Visual information, such as images, is one of the most important parts of the digital realm. Its volume quickly increases due to better resolution of imagers and a large amount of images acquired each day. The acquired images should be stored on personal computers, servers, etc., and/or transferred via communication lines. A common way to reduce the data size is to apply compression techniques where lossy compression is often preferable because it is able to provide a significantly higher compression ratio compared to lossless compression. Meanwhile, it is necessary to control quality of lossy compressed images to avoid (minimize) negative consequences of introduced distortions. To solve this task, this paper proposes ways to predict mean squared error (MSE) of introduced distortions for better portable graphics (BPG) lossy compression. Such a prediction can be helpful in scenarios when an image has to be compressed in visually lossless manner or an appropriate compromise between the attained compression ratio (CR) and compressed image quality should be produced. It is shown that MSE is highly correlated not only with compression control parameter Q used in the BPG encoder, but with characteristics (complexity) of an image to be compressed. We present and compare several approaches to MSE prediction based on image fast preliminary analysis using local image activity and entropy. The practical recommendations for the MSE prediction are given.

Digital images of a rather large size are often employed in medical practice and other applications. It is desired to compress them if transmission via communication channels and/or efficient storage is needed. Then, lossy compression is mostly applied and an appropriate quality of compressed images has to be provided. In this paper, we consider pre-requisites for predicting mean square error (MSE) in lossy image compression by better portable graphics (BPG) coder, which is often treated as possible substitution for JPEG. It is shown that MSE and, respectively, peak signal-to-noise ratio (PSNR) are well controlled by a parameter Q used in the BPG-coder to vary its characteristics. However, MSE also depends on the characteristics of the image, which can be described using entropy. Thus, it is necessary to take into account the image characteristics when compressing an image. This study investigates how well the entropy can describe image characteristics, namely the image complexity for future MSE prediction for BPG-based lossy compression. It is proposed to use entropy for MSE prediction in the BPG-based lossy compression as a classification factor.

Lossy image compression becomes a standard way to solve the problem of the rapidly increasing image size that is faced due to better quality of sensors and spatial resolution. Compression of noise-free images is mostly considered. However, images are often corrupted by noise and this property needs to be taken into account in solving the problem of efficient lossy compression. One of the peculiarities of lossy compression of noisy images is the filtering effect that often leads to existence of the so-called optimal operation point (OOP) for which a compressed image in sense of quality is closer to noise free compared to the noisy image. OOP existence can be predicted for some simple noise models such as Gaussian noise for greyscale and color images. Here our study deals with OOP prediction for images corrupted by Poisson noise compressed by Better Portable Graphics (BPG) coder. We demonstrate the possibility of OOP prediction for such metrics as PSNR and PSNR-HVS-M and verify the proposed approach performance using images that have not been used in the preliminary “training”. In addition, the formula for the OOP position determination is presented.

With a resolution improvement, the size of modern remote sensing images increases. This makes it desirable to compress them, mostly by using lossy compression techniques. Often the images to be compressed (or some component images of multichannel remote sensing data) are noisy. The lossy compression of such images has several peculiarities dealing with specific noise filtering effects and evaluation of the compression technique's performance. In particular, an optimal operation point (OOP) may exist where quality of a compressed image is closer to the corresponding noise-free (true) image than the uncompressed (original, noisy) image quality, according to certain criterion (metrics). In such a case, it is reasonable to automatically compress an image under interest in the OOP neighborhood, but without having the true image at disposal in practice, it is impossible to accurately determine if the OOP does exist. Here we show that, by a simple and fast preliminary analysis and pre-training, it is possible to predict the OOPs existence and the metric values in it with appropriate accuracy. The study is carried out for a better portable graphics (BPG) coder for additive white Gaussian noise, focusing mainly on one-component (grayscale) images. The results allow for concluding that prediction is possible for an improvement (reduction) in the quality metrics of PSNR and PSNR-HVS-M. In turn, this allows for decision-making about the existence or absence of an OOP. If an OOP is absent, a more "careful" compression is recommended. Having such rules, it then becomes possible to carry out the compression automatically. Additionally, possible modifications for the cases of signal-dependent noise and the joint compression of three-component images are considered and the possible existence of an OOP for these cases is demonstrated.

