 3.7_ with one level of decomposition against the classification methods for Exp. 5 and 6, respectively. Figure 8a shows that the _haar_ wavelet yielded the best result, followed by _bior 1.3_ and _bior 2.2_. Figure 8b shows that _bior 2.6_ and _bior 3.3_ performed better. They improved the accuracy results by 0.8% (from 98% using _haar_ to 98.8% using _bior 2.6/bior 3.3_).  
In the subsequent investigation, we examined the effect of variations inside DWT/IDWT-IF from Exp. 6. Different from MRA-DWT/IDWT, various wavelet families inside DWT/IDWT-IF have the effects of decomposing input features and reconstructing them into fused features for image fusion purposes.  
Figure 7: The comparison of processing times for the AT&T Face Dataset; Exp. 5; Exp. 6 using _db2_ in DWT/IDWT-IF with levels of decomposition: one (Exp. 6a); three (Exp. 6b); five (Exp. 6c); and seven (Exp. 6d).  
To investigate DWT/IDWT-IF, we employed _bior 3.3_ for MRA-DWT/IDWT since it yielded the best results from the previous investigation. First, we checked using the _db2_ wavelet for one, three, five, and seven levels of decomposition. The peak of the best accuracy results came from five levels of decomposition. Figure 9 shows the results of this investigation. Knowing that five levels of decomposition performed best, we then varied the wavelet family for DWT/IDWT-IF, using _haar_, _db2_, _sym2_, and _bior 3.3_. The results in Figure 10 show that _db2_ performed the best among others for DWT/IDWT-IF if paired with five levels of decomposition.  
From these wavelet filter variations, we summarized for the AT&T Face Dataset, using _haar_ with one level of decomposition for MRA-DWT/IDWT, yielded 99.2% accuracy for Experiment 5; using _bior 3.3_ with one level of decomposition for MRA-DWT/IDWT, and _db2_ with five levels of decomposition for DWT/IDWT-IF, yielded 98.8% accuracy for Experiment 6. As mentioned, the AT&T Face Dataset has variations such as lighting conditions, facial expressions, facial attributes using glasses and no glasses, and image acquisition with a time gap. Our proposed method produced high recognition accuracy against these challenges inside the AT&T Face Dataset.  
Figure 8: Accuracy results (%) for the AT&T Face Dataset (proposed method) using different wavelet families in MRA-DWT/IDWT with one level of decomposition: (**a**) Experiment 5; (**b**) Experiment 6.