Digital images obtained from remote sensing (RS) systems have become essential in numerous technological applications across diverse domains, including environmental monitoring, agriculture, urban planning, and defense. These images are typically characterized by high spatial and spectral resolution, resulting in large data volumes. Compared to other data types, their substantial size presents challenges in terms of the efficient application of machine learning (ML) and computer vision (CV) methods. In particular, the processing of such large-scale data can be computationally intensive and time-consuming, making it difficult to deploy conventional ML and CV techniques in scenarios requiring real-time responses or in systems with limited processing resources, such as autonomous platforms. One of the key issues in this context is the development of compact image representations that retain essential features for further analysis. These representations must reduce data dimensionality without losing critical information required for classification, clustering, and other ML/CV tasks. In this study, we explore the discrete atomic transform (DAT), which is based on atomic functions, as a potential solution to this problem. Previous research has demonstrated that DAT provides valuable benefits in terms of data compression and encryption, thereby enabling secure and efficient storage and transmission. The focus of this work is to assess whether DAT is suitable for ML and CV applications, particularly in the context of image clustering. We evaluated the performance of the well-known k-means clustering algorithm when applied to DAT images. The experimental results demonstrate that using DAT significantly reduces computation time, achieving multiple-fold acceleration, without compromising clustering quality. This suggests that DAT not only minimizes data size and preserves structural and statistical features relevant to learning-based tasks. These results indicate that the integration of DAT into preprocessing pipelines for RS imagery is a promising approach. The proposed method can enhance the efficiency of downstream ML and CV algorithms, especially in constrained environments where computational resources are limited. Overall, the discrete atomic transform is a practical and versatile method for improving the scalability and applicability of intelligent image analysis in remote sensing and related fields.

Satellite Light Detection and Ranging (LiDAR) systems produce high-resolution data essential for confronting critical environmental challenges like climate change, disaster management, and ecological conservation. A HyperHeight Data Cube (HHDC) is a novel representation of LiDAR data. HHDCs are structured three-dimensional tensors, where each cell captures the number of photons detected at specific spatial and height coordinates. These data structures preserve the detailed vertical and horizontal information essential for ecological and topographical analyses, particularly Digital Terrain Models and canopy height profiles. In this paper, we investigate lossless compression techniques for large volumes of HHDCs to alleviate constraints on onboard storage, processing resources, and downlink bandwidth. We analyze several methods, including bit packing, Rice coding (RC), run-length encoding (RLE), and context-adaptive binary arithmetic coding (CABAC), as well as their combinations. We introduce the block-splitting framework, which is a simplified version of octrees. The combination of RC with RLE and CABAC within this framework achieves a median compression ratio greater than 24, which is confirmed by the results of processing two large sets of HHDCs simulated using the Smithsonian Environmental Research Center NEON data.

Image classification is an essential part of computer vision. A lot of approaches, in particular, based on applying convolutional neural networks have been proposed. In this paper, we investigate the impact of discrete atomic compression (DAC) on state-of-the-art models. The DAC algorithm ensures low resource intensive image encryption and compression features. Such a combination makes its usage promising, especially taking into account a huge number of digital images and current data protection requirements. DAC has lossy and lossless compression modes. The first one provides a higher compression ratio in combination with distortions. The aim of this research is to answer the following question: how does quality loss, which is introduced by DAC, affect the efficiency of the MobileNetV2, VGG16, VGG19, ResNet50, NASNetMobile and NASNetLarge models? It is shown that the difference between classifying images before and after lossy DAC-compression is insignificant.

Digital images play a particular role in a wide range of systems. Image processing, storing and transferring via networks require a lot of memory, time and traffic. Also, appropriate protection is required in the case of confidential data. Discrete atomic compression (DAC) is an approach providing image compression and encryption simultaneously. It has two processing modes: lossless and lossy. The latter one ensures a higher compression ratio in combination with inevitable quality loss that may affect decompressed image analysis, in particular, classification. In this paper, we explore the impact of distortions produced by DAC on performance of several state-of-the-art classifiers based on convolutional neural networks (CNNs). The classic, block-splitting and chroma subsampling modes of DAC are considered. It is shown that each of them produces a quite small effect on MobileNetV2, VGG16, VGG19, ResNet50, NASNetMobile and NASNetLarge models. This research shows that, using the DAC approach, memory expenses can be reduced without significant degradation of performance of the aforementioned CNN-based classifiers.

The atomic functions-based image processing system (AFIPS) is based on discrete atomic transform (DAT). It provides a combination of image encryption and compression features with a machine learning-oriented data format. Taking into account the current data processing and analysis trends, applying AFIPS is promising. In this paper, a problem of its complexity reduction is considered. The new coding scheme, which ensures a significant decrease in the number of arithmetic operations, is proposed, and its efficiency exploration is given in terms of different indicators. In particular, it is shown that the proposed modification of AFIPS provides a higher compression ratio and, hence, greater memory savings when applying this algorithm with three modes of the DAT procedure: classic, block-splitting, and chroma-subsampling. Also, the suggested improvement reduces the time complexity that is illustrated by processing a satellite image dataset. In addition, the practical aspects of the further applications, including UAV image processing and analysis, are discussed.

