###### Abstract
Second, due to this, a so-called optimal operation point (OOP) can be observed, i.e., such a parameter of a coder that the \"distance\" between the compressed and true (noise-free) images is minimal. By distance, we mean some similarity measure, and this can be a mean square error (MSE, then the OOP would correspond to its minimum) or the peak signal-to-noise ratio (PSNR, then the OOP would correspond to its maximum) [22; 23; 24]. The OOP can also be observed for visual quality metrics [24; 25] such as PSNR-HVS-M [26] and MS-SSIM [27]. Note that the use of visual quality metrics has become popular in many modern applications including in stereoscopic, panoramic and 360 degree imaging [28; 29; 30]. Compression in the OOP (or its neighborhood if the OOP is determined with some error), if it exists, has two advantages. First, the provided CR is usually quite high. Second, the quality of the compressed image appears to be better than the quality of the uncompressed (original, noisy, or compressed in a lossless manner) image. This can be, e.g., favorable for image classification [31]. Additionally, note that the OOP might exist not only for additive noise but also for other types of noise including signal-dependent and multiplicative for methods that employ a variance stabilizing transform (VST) or that perform compression without VST. An OOP might also exist for different coders, based both on a discrete cosine transform (DCT) or wavelets (for example, JPEG2000) [32]. Recently, the possible existence of an OOP [33; 34] has been demonstrated for the coder, BPG (better portable graphics) [35; 36; 37]. This compression technique has several advantages. It outperforms JPEG considerably in the sense of a better quality for a given size of compressed images and the compression is fast enough with clear rules of providing a desired PSNR. Due to this, the encoder has become popular in different portable devices as well as for online encoding applications and these advantages were the reasons why BPG has attracted our attention [36; 37]. The current paper incorporates the results of [36] and concentrates on the prediction of the OOP's existence and estimating the performance parameters for it. This is explained by the following. Since the true image is absent, the OOP cannot be determined exactly and its existence or absence can only be predicted (at least, this has been shown for coders other than BPG coders) [24; 29]. Assuming that it is also possible for BPG, it can then be supposed that it will be possible to give recommendations for how to set the compression parameters (namely, the quality parameter Q for BPG) to provide an appropriate quality. This is the main goal of this paper. The paper contributions consist in the following. First, based on the results of many test images corrupted by AWGN having different values of noise variance, a Q for a possible OOP is established depending on the noise standard deviation; this dependence is shown to be logarithmic opposite to the linear dependences established in [24] for other coders. Second, a modification of the procedure [24] is proposed and its thorough analysis is carried out. In particular, it is proposed to use rational functions in curve fitting into scatter-plots. This analysis shows that there are, at least, two statistical parameters that can be quickly and easily calculated in the DCT domain that can be used for predicting an improvement or reduction in two metrics. Third, the accuracy of prediction is analyzed and factors such as noise realization and the number of blocks that influence the accuracy are considered. Based on this analysis, practical recommendations are given that allows compression automation. Fourth, initial data concerning the lossy compression of single-channel images corrupted by Poisson noise and three-channel images corrupted by AWGN are presented, demonstrating the possible existence of OOPs for these cases. Finally, we show that the BPG coder is more efficient compared to other coders earlier considered in [24].