# Post-Filtering of Noisy Images Compressed by HEIF
## 1 Introduction and Related Work  
An obvious tendency in modern computer vision (CV), remote sensing (RS), and medical diagnostics (MD) is the increased number of acquired images and their size [1, 2, 3, 4]. For some applications, the acquired images should be processed and passed to potentialcustomers or decision undertaking systems quite quickly. For other practical situations, the acquired data have to be effectively saved for their future use such as in medical and multitemporal imaging [3; 5]. In these cases, efficient compression may be needed [5; 6; 7]. Existing compression techniques can be divided into two large groups: lossless [6] and lossy [7]. Both are widely used depending on the application, priority of requirements, and imposed restrictions. Lossless compression methods introduce no distortions into compressed images (data) but the produced compression ratio (CR) is usually not large (especially for images contaminated by noise) and cannot be varied (for given data, it can only be slightly improved by using a more efficient coder). If the attained CR is not appropriate, one has to apply a lossy compression technique [7; 8; 9]. The advantages of the compression techniques in this group consist of a considerably larger attained CR and a possibility of its variation, however, this is at the expense of distortions being introduced. A typical situation is that a larger produced CR leads to larger distortions that can become inappropriate or even annoying [1; 8]. Then, one has to provide a reasonable trade-off between the attained CR and quality of the lossy compressed images, which happens in optical RS [9] and medical [10] imaging. This takes place in SSIM-based optimization [11], approaches to compression based on the just noticeable difference (JND) [12], and a better portable graphics (BPG) coder [13]. Note that such a trade-off should often be provided quickly and with the appropriate accuracy [13; 14]. A positive feature in this sense is that the dependences of a metric characterizing lossy compressed image quality (e.g., mean square error (MSE) and CR) on a parameter that controls compression (PCC), such as the quality factor (QF) for compression techniques JPEG and HEIF [15], are usually monotonous (e.g., the MSE increases if the QF decreases for the mentioned coders). This allows for a potential reaching of the desired metric value with better or worse accuracy depending on the coder used, PCC employed, the metric exploited in image quality characterization, the procedure used for PCC variation, etc. [16]. In some practical situations, it is possible to ensure the high accuracy of providing a desired metric value if the PCC values are not discrete [16], but at the expense of several iterations when multiple compressions/decompressions of a considered image are needed. In other situations, the provided accuracy is lower (but can still be appropriate) with less computational expenses [15; 17]. One reason can be the discrete nature of PCC [17]; another reason could be the residual errors of a two-stage procedure [13; 15] or metric value prediction [12]. It is worth noting here that distortions can be characterized by conventional metrics such as the MSE or peak signal-to-noise ratio (PSNR), visual quality metrics (e.g., SSIM [11]), and their visibility threshold (see the just noticeable distortion (JND) concept in [12]). It is also possible to characterize introduced distortions by their impact on the classification or recognition of compressed images [11; 18]. The described dependences and properties take place in lossy image compression if an image subject to compression is noise-free or, at the very least, the noise can hardly be noticed. However, for many classes of images, this assumption is not valid, for example, synthetic aperture radar (SAR) images that are always noisy due to speckle [19]. Conventional color images acquired in bad conditions can also be noisy [20]. A certain percentage of noisy (junk) component images are always present in hyperspectral [21] images.