This paper deals with the compression of three-channel images that offers near-lossless and lossless options. The lossy compression is based on discrete atomic functions. They provide several benefits such as easy control of introduced distortions, privacy protection, and quite efficient compression. Lossless mode is provided due to archiving the differences between the original and lossy compressed images. An increase in a compression ratio of the lossy compression part leads to larger differences and worse lossless compression. Due to this, an optimum has to be found. We look for this optimum using a set of color images of different complexity. It is shown that the maximal compression ratio of lossless compression is achieved for traditional modes of atomic compression when the peak signal-to-noise ratio of the lossy compressed part is about 40-42 dB, i.e. practically near-lossless or visually lossless compression is carried out.

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.

Green computing is a popular trend nowadays. In this paper, we show a way to incorporate this tendency in lossy image compression by an efficient coder based on discrete cosine transform. We study the case when it is desired to provide distortions characterized by mean square error not worse than a given threshold. In opposite to two-step and iterative methods that require, at least, two compression and one decompression of an image subject to processing, the proposed approach is based on quite accurate prediction of errors due to lossy compression in each block and, thus, for the entire image. Prediction employs information about quantization step and local activity in each block characterized by local standard deviation that can be calculated very quickly. Using test images, the dependences of introduce errors’ statistics on local standard deviation of information component are obtained by curve fitting into scatter-plots. This is done in advance and the obtained dependences can be then used for any image subject to lossy compression. The accuracy of the proposed approach is analyzed and shown appropriate for practical applications.

Digital images are a particular type of data. They have numerous applications. Taking into account current challenges and trends, image compression and protection have to be ensured. Data format, which provides fast analysis of the image compressed, is needed. In order to satisfy a combination of these requirements, an appropriate information system should be developed. In this paper, we design such a system based on atomic functions (AF) that are solutions of special functional differential equations and, in terms of function theory, are as good constructive tools as trigonometric polynomials. AF-based image processing system (AFIPS), which satisfies the requirements considered, is developed. A core of this system is discrete atomic transform (DAT). Data protection feature of AFIPS is provided by the possibility to vary a structure of the procedure DAT. Constructive approximation properties of AF ensure high lossy and lossless image compression, as well as good image representation by DAT-coefficients. Software implementation of AFIPS is investigated. The results of test data processing are given.

Digital images are a particular type of data. They have a lot of applications. Huge image datasets have been collected. Their processing, storing, analyzing, and transferring via networks require great expenses. For this reason, a development of low resource intensive image processing algorithms is of particular importance. Discrete atomic compression (DAC) is an image compression algorithm based on atomic functions. It provides a combination of data compression and protection features with machine learning oriented data representation. Also, DAC has low time and spatial complexity, which makes its application promising. In this paper, we improve a compression performance of this algorithm. It is shown that, by applying the proposed coding scheme a compression ratio can be increased and, hence, greater memory savings can be obtained.

Digital images are used in various technological, financial, economic, and social processes. Huge datasets of high-resolution images require protected storage and low resource-intensive processing, especially when applying edge computing (EC) for designing Internet of Things (IoT) systems for industrial domains such as autonomous transport systems. For this reason, the problem of the development of image representation, which provides compression and protection features in combination with the ability to perform low complexity analysis, is relevant for EC-based systems. Security and privacy issues are important for image processing considering IoT and cloud architectures as well. To solve this problem, we propose to apply discrete atomic transform (DAT) that is based on a special class of atomic functions generalizing the well-known up-function of V.A. Rvachev. A lossless image compression algorithm based on DAT is developed, and its performance is studied for different structures of DAT. This algorithm, which combines low computational complexity, efficient lossless compression, and reliable protection features with convenient image representation, is the main contribution of the paper. It is shown that a sufficient reduction of memory expenses can be obtained. Additionally, a dependence of compression efficiency measured by compression ratio (CR) on the structure of DAT applied is investigated. It is established that the variation of DAT structure produces a minor variation of CR. A possibility to apply this feature to data protection and security assurance is grounded and discussed. In addition, a structure or file for storing the compressed and protected data is proposed, and its properties are considered. Multi-level structure for the application of atomic functions in image processing and protection for EC in IoT systems is suggested and analyzed.

Remote sensing (RS) digital images have a great variety of applications in solving real-world problems. Modern sensors provide this type of data of a very high resolution, which, in combination with a great number of acquired images, makes a problem of compressing RS images of particular importance. In this letter, discrete atomic compression (DAC) and a problem of its spatial complexity reduction are considered. This approach provides data compression and protection features in combination with such image representation that is ready for applying different artificial intelligence methods. For this reason, its application to image processing is relevant. Several modifications that provide reducing the spatial complexity of DAC are proposed, and their efficiency is analyzed. In particular, it is shown that using a block splitting procedure, it is possible to get a significant decrease in additional memory expenses without DAC's efficiency degradation in terms of lossy image compression.