The subject matter is lossy compression using the BPG encoder for medical images with varying levels of visual complexity, which are corrupted by Poisson noise. The goal of this study is to determine the optimal parameters for image compression and select the most suitable metric for identifying the optimal operational point. The tasks addressed include: selecting test images sized 512x512 in grayscale with varying degrees of visual complexity, encompassing visually intricate images rich in edges and textures, moderately complex images with edges and textures adjacent to homogeneous regions, and visually simple images primarily composed of homogeneous regions; establishing image quality evaluation metrics and assessing their performance across different encoder compression parameters; choosing one or multiple metrics that distinctly identify the position of the optimal operational point; and providing recommendations based on the attained results regarding the compression of medical images corrupted by Poisson noise using a BPG encoder, with the aim of maximizing the restored image’s quality resemblance to the original. The employed methods encompass image quality assessment techniques employing MSE, PSNR, MSSIM, and PSNR-HVS-M metrics, as well as software modeling in Python without using the built-in Poisson noise generator. The ensuing results indicate that optimal operational points (OOP) can be discerned for all these metrics when the compressed image quality surpasses that of the corresponding original image, accompanied by a sufficiently high compression ratio. Moreover, striking a suitable balance between the compression ratio and image quality leads to partial noise reduction without introducing notable distortions in the compressed image. This study underscores the significance of employing appropriate metrics for evaluating the quality of compressed medical images and provides insights into determining the compression parameter Q to attain the BPG encoder’s optimal operational point for specific images. Conclusions. The scientific novelty of the findings encompasses the following: 1) the capability of all metrics to determine the OOP for images of moderate visual complexity or those dominated by homogeneous areas; MSE and PSNR metrics demonstrating superior results for images rich in textures and edges; 2) the research highlights the dependency of Q in the OOP on the average image intensity, which can be reasonably established for a given image earmarked for compression based on our outcomes. The compression ratios for images compressed at the OOP are sufficiently high, further substantiating the rationale for compressing images in close proximity to the OOP.

This chapter contains the results obtained during execution of Ukrainian-French Project within “Dnipro” framework in 2022 intended on design of methods and means for processing multichannel remote sensing data using the trained neural networks. Neural net

Remote sensing provides data (images) important for many modern applications. Image number and average size tend to increase. This makes their transfer via communication lines, storage, and dissemination problematic. Thus, compression should be applied where lossy compression is mostly used. Most methods of lossy compression assume that images do not contain noise. Meanwhile, images are often noisy, and this should be considered in the design and performance analysis of image compression techniques. Lossy compression has already been studied by several coders. However, it has not been investigated for the recently proposed atomic transform-based techniques that possess several advantages, in particular, the ability to provide privacy of compressed data. The main subject of this paper is the peculiarities of noisy image lossy compression by an atomic transform-based coder. Our goal is to analyze whether the considered compression method provides the noise filtering effect and the so-called optimal operation point. The task is to obtain rated distortion curves for the atomic transform-based coder applied to noisy images and to analyze their behavior for several performance characteristics such as quality metrics and compression ratio. In the first order, the monotonicity of the main dependence is of interest. The main results are as follows. First, it is shown that the dependencies have non-monotonic behavior and the appearance of analogs of optimal operation point is possible, at least, for such metric as maximal absolute error. Second, there is a specific dependence of compression ratio on a parameter called UBMAD that controls compression. Experiments have been performed on several noisy test images having different complexity and contaminated by noise of different intensities. In conclusion, it is demonstrated that one more coder might have optimal operation points for images having a rather simple structure. However, at the moment, it is difficult to predict its existence and the corresponding coder parameters.

This chapter considers the lossy compression of three-channel images corrupted by additive white Gaussian noise. The better portable graphics (BPG) encoder that has three different operation modes is studied. As for other encoders, a noise filtering effect is observed and it influences the encoder performance. For certain conditions (image complexity and noise intensity), the so-called optimal operation point (OOP) may exist. The main property of OOP is that the quality of a compressed image (calculated with respect to the true image) is better than the quality of the corresponding noisy image according to a given metric (either conventional such as mean square error or some visual quality metric). Knowledge concerning the OOP existence and compression parameters in it for a given noisy image can be useful. In the case of OOP existence, it is reasonable to compress a given image in OOP or its neighborhood. If OOP does not exist, a more “careful” lossy compression is expedient. The problem is that in practice the true image is not available, and, thus, it is impossible to calculate full-reference metrics for compressed and noise-free images. Meanwhile, we show in this paper that it is possible to predict compression parameters for a given noisy image in advance. Moreover, this prediction is fast and accurate enough for a decision undertaking on what coder parameter to set to reach OOP. In addition, in this paper, we demonstrate that it is possible to predict the compression parameters not only in OOP but also in its neighborhood. This allows for undertaking more reliable decisions. Prediction opportunities are shown for two visual quality metrics and three typical modes of the BPG coder operation: 4:4:4, 4:2:2, and 4:2:0. One novel way of prediction accuracy improvement based on the joint use of two input parameters is shown.

