# Post-Filtering of Noisy Images Compressed by HEIF
## 5 Discussion  
In the sections above, we considered the simplest possible model of AWGN that contaminates a single component (grayscale) image. A question that arose is what are the differences that can be met in practice? Note that one can deal with an image corrupted by signal-dependent noise. Then, two ways are possible. One can follow the quite standard approach described in our paper [17] (i.e., apply a proper VST to convert the original image corrupted by signal-dependent noise to the image contaminated by pure additive noise). After this, the image should be compressed with QF, as recommended in Section 4.2, and stored or passed via the communication line. At the decompression and post-processing stage, just standard decompression by HEIF is carried out; after this, post-filtering is applied, and then inverse VST is performed. Within this procedure, the following is supposed: (1) the parameters of signal-dependent noise are a priori known or pre-estimated with high accuracy; (2) a proper variance-stabilizing transform exists and allows for the variance of pure additive noise to be determined; and (3) a priori information for carrying out inverse VST is available at the decompression stage (e.g., this information is passed as auxiliary data together with the compressed image in header). Another method is to study the application of HEIF to images corrupted by signal-dependent noise without VST, with proper recommendations. However, this method presumes additional investigations that need to be carried out. Second, what does one do if the image to be compressed is multichannel? Currently, we are not ready to answer this question precisely. However, several analogies and preliminary solutions can be found. Note that a variety of possible situations is possible. It can be that a multichannel image contains one or two component images that are corrupted by the noise while other components are practically noise-free. Then, a noisy component image can be compressed separately, as described above, while other component images can be compressed (without post-filtering) separately or jointly, according to the approaches typical for the compression of noise-free multichannel images [7]. However, to the best of our knowledge, there have been no attempts to apply HEIF for the compression of multispectral or hyperspectral data. If all or a large group of component images are noisy, then the approach described in [42] seems reasonable, as it presumes the use of proper VST for all component images  
Figure 9: Noisy image Fricco **(a)**, the results of its compression in the OOP by HEIF **(b)**, compressed with QF = 36 and post-filtered with the optimal \(\beta\) after decompression **(c)**, noisy image Diego **(d)**, the results of its compression in the OOP by HEIF **(e)**, compressed with QF = 36 and post-filtered with the optimal \(\beta\) after decompression **(f)**. and their joint compression (note that joint compression usually produces an approximately twice larger CR than component-wise compression for the same quality of compressed data). However, such an approach using HEIF as the basis needs additional studies. An important item is to understand (predict) whether an OOP exists or not for HEIF. Currently, we do not know of such studies. However, since it has been shown for the BPG coder that such a prediction is possible [38], and the BPG and HEIF coders have similar performance characteristics [17], then it is reasonable to expect that the prediction of the existence of an OOP for HEIF is also possible. In other words, there are many options in which to study the applicability of HEIF for the compression of remote sensing images, both single- and multichannel. Finally, a future direction could focus on whether or not the compression of noisy images with post-filtering can influence the image classification [11], feature selection [71], image segmentation and edge detection [72], and object recognition [18].