Lossy compression of remote sensing data has found numerous applications. Several requirements are usually imposed on methods and algorithms to be used. A large compression ratio has to be provided, introduced distortions should not lead to sufficient reduction of classification accuracy, compression has to be realized quickly enough, etc. An additional requirement could be to provide privacy of compressed data. In this paper, we show that these requirements can be easily and effectively realized by compression based on discrete atomic transform (DAT). Three-channel remote sensing (RS) images that are part of multispectral data are used as examples. It is demonstrated that the quality of images compressed by DAT can be varied and controlled by setting maximal absolute deviation. This parameter also strictly relates to more traditional metrics as root mean square error (RMSE) and peak signal-to-noise ratio (PSNR) that can be controlled. It is also shown that there are several variants of DAT having different depths. Their performances are compared from different viewpoints, and the recommendations of transform depth are given. Effects of lossy compression on three-channel image classification using the maximum likelihood (ML) approach are studied. It is shown that the total probability of correct classification remains almost the same for a wide range of distortions introduced by lossy compression, although some variations of correct classification probabilities take place for particular classes depending on peculiarities of feature distributions. Experiments are carried out for multispectral Sentinel images of different complexities.

Image processing and compression algorithms might introduce various types of distortions. Thus, a question of estimating the effect of image compression on the accuracy of data classification using criteria specific only for image classification is relevant. In this paper, the effect of lossy compression on three-channel image classification using a multilayer neural net-work are analysed. It is shown that overall probability of correct classification remains almost the same for a wide range of distortions introduced by lossy compression using atomic wavelets al-though some variations of correct classification probabilities take place for particular classes depending on peculiarities of feature distributions. Experiments are carried out for multispectral Sen-tinel images of different complexity.

In this paper, a progressive DCT-based coder (PDCTC), which implements a lossy image compression algorithm based on discrete cosine transform (DCT) and provides progressive data reconstruction, is introduced. It is compared to JPEG as well as to discrete atomic compression (DAC) that is an algorithm based on discrete atomic transform (DAT). It is shown that the algorithm proposed provides higher compression ratio (CR) than JPEG with the same quality loss measured by PSNR-metric. Also, it is proved that PDCTC and DAC have almost the same efficiency in terms of rate/distortion curve (dependence of PSNR and compression ratio). Besides, the complexity of these algorithms is analyzed.

Multichannel systems of remote sensing provide a huge amount of data useful for different applications. However, such images occupy a large space that poses problems of processing, storage, transmission, and management. Lossy compression is widely used to decrease the size of data. In lossy compression, one has to provide a reasonable trade-off between compression ratio (CR) and introduced losses or quality of compressed data. Quality can be characterized in various ways including traditional criteria as peak signal-to-noise ratio (PSNR) or some others as well as criteria that describe efficiency of solving the final tasks of remote sensing as, e.g., probability of correct classification. In this paper, we concentrate on classification of three-channel images that can be either color images or three components of multi- or hyperspectral data acquired, e.g., by Sentinel-2 sensor. In lossy compression of color images, downscaling of color components is often applied to increase CR without essential loss of quality. The goal of this paper is to study the influence of such downscaling on classification accuracy for three-channel remote sensing data. The compression method based on atomic functions is considered since this method allows easy control of compressed image quality and its providing. The neural networks trained for distorted-free images are applied for image classification. Analysis is carried out for four images of different complexity. Based on it, practical recommendations are given.

It is well known that image processing efficiency considerably depends on image properties. Among operations of image processing, we mean quality assessment, noise characteristic estimation, lossless and lossy compression, denoising, etc. In many papers, such terms as “image complexity”, “rich image content”, “highly textural image” are used. Their meaning is intuitively clear and described verbally but there is a limited amount of quantitative estimation and analysis. In this paper, we show that there is a very high correlation of performance of different operations of image processing like characteristics of lossless and lossy compression, blind variance estimation and denoising and so on. We also recall what quantitative parameters indirectly describe image complexity for different operations of image processing.

Acquired images often have a large size while there can be limitations on communication line capacity and/or storage memory. Then, there is a need to compressed them. If lossy compression is applied, compressed images should have quality enough high for solving the tasks of their further processing as segmentation, classification, object detection. Here, we consider the influence of lossy compression on classification accuracy of three-channel remote sensing images. A specific feature of our analysis is that discrete atomic transform is studied as the basis of lossy compression and maximum likelihood method is applied at classification stage. It is shown that classification accuracy depends on both compression degree that can be characterized in different ways and image complexity. Under certain conditions, classification accuracy remains practically the same as in case of classifying an original (uncompressed) image. Then, it starts to worsen. We show how to provide quite large compression ratio with avoiding sufficient degradation of classification accuracy.