Adaptive block size selection in a hybrid image compression algorithm employing the DCT and SVD

Image compression is essential to numerous fields, such as telecommunications, digital storage, and multimedia applications. Traditional compression techniques, such as DCT and SVD, have demonstrated their effectiveness, but they have limitations. The DCT excels at representing spatial frequency components of images, whereas SVD excels at extracting singular values from matrices. However, these techniques operate independently and may not optimize image compression in every region. The proposed hybrid algorithm is a response to the imperative need for a more versatile and effective compression approach. By incorporating the benefits of the DCT and SVD, the algorithm attempts to take advantage of their complementary characteristics, thereby ensuring a well-rounded compression strategy. This integration does not merely combine the techniques in a linear fashion; rather, it introduces a novel interaction governed by an adaptive block size selection mechanism. The algorithm’s introduction of adaptive block size selection is an innovation. Traditional compression techniques use fixed block sizes and disregard the varying characteristics of various image regions. The adaptive approach takes into account the inherent diversity of image content by selecting optimal block sizes dynamically based on local attributes. Intricately textured and jagged regions may require smaller blocks, whereas smoother regions may profit from larger blocks. This dynamic approach ensures that the algorithm adapts its compression to the particular needs of each region, thereby enhancing the overall compression efficiency. The algorithm relies on the judicious hybridization of the DCT and SVD, capitalizing on their unique properties to improve compression [5, 6]. Each block is subjected to the DCT, and the coefficients with the highest significance are retained based on a predetermined threshold. Simultaneously, SVD is performed, with the algorithm conserving essential singular values while quantizing others. The most important innovation here is the cohesion between these two techniques, orchestrated by the results of adaptive block size selection. This enables the algorithm to exploit the DCT’s proficiency in capturing spatial frequency components and SVD’s proficiency in matrix decomposition in a fashion optimized for each block’s properties.

The exponential development of digital images across multiple domains has emphasized the need for efficient image compression approaches. This study presents a novel approach for picture compression, which combines the advantages of the DCT and SVD. The proposed approach also features a unique adaptive block size selection mechanism. The motivation for this study stems from the imperative to reconcile the disparity between compression efficiency and image quality. The DCT and SVD are well-recognized methodologies, each possessing distinct advantages [7]. However, they function autonomously and may not adequately tackle the intricacies of modern picture material optimally. Furthermore, conventional approaches that utilize set block sizes are limited in their ability to adjust to the diverse nature of pictures. The inspiration for the suggested hybrid algorithm is from the aspiration to overcome these limitations and offer a solution that is adaptable and versatile.

This article’s contributions comprise a novel hybrid algorithm that combines DCT, SVD, and adaptive block size selection. Its novel aspect is the way these parts work together dynamically to enhance compression performance while keeping image quality constant. The outline of the article is as follows: In Section II, we take a closer look at the process and break down the algorithm’s steps. The experimental design, datasets, and measurements of success are described in Section III. The results are analyzed critically and compared to current state-of-the-art models in Section IV. Section V discusses the algorithm’s broader implications and potential future enhancements. Section VI concludes by summarizing the significance and contributions of the algorithm. The proposed hybrid algorithm heralds a new era in image compression by redefining the paradigms of efficiency and quality preservation. By combining well-established techniques with innovative adaptability, it positions itself as a formidable competitor among image compression algorithms.

The existing literature presents a wide range of image compression techniques, spanning from conventional approaches such as DCT and Huffman coding to more sophisticated approaches that use neural networks, wavelet transformations, and contextual analysis. Each approach presents distinct advantages and may be appropriate for varying use scenarios. Nevertheless, the DCT-SVD hybrid image compression technique incorporates the advantageous feature of adaptive block size selection. This hybrid approach leverages the advantages of both the DCT and SVD. Specifically, it combines the DCT’s ability to efficiently encode spatial frequencies with SVD’s robust matrix decomposition technique. The algorithm’s adaptation to different picture areas is further improved by the use of adaptive block size selection, which effectively optimizes compression efficiency. In contrast to several conventional approaches, our suggested methodology aims to achieve a harmonious equilibrium between compression efficacy and the preservation of picture quality. The utilization of the DCT-SVD hybrid technique, under the guidance of adaptive processing, helps attain significant compression ratios while simultaneously minimizing the loss of perceptual information. The comprehensive methodology employed in our hybrid algorithm makes it a formidable solution, offering superior compression efficiency and enhanced image quality when compared to singular approaches. The selected hybrid methodology exemplifies a cohesive integration of well-established methodologies, facilitating a proficient balance between the efficacy of compression and the quality of images.

