IGHF-DL: PARAMETER-EFFICIENT HYBRID IMAGE DENOISING USING CLASSICAL MATHEMATICAL FILTERING AND DEEP LEARNING

Öz

There is a critical balance between denoising and detail preservation that requires careful consideration. There is also a need for mathematically grounded, computationally efficient denoising models that are practical for real-world applications. In this study, we propose the IGHF-DL model, which improves the mathematical edge preservation power of the classic Inverse Gaussian Harmonic Filter (IGHF) by incorporating a CNN structure that includes six residual blocks, a channel attention mechanism, and an edge-sensitive enhancement block. In our model, training was performed with a low computational cost, reducing the number of DnCNN parameters by 54%. In comprehensive experiments performed on the BSD68, CBSD68, McMaster, Kodak24, Set12, and Urban100 datasets, our model achieved a PSNR value of 28.72 dB for BSD68, outperforming the BM3D (+0.15 dB) model and reaching 98.3% of the DnCNN performance, demonstrating competitive performance. Our model is successful not only in terms of metrics but also in terms of edge preservation and perceptual quality. On datasets with textured images such as Urban100, IGHF-DL outperforms the IGHF model in edge preservation and perceptual quality with FOM: 0.8252 and LPIPS: 0.1147, demonstrating its robustness on a mathematical basis and showing potential for further development in integration with next-generation methods. At the same time, compared to the IGHF model, IGHF-DL showed the best improvement in metrics at high noise levels with a +7.44 dB improvement. The proposed hybrid approach offers a practical and efficient solution with parameter efficiency that reduces computational costs for resource-constrained environments.

Anahtar Kelimeler

• IGHF Image Denoising
• Deep Learning
• Hybrid CNN
• Perceptual Quality and Edge Preservation
• Parameter Efficiency

IGHF-DL: KLASİK MATEMATİKSEL FİLTRELEME VE DERİN ÖĞRENME İLE PARAMETRE VERİMLİ HİBRİT GÖRÜNTÜ GÜRÜLTÜ GİDERME

Öz

Görüntü gürültüsünün giderilmesi ile ayrıntının korunması arasında dikkat gerektiren bir denge bulunmaktadır. Aynı zamanda matematiksel temelli ve pratikte kullanılabilen düşük hesaplama maliyetli gürültü giderme modellerine ihtiyaç duyulmaktadır. Bu çalışmada klasik Ters Gauss Harmonik Filtreleme (Inverse Gaussian Harmonic Filter- IGHF) filtresinin matematiksel kenar koruma gücünü altı artık blok, kanal dikkat mekanizması ve kenar duyarlı iyileştirme bloğu içeren CNN yapısı ile iyileştiren IGHF-DL modelini öneriyoruz. Modelimizde, DnCNN parametre sayısının %54’ü kadarıyla düşük hesaplama maliyeti sağlayan bir eğitim gerçekleştirilmiştir. BSD68, CBSD68, McMaster, Kodak24, Set12 ve Urban100 veri setleri üzerinde yapılan kapsamlı deneylerde modelimiz BSD68 için 28.72 dB PSNR değeri elde ederek BM3D (+0.15 dB) modelini geçmiş ve DnCNN performansının %98.3’üne ulaşarak rekabetçi performans göstermektedir. Modelimiz sadece metrik olarak değil aynı zamanda kenar koruma ve algısal kalite açısından da başarılıdır. Urban100 gibi dokulu görüntülerin olduğu veri setinde IGHF modeline göre IGHF-DL, kenar koruma ve algısal kalitede FOM: 0.8252 değeri, LPIPS: 0.1147 ile matematiksel temeldeki sağlamlığını göstererek yeni nesil yöntemlerle entegrasyonunda daha da gelişebileceğini göstermektedir. Aynı zamanda IGHF modeline göre IGHF-DL metrik olarak en iyi gelişimi yüksek gürültü seviyelerinde +7.44 dB gelişim göstermiştir. Önerilen hibrit yaklaşım, kaynak kısıtlı ortamlar için hesaplama maliyetini düşüren parametre verimliliği ile pratik ve verimli bir çözüm sunmaktadır.

Anahtar Kelimeler

• IGHF Gürültü Giderme
• Derin Öğrenme
• Hibrit CNN
• Algısal Kalite ve Kenar Koruma
• Parametre Verimliliği

Kaynakça

1. B. Charles, “Image Noise Models,” in Handbook of Image and Video Processing, Elsevier, 2005, pp. 397–409. doi: 10.1016/B978-012119792-6/50087-5.
2. U. Erkan, D. N. H. Thanh, L. M. Hieu, and S. Enginoglu, “An Iterative Mean Filter for Image Denoising,” IEEE Access, vol. 7, pp. 167847–167859, 2019, doi: 10.1109/ACCESS.2019.2953924.
3. D. N. H. Thanh and S. D. Dvoenko, “A method of total variation to remove the mixed Poisson-Gaussian noise,” Pattern Recognit. