Adaptive multi-level wavelet decomposition for efficient image compression

Öz

Image compression is a crucial technique for reducing storage requirements and improving transmission efficiency of digital images, especially given the ever-increasing volume of image data. However, conventional lossy compression methods such as JPEG and JPEG2000 often introduce significant quality degradation, particularly when compressing highly detailed images. This study presents an optimized wavelet transform-based image compression method designed to minimize information loss while maximizing compression efficiency. The proposed method integrates adaptive thresholding, the selection of optimized wavelet functions, and multi-level wavelet decomposition to address the limitations of traditional approaches. Specifically, adaptive thresholding is used to dynamically adjust compression parameters, reducing unnecessary data retention, while the wavelet function selection process ensures the most suitable basis for image features. Multi-level wavelet decomposition enables the retention of important image details across various resolution scales, improving compression without compromising visual quality. The performance of the proposed method is evaluated on several image types, including well-known test images, and compared against standard image compression techniques such as JPEG and JPEG2000. Experimental results show that the proposed method outperforms the conventional methods in terms of both compression ratio and image quality preservation, achieving higher Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index (SSIM) scores. The proposed approach is particularly effective for applications requiring high-quality image storage and transmission, such as medical imaging, satellite imagery, and multimedia communication.

Anahtar Kelimeler

• Wavelet Transform
• Image Compression
• Adaptive Quantization
• Image Processing

Etkin görüntü sıkıştırma için adaptif çok seviyeli dalgacık dönüşümü yöntemi

Öz

Görüntü sıkıştırma, özellikle görüntü verilerinin giderek artan hacmi göz önüne alındığında dijital görüntülerin depolama gereksinimlerini azaltmak ve iletim verimliliğini artırmak amacıyla kullanılan kritik bir tekniktir. Ancak, JPEG ve JPEG2000 gibi geleneksel kayıplı sıkıştırma yöntemleri, özellikle yüksek detaylı görüntüleri sıkıştırırken önemli kalite bozulmalarına yol açar. Bu çalışma, bilgi kaybını minimize ederken sıkıştırma verimliliğini maksimize etmek amacıyla optimize edilmiş bir dalgacık dönüşümü tabanlı görüntü sıkıştırma yöntemi sunmaktadır. Önerilen yöntem, geleneksel yaklaşımların sınırlamalarını aşmak için adaptif eşikleme, optimize edilmiş dalgacık fonksiyonları seçimi ve çok seviyeli dalgacık dekompozisyonunu entegre etmektedir. Özellikle, adaptif eşikleme, sıkıştırma parametrelerini dinamik olarak ayarlamak için kullanılarak, gereksiz veri saklamayı azaltırken, dalgacık fonksiyonu seçimi, görüntü özellikleri için en uygun temeli sağlamaktadır. Çok seviyeli dalgacık dekompozisyonu, çeşitli çözünürlük ölçeklerinde önemli görüntü detaylarının korunmasını sağlayarak görsel kaliteyi bozmadan sıkıştırmayı iyileştirir. Önerilen yöntemin performansı, iyi bilinen test görüntüleri üzerinde değerlendirilmiş ve JPEG ve JPEG2000 gibi standart görüntü sıkıştırma teknikleriyle karşılaştırılmıştır. Deneysel sonuçlar, önerilen yönteminin hem sıkıştırma oranı hem de görüntü kalitesinin korunması açısından geleneksel yöntemleri geride bıraktığını, daha yüksek Tepe Sinyal-Gürültü Oranı (PSNR) ve Yapısal Benzerlik Endeksi (SSIM) puanları elde ettiğini göstermektedir. Önerilen yaklaşım, yüksek kaliteli görüntü depolama ve iletimi gerektiren uygulamalarda, örneğin tıbbi görüntüleme, uydu görüntülemesi ve multimedya iletişimi gibi alanlarda etkilidir.

Anahtar Kelimeler

• Dalgacık Dönüşümü
• Görüntü Sıkıştırma
• Adaptif Kuantalama
• Görüntü İşleme

Kaynakça

1. [1] Wallace GK. "The JPEG still picture compression standard". Communications of the ACM, 34(4), 30-44, 1992.
2. [2] Taubman DS, Marcellin MW. JPEG2000: Image Compression Fundamentals, Standards and Practice (The International Series in Engineering and Computer Science). 2002nd ed. Springer, 2001.
3. [3] Mallat S. A Wavelet Tour of Signal Processing: The Sparse Way. 3rd ed. Academic Press, Elsevier Inc, 2009.
4. [4] Donoho DL, Johnstone, IM. "Adapting to unknown smoothness via wavelet shrinkage". Journal of the American Statistical Association, 90(432), 1200-1224, 1995.
5. [5] Chang SG, Yu B, Vetterli, M. "Adaptive wavelet thresholding for image denoising and compression". IEEE Transactions on Image Processing, 9(9), 1532-1546, 2000.
6. [6] Anju MI, Mohan J. ‘’Deep image compression with lifting scheme: Wavelet transform domain based on high-frequency subbband prediciton’’. International Journal of Intelligent Systems, 37(3), 2163-2187, 2022.
7. [7] Öz İ. "Comparative analysis of wavelet families in image compression, featuring the proposed new wavelet". Turkish Journal of Science and Technology, 19(1), 279-294, 2024.
8. [8] Villota S, Inga E. "Sparse transform and compressed sensing methods to improve efficiency and quality in magnetic resonance medical imaging". Sensors (Basel). 25(16), 5137, 2025.

9. [9] Chakib H, Idrissi N, Jannani O. "Hybrid schemes based on wavelet transform and convolutional auto-encoder for image compression". International Journal of Engineering Science Technologies, 7(2), 37-49, 2023.
10. [10] Kumar HS, Moiz A, Kalshetti KV, Jain V, Kumar K. "Image compression and enhancement using deep learning algorithm". International Conference on Emerging Smart Computing and Informatics (ESCI), Pune, India, 5-7 March 2025.
11. [11] Gao Y, Zhou M, Liu D, Yan Z, Zhang S, Metaxas DN. ‘’A data-scalable transformer for medical image segmentation: architecture, model efficiency, and benchmark’’. arXiv, 2022. https://arxiv.org/pdf/2203.00131.pdf.
12. [12] Roy S, Koehler G, Ulrich C, Baumgartner M, Petersen J, Isensee F, Maier-Hein KH. ‘’Mednext: transformer-driven scaling of convnets for medical image segmentation’’. International Conference on Medical Image Computing and Computer-Assisted Intervention. Vancouver, Canada, 8-12 October 2023.
13. [13] Li W, Feng C, Yu K, Zhao D. “MISS-D: a fast and scalable framework of medical image storage service based on distributed file system”. Computer Methods and Programs in Biomedicine, 186, 105189, 2020.
14. [14] Malayil MV, Vedhanayagam M. “A novel image scaling based reversible watermarking scheme for secure medical image transmission”. ISA Trans., 108, 269-81, 2021.
15. [15] Padhy S, Dash S, Shankar TN, Rachapudi V, Kumar S, Nayyar A. “A hybrid crypto-compression model for secure brain mri image transmission”. Multimedia Tools and Applications, 83, 24361-24381, 2024.
16. [16] Xue X, Marappan R, Raju SK, Raghavan R, Rajan R, Khalaf OI, Abdulsahib GM. “Modelling and analysis of hybrid transformation for lossless big medical image compression”. Bioengineering, 10(3), 333, 2023.
17. [17] Reddy VP, Prasad RM, Udayaraju P, Naik BH, Raja C. ‘’Efficient medical image security and transmission using modified LZW compression and ECDH-AES for telemedicine applications’’. Soft Computing Fusion Found Methodologies and Applications, 27(13), 1-18, 2023.
18. [18] Zhou D, Cai Z, He D. ‘’A new biorthogonal spline wavelet-based k-layer network for underwater image enhancement’’. Mathematics, 12(9), 1366, 2024.
19. [19] Zhang H, Liu C, Feng L, Yu Y. "Improved Canny edge detection algorithm". 9th International Conference on Intelligent Informatics and Biomedical Sciences (ICIIBMS), Okinawa, Japan, 21-23 November 2024.
20. [20] Jin Y, Li Z, Tian Y, Wei X, Liu C. “A novel interpretable multilevel wavelet decomposition deep network for actual heartbeat classification”. Science China Technological Sciences, 67, 1842-1854, 2024.
21. [21] Eulig E, Ommer B, Kachelrieß M. ‘’Benchmarking deep learning-based low-dose CT image denoising algorithms’’. The International Journal of Medical Physics Research and Practice, 51(12), 8776-8788, 2024.
22. [22] Dziembowski A, Nowak W, Stankowski J. ‘’IV-SSIM-The structural similarity metric for immersive video”. Applied Sciences, 14(16), 7090, 2024.
23. [23] Durdu A. “24-bit renkli imge içine 24-bit renkli imge gizleyen yüksek kapasiteli düşük bozulumlu tersinir kayıplı yeni bir veri gizleme yöntemi (YKKG)”. Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi, 27(2), 96-113, 2021.
24. [24] Mishra J, Kumar V. "Study of digital image compression techniques and framework for suitability selection based on similarity measuring metrics." 15th International Conference on Computing Communication and Networking Technologies (ICCCNT), Kamand, India, June 2024.
25. [25] Can E, Karaca AC, Urhan O, Güllü MK. “Compression of hyperspectral images using automatic adaptive luminance transform and 3D-DCT method”. Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi, 26(5), 868-883, 2020.
26. [26] Ince IF, Bulut F, Kilic I, Yildirim ME, Ince OF. “Low dynamic range discrete cosine transform (LDR-DCT) for high-performance JPEG image compression”. The Visual Computer, 38(5), 1845-1870, 2022.
27. [27] Bulut F, Ince IF. “Iterative histogram equalization using discrete wavelet transform in low-dynamic range”. Journal of Electronic Imaging, 32(2), 023034-023034, 2023.