The combination of DCT-SVD and adaptive block size selection effectively mitigates the constraints inherent in each individual approach, thus establishing a very viable solution for picture compression in many application domains. A hybrid that incorporates both spatial frequency components and matrix decomposition is achieved by combining the DCT and SVD. SVD emphasizes matrix interactions, whereas DCT focuses on collecting picture structures. The hybrid algorithm can better represent complex visual material, thanks to its dual strategy. Furthermore, a major flaw in many current approaches is fixed by the adaptive block size selection process. For many picture areas, fixed block sizes may not be the best option. This approach optimizes compression for various areas of the picture by tailoring compression processing to local variables. The suggested hybrid approach offers a possible path forward for picture compression. Although the DCT and SVD are well-known approaches, the addition of adaptive block size selection gives a new perspective. This hybridization is justified by the complementarity of the DCT and SVD as well as the flexibility provided by the choice of block size.

The suggested approach seeks to strike a compromise between compression effectiveness and image quality by smoothly combining these components. This section shows the development of image compression approaches, displaying a variety of strategies that have influenced the industry. Every approach, from traditional ones such as DCT and Huffman coding to cutting-edge ones such as fractal compression and content-adaptive schemes, helps us comprehend the trade-offs involved in compression. From this rich genealogy, the proposed hybrid approach, which combines the DCT and SVD with adaptive block size selection, arises. It aims to overcome obstacles and establish new benchmarks for effective image compression while maintaining picture quality. This hybrid approach is positioned as a viable candidate in the search for the best picture compression techniques, thanks to the incorporation of tried-and-true techniques and the use of creative adaptations.

This subsection presents the adopted experimental setup for the evaluation of the proposed algorithm, which includes hardware configuration, software environment, and datasets.

The novel methodology employed for the hybrid image compression algorithm uses the DCT-SVD technique, along with an adaptive block size selection strategy, consisting of multiple stages. The primary objective of this comprehensive technique is to achieve optimal compression efficiency while simultaneously maintaining the integrity of image quality. The adopted methodology of the proposed hybrid algorithm is depicted in Figure 2 and explained in the following paragraph. The key steps of the adopted methodology are image preprocessing, adaptive block size selection, DCT compression, SVD compression, entropy encoding, decompression, and postprocessing.

Figure 2:

The key features of the adopted methodology are hybrid approach, adaptive block size selection, quality preservation, and versatility.

The methodology being offered presents a comprehensive approach to image compression through the integration of the DCT and SVD, alongside the incorporation of adaptive block size selection. The integration of these algorithms achieves an ideal equilibrium between compression efficiency and the preservation of picture quality, hence showcasing its potential use in many sectors that heavily rely on images.

The proposed hybrid image compression algorithm employing the DCT and SVD with adaptive block size selection is depicted in Figure 3. The detailed description of the proposed algorithm is described in the following paragraph.

Figure 3:

The compression ratio quantifies the degree of compression applied to the original image. The calculation involves determining the ratio between the dimensions of the original image and the dimensions of the compressed image. The compression ratio is determined by dividing the original image size by the compressed image size. Table 3 displays the compression ratios attained for several image datasets using the DCT-SVD hybrid technique. The graphical representation of the compression ratio is provided in Figure 4, which compares the existing image compression techniques such as JPEG, JPEG2000, and pure DCT-based compression with the proposed hybrid DCT-SVD hybrid technique.

Figure 4:

The outcomes given in Table 3 reveal that the objective of our proposed technique is to obtain compression ratios that are comparable to other algorithms while simultaneously preserving image quality at a high level.