An increase in the number of images and their average size is the general trend nowadays. This increase leads to certain problems with data storage and transfer via communication lines. A common way to solve this problem is to apply lossy compression that provides sufficiently larger compression ratios compared to lossless compression approaches. However, lossy compression has several peculiarities, especially if a compressed image is corrupted by quite intensive noise. First, a specific noise-filtering effect is observed. Second, an optimal operational point (OOP) might exist where the quality of a compressed image is closer to the corresponding noise-free image than the quality of the original image according to a chosen quality metric. In this case, it is worth compressing this image in the OOP or its closest neighborhood. These peculiarities have been earlier studied and their positive impact on image quality improvement has been demonstrated. Filtering of noisy images due to lossy compression is not perfect. Because of this, it is worth checking can additional quality improvement be reached using such an approach as post-filtering. In this study, we attempt to answer the questions: “is it worth to post-filter an image after lossy compression, especially in OOP’s neighborhood? And what benefit can it bring in the sense of image quality?”. The study is carried out for better portable graphics (BPG) coder and the DCT-based filter focusing mainly on one-component (grayscale) images. The quality of images is characterized by several metrics such as PSNR, PSNR-HVS-M, and FSIM. Possible image quality increasing via post-filtering is demonstrated and the recommendations for filter parameter setting are given.

This chapter deals with lossy compression of images that have been corrupted by additive noise. The chapter's key contribution is that the analysis is done from the perspective of compressed image visual quality. Several coders are explored for which the compression ratio is regulated in various ways. Lossless coding usually does not produce sufficient compression ratios for many practical applications. Visual quality metrics that are the most adequate for the considered application (WSNR, MS-SSIM, PSNR-HVS-M and PSNR-HVS) are used. The objective is to analyze is optimal operation point (OOP) possible according to visual quality metrics. It is demonstrated that, under certain conditions, visual quality of compressed images can be slightly better than quality of original noisy images due to image filtering through lossy compression, i.e., OOP might exist. The “optimal” parameters of coders for which this positive effect can be observed depend upon standard deviation of the noise. We propose an algorithm to determine coder parameters in OOP. This enables the development of automated techniques for compressing noisy images at the vicinity of the optimal operation point, i.e. when visual quality improves or declines insufficiently. Another advantage is that compression ratio for this case is quite high. The results of a series of grayscale test images with various noise variations are shown.

Lossy image compression is a popular way to get higher compression ratio, it also has several peculiarities if one deals with compressing images corrupted by noise. First, a specific noise filtering effect is observed. Second, optimal operational point (OOP) might exist where quality of a compressed image is closer to the corresponding noise-free image according to a chosen quality metric. In this case, it is worth compressing this image in OOP area. These peculiarities have been earlier mainly studied for grayscale images. In this paper, we analyze compression of color images corrupted by additive white Gaussian noise using better portable graphics (BPG) encoder in the cases of different chroma subsampling. Based on simulation results obtained for a set of color images, the initial recommendations on encoder parameter setting are given.

A BPG (better portable graphics) coder is a novel approach that aims to replace common standards of compression such as JPEG, JPEG2000 and so on. That is why, the BPG coder needs a detailed analysis of its basic characteristics from the viewpoint of visual quality and compression ratio. The BPG coder can use different modes of chroma subsampling for color and three-channel images and it is worth analyzing and comparing them. In practice, images to be compressed are often noisy. Then, lossy compression of such images has a specific noise filtering effect. In particular, optimal operation point (OOP) might exist where compressed image quality is closer to the corresponding noise-free (true) image than uncompressed (original, noisy) image quality according to certain criterion (metric). It is also needed to analyze the coder performance from compression ratio point of view. In this paper, we pay attention on impact of different chroma subsampling modes on image quality and compression ratio. Based on simulation results obtained for a set of color images, the best possible ways of compression are recommended.

Image lossy compression is widely used nowadays. A common assumption is that images subject to compression are noise-free. If intensive (visually noticeable) noise is present, lossy compression has several peculiarities that have to be taken into account. These peculiarities have been earlier studied for several coders, but they have not yet been analyzed for Better Portable Graphics (BPG) coder proposed recently and controlled by a quality parameter Q. In this paper, performance of this coder is analyzed for the case of additive white Gaussian noise using two known visual quality metrics, PSNR-HVS-M and MS-SSIM. It is demonstrated that for both metrics it is possible that optimal operation point exists. This usually happens for quite simple structure images and/or if noise intensity is high enough. Based on simulation results obtained for a set of grayscale images initial recommendations concerning Q setting are given for practice.