*3.2. Lossy Compression Algorithms for Aerial Images*

In this work, three lossy transform-based compression algorithms, namely, JPEG2000 [41], ECW [42,43], and JPEG [44], were selected as alternatives for MCDM methodology to evaluate them by compression efficiency. JPEG2000 is a still image (greyscale, color etc.) encoding and decoding system that defines both lossy and lossless compression techniques based on the discrete wavelet transform (DWT) method [45]. ECW is a proprietary lossy compression format based on the DWT method, targeted for satellite imagery and aerial photography [46]. JPEG is a commonly used image encoding and decoding system, using a lossy compression technique based on the DCT [47].

It has been stated [48] that the transform-based compression is less sensitive to changes in the statistical image properties, and the subjective image quality is preserved better. The proper lossy compression technique uses the image data decomposition to reduce the redundant information and maintain the quality of the image. The generalized scheme for lossy aerial image compression and decompression is presented in Figure 2. It consists of the reduction in redundancy, entropy coding, bit stream transmission, decoding, and data reconstruction. The typical encoder performs color space conversion and image decomposition, transformation, quantization and coding [49,50]. The decoder performs

entropy decoding, dequantization, inverse transformation, and inverse color space conversion [49,50].

**Figure 2.** Basic procedures for aerial image transform-based lossy compression–decompression.

As shown in Figure 1, the encoder converts the original image into the bit stream. The encoded bit stream is received by the decoder, and the restored image is obtained. For the lossy compression system, the total data quantity of the original image is larger than the data quantity of the compressed image. The ratio between these images is called the compression ratio [7,51] and can be expressed as:

*C<sup>r</sup>* = *Usize Csize* , (1)

where *Usize*—uncompressed image size; *Csize*—the size of a compressed image file stored in a disk.

It must be noted that the compression ratio is calculated for the storage size, not the image data, so storing the same compressed image in the different storage formats will affect the compression ratio because of the additional data, introduced by the file format.

The aerial image is transformed from the spatial domain to the frequency domain at the decomposition stage. This process is usually lossless. The JPEG2000 and ECW algorithms use DWT to decompose an image into sub-images (sub-bands) of low-pass (approximate) and high-pass (detail) coefficients at different resolutions. The ECW algorithm exploits this decomposition during compression of images to maintain the quality close to the uncompressed imagery, and the quality at different compression ratios changes less compared to JPEG2000. The difference between JPEG2000 and ECW is the analysis and synthesis filters used for DWT. The JPEG uses a discrete cosine transform (DCT) to obtain the approximation blocks, representing the magnitude of the appropriate frequencies. DWT and DCT coefficients of the decomposed image are ordered by their impact, and coefficients contributing insignificant information to image content may be omitted. Properties like energy compaction, data decorrelation, computational speed characterize the discrete transforms and can be reused in data compression.

The quantization is an irreversible process in the lossy compression pipeline. It is a compromise between the quality of the image and the compression ratio. As the lower frequencies provide the most important part of the information in the image, there is a possibility to discard high-frequency components and reduce the amount of data considering the human eye is almost insensitive to the rapidly varying differences in brightness (high frequencies). In the JPEG pipeline, blocks containing high-frequency and thus lowimportance coefficients that are close to zero are discarded to get an enhanced compression rate. The visually weighted quantization tables are exploited for the minimization of the perceptible loss of information. Considering that each sub-band has different importance based on the human perceptibility, the selection of the quantizer step-size can exploit the human visual system (HVS) model like DCT quantization tables in JPEG. The JPEG2000 uses a uniform scalar quantizer to quantize wavelet sub-band coefficients, for which the magnitudes are below the quantizer step-size. The sub-bands of each JPEG2000 image tile are further divided into non-overlapping blocks—the rectangular arrays for entropy cod-

ing. Similar to JPEG2000, the ECW quantization is adopted to the coefficients of separate wavelet sub-bands. The image compression is achieved after the quantization.

For the creation of the compressed bit stream, the JPEG2000 algorithm uses Embedded Block Coding with Optimized Truncation (EBCOT) that encompasses the arithmetic coding system. The entropy coder of JPEG uses Huffman coding. The encoded bit stream can be transmitted over communication channels or stored in repositories. The encoding procedure is lossless.

The compressed image is reconstructed via decoding, dequantization, and transformation, inverse DWT for JPEG2000/ECW and inverse DCT for JPEG. Finally, the color transform from YCbCr to the presentation color space is performed. The reconstructed aerial image is a close approximation of the original image, as distortions are introduced during lossy compression.

Since ECW is a proprietary algorithm, only the compression results can expose its peculiarities. The aerial images were compressed by the ECW algorithm using Global Mapper v20.0.1 software package [52] in our work.