The PSNR is a commonly used statistic in image processing to assess the fidelity of a reconstructed image by quantifying the disparity between the original and compressed images. Greater PSNR levels are indicative of superior image quality. The PSNR is a commonly used measure in the field of image processing to assess the fidelity of a reconstructed image. It does this by quantifying the disparity between the original image and its compressed counterpart. A higher PSNR is indicative of superior image quality. The PSNR is computed using Eq. 12: (12) PSNR=10 log MAX2552MSE {\rm{PSNR}} = 10\;\log \;{{{{\left( {{\rm{MAX}}\left( {255} \right)} \right)}^2}} \over {{\rm{MSE}}}} where the variable MAX represents the maximum pixel value in an 8-bit grayscale image, which is typically 255. The mean squared error (MSE) represents the average squared difference between the original and reconstructed images. Table 4 presents the PSNR values acquired for several image datasets using the technique described in this article.

To evaluate the efficacy of the DCT-SVD hybrid compression algorithm, a comparative analysis was conducted, whereby existing image compression techniques such as JPEG, JPEG2000, and pure DCT-based compression were considered for comparison. Figure 5 depicts the PSNR values attained by each technique in relation to different test image datasets.

Figure 5:

The evaluation of a compression algorithm’s performance is equally reliant on the assessment of visual quality. The SSIM is a perceptual measure used for evaluating the degree of structural similarity between the original and compressed images. The SSIM is a metric that quantifies the similarity between two images. It produces values within the range of −1 to 1, where larger values correspond to a higher degree of similarity between the images. Table 5 presents the SSIM values acquired for several image datasets using the technique proposed in this study.

c.i.

Validation of the SSIM

Figure 6 depicts a visual comparison of the original image, the image compressed using the hybrid approach, and the image compressed using an alternative technique.

Figure 6:

The SSIM values provided further evidence of the algorithm’s capacity to maintain the image structure and visual quality. As shown in Figure 6, the hybrid DCT-SVD technique showed superior performance compared to conventional compression approaches in terms of preserving structural similarities. Our method repeatedly demonstrated superior performance compared to existing approaches, as shown by higher PSNR and SSIM values. The use of hybrid techniques in our approach allowed attaining superior image quality while maintaining comparable compression ratios.

The perceptually justified measure known as CID is used to quantify the visual disparity between the original images and the images that have undergone compression. The consideration of the properties of the human visual system (HVS) is included in this approach, resulting in a more precise depiction of perceived image quality than conventional measurements. Table 6 presents PSNR values acquired for several image datasets using the proposed technique. Figure 7 depicts compression image difference (CID) values attained by each technique in relation to different test image datasets.

Figure 7:

One advantage of using a hybrid approach is that it combines the strengths of many methods or strategies, resulting in a more comprehensive and effective solution. The use of a hybrid approach in the suggested method leverages the advantageous characteristics of both the DCT and SVD approaches. The DCT is an effective method for representing spatial frequency information, but SVD is adept at capturing global correlations and redundancies. The hybridization process results in enhanced compression performance, as seen by the increased compression ratios, PSNR values, and visual quality.

Computational complexity refers to the study of the resources required to solve a computational problem. While the hybrid approach demonstrates enhanced compression outcomes, it is crucial to take into account its computational intricacy. It is necessary to compare the processing time of the combined DCT-SVD compression technique with that of the separate techniques to ascertain its practical usefulness.

The algorithm’s notable performance renders it highly suitable for applications that prioritize the preservation of image quality, such as medical imaging and archive systems. The attraction of the technology is further enhanced by its compliance with current compression standards and its adaptability in processing different sorts of images. Thus, the use of the hybrid image compression technique including DCT-SVD technique demonstrates notable efficacy in compression, while concurrently preserving high-quality image representation. The aforementioned findings underscore the capacity of this methodology to surpass current compression techniques, making it a very promising strategy for a wide range of practical applications.

The proposed hybrid image compression technique represents a significant advancement in the field of image compression. Moreover, it has the potential to revolutionize other fields that heavily rely on effective management of picture data. The capacity to effectively balance compression efficiency and preserve picture quality holds significance in several fields, including multimedia, medical imaging, remote sensing, and artificial intelligence. With the ongoing progress in research and technology, it is anticipated that forthcoming advancements may significantly boost the capability of algorithms, leading to a transformative impact on the processing, storage, and transmission of pictures across many applications.