# Post-Filtering of Noisy Images Compressed by HEIF
## 4 Post-Filtering Opportunities and Results
### Post-Filtering Performance Analysis
Meanwhile, there was an OOP according to the metric PSNR-HVS-M for the test image Frisco (Figure 7e), although the PSNR-HVS-M\({}_{\text{p}\text{t}}\) in this OOP was not large (slightly exceeded 1 dB). As in the previous case of analysis, the PSNR-HVS-M\({}_{\text{p}\text{f}}\) was always larger than PSNR-HVS-M\({}_{\text{p}\text{t}}\) across the entire range of analyzed CR. However, the difference between PSNR-HVS-M\({}_{\text{p}\text{f}}\) and PSNR-HVS-M\({}_{\text{p}\text{t}}\) quickly reduced if the CR was increased (i.e., post-filtering became useless). In our opinion, it became practically useless for CR \(>\) 10 in Figure 7d, CR \(>\) 59 in Figure 7e, CR \(>\) 14 in Figure 7f) when the difference between the PSNR-HVS-M\({}_{\text{p}\text{f}}\) and PSNR-HVS-M\({}_{\text{p}\text{t}}\) was less than 1 dB (recall that a difference of less than 1 dB in the PSNR and PSNR-HVS-M of two images could hardly be noticed). Nevertheless, in our opinion, the use of post-filtering could be reasonable for a smaller CR (e.g., for CR \(\approx\) 8 (Figure 7a,d), CR \(\approx\) 30 (Figure 7b,e), and CR \(\approx\) 11 (Figure 7c,f), i.e., for a CR about 1.5 smaller than that one that corresponds to the OOP (if it exists)). Based on the results presented above in this subsection and in Table 1 (as well as the results obtained for other test images and several noise variance values), it is possible to recommend setting the QF at 8-10 larger than the QF for the OOP. Keeping in mind the recommendations in [17], we offer the following recommendations on setting the QF, depending on the noise variance (supposed to be known in advance or accurately pre-estimated) for post-filtering to be reasonably applied. The recommended QF values are given in Table 6. As seen, the recommended QF decreases if the AWGN variance increases. In addition, we provide the ranges of PSNR\({}_{\text{p}\text{f}}\), PSNR-HVS-M\({}_{\text{p}\text{f}}\), and CR\({}_{\text{p}\text{f}}\). The parameter QF\({}_{\text{OOP}}\) as well as the ranges of PSNR\({}_{\text{OOP}}\), PSNR-HVS-M\({}_{\text{OOP}}\), and CR\({}_{\text{OOP}}\) are also presented. As seen, the values of PSNR\({}_{\text{p}\text{f}}\) were larger than the corresponding PSNR\({}_{\text{OOP}}\) by about 1-3 dB, and the PSNR-HVS-M\({}_{\text{p}\text{f}}\) values were sufficiently larger than the corresponding PSNR-HVS-M\({}_{\text{OOP}}\) for a noise variance smaller than 130. Meanwhile, the CR for image compression with post-filtering was 1.5-4 times smaller than for QF\({}_{\text{OOP}}\), which is the price for better quality. To ensure that the presented tendencies and recommendations were valid, we analyzed six additional images. Three of them were the optical test images Baboon (that has complex structure), Goldhill (middle-complexity structure), and Peppers (low complexity image). These images can be found at [[https://ponomarenko.info/agu.htm](https://ponomarenko.info/agu.htm)]([https://ponomarenko.info/agu.htm](https://ponomarenko.info/agu.htm)) (accessed on 1 March 2025). Three other images were medical (Figure 8). These images have quite a simple structure since they contain rather large homogeneous image regions. The results obtained for the six test images above-mentioned are shown in Table 7. We present the PSNR for the original noisy image, PSNR\({}_{\text{f}}\) for the filter output applied to the non-compressed image, PSNR\({}_{\text{OOP}}\) for the OOP (according to data in Table 1), PSNR\({}_{\text{p}\text{f}}\) for the post-filtered images if the Q is set according to the recommendation in Table 6 and \(\beta\) is optimal, and the optimal \(\beta\) for each particular case.