**1. Introduction**

The use of modern technologies increases the capabilities to explore the landscape using satellite images and aerial photography. Remote sensed data provide us with the information for studying and surveying the Earth and its bodies. The land cover patterns– vegetation, soil, rock, water, buildings, roads, and other elements–are continually changing due to anthropogenic impact and climate variations. The monitoring of land cover changes and use, and emergency management [1] is accomplished through a large amount of remote sensing data. These changes are related to urban planning [2], deforestation, biodiversity loss [3–5] and other causes, like natural disasters [6]. This amount of data requires compression for effective management–storage, transmission, view, manipulation, processing, etc. of the information. Uncompressed high-resolution images, containing remote sensing data, tend to fill the storage space ineffectively and require long transmission time. Effective data compression reduces the amount of data at the expense of their quality. Therefore, it is important to determine the balance between the quality of remote sensing data and the degree of compression.

Both lossy and lossless compression can be used for remote sensing imagery, reducing the amount of data with significantly different compression ratios. Lossless compression can be considered symmetric compression, which does not introduce the loss and distortions into information, so the compression ratios in most cases are low [7]. Higher compression ratios are achievable using lossy compression methods at the expense of image quality [7] as this type of compression is asymmetric (the original file does not match

**Citation:** Bausys, R.; Kazakeviciute-Januskeviciene, G. Qualitative Rating of Lossy Compression for Aerial Imagery by Neutrosophic WASPAS Method. *Symmetry* **2021**, *13*, 273. https:// doi.org/10.3390/sym13020273

Academic Editors: Zenonas Turskis, Jurgita Antucheviˇciene and ˙ Edmundas Kazimieras Zavadskas Received: 28 December 2020 Accepted: 2 February 2021 Published: 5 February 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

the decompressed file). For extremely large image files, lossy compression is the obvious solution. Simultaneously, it is essential to evaluate the quality of the compressed images to preserve the detailed and important visual features of the aerial images [8]. In this article, an image that is reconstructed after compression will be referred to as a compressed image.

The degree of image degradation during each lossy compression process depends on the compression algorithm, compression ratio, and the image itself. It is important to select the proper lossy compression format and compression quality for the appropriate aerial image to minimize the compression impact [8,9]. Different algorithms are used to save satellite images and aerial photography data into the lossy compression formats [10–12]. The majority of the popular compression algorithms for aerial imagery are wavelet-based [13]. The most used are the proprietary Enhanced Compression Wavelet (ECW) [14] and Joint Photographic Experts Group (JPEG2000) [15]. The Consultative Committee for Space Data Systems (CCSDS) is mostly used for real-time remote sensing data transmission [16]. The ICER (Progressive Wavelet Image Compressor) is used for onboard image compression by the NASA Mars Rovers [17]. The ECW method, in comparison to the proprietary waveletbased method Multiresolution Seamless Image Database (MrSid), produces smaller and better quality images and in less time [18]. JPEG image compression is based on the discrete cosine transform (DCT) and is the most well-known and widely applied [19]. All these algorithms offer excellent compression performance, which is usually evaluated by efficiency and computational requirements [13]. There are works [13,19–21] devoted to the analysis of lossy compression performance comparing different algorithms at various conditions. We are interested in the compression efficiency as it relates to the ability to maintain the highest possible visual quality of the compressed aerial image by increasing the number of bits per pixel for data storage. Our analysis and selection of lossy compression for aerial images do not target the real-time applications, and the compression and decompression times are not a priority. Considering the peculiarities of the algorithms used for satellite and aerial images, we selected three of them for qualitative evaluation: ECW, JPEG2000, and JPEG. The CCSDS method, compared to ECW and JPEG2000, retains the lower qualitative result when reconstructing the original image after compression but is faster [13].

Continuous improvement of the current state-of-the-art lossy compression methods requires proper methods and methodologies for qualitative evaluation of lossy compression. Usually, the single objective metrics are used to examine images' lossy compression quality [9–13]. We think the related and weighted combination of different qualitative parameters can evaluate the influence of lossy compression on the image content more precisely. We proposed and verified a set of qualitative parameters evaluating the compressed aerial images using the MCDM framework. We formulated a new MCDM problem dedicated to the rating of lossy compression algorithms governed by appropriate qualitative parameters of compressed images and visually acceptable lossy compression for them. Herewith, we performed ranking for lossy compression algorithms with different compression ratios by their suitability for the different resolution aerial images. To ensure the stability of MCDM ranking results, we chose the direct weight determination and weighted aggregated sum product assessment (WASPAS) methods in the neutrosophic environment. These methods show great stability in solving various real-life problems. We created the original multi-criteria decision-making methodology for the qualitative selection of the aerial images' lossy compression, which also provides the means of solving different subtasks, either altering the weights or the set of aspects.

The article consists of five sections. Section 2 provides a summary of published papers on the qualitative assessment of compressed aerial images. Section 3 describes the general framework of the methodology, a set of alternatives and criteria for a multi-criteria task of the qualitative rating of aerial images' lossy compression, and defines the direct weight determination and MCDM neutrosophic WASPAS methods for data processing. Section 4 presents the set of selected aerial images, qualitative evaluation, the ranking of compression results of the set by the neutrosophic WASPAS-SVNS method, and discussion of the results. Concluding remarks and future directions are presented in Section 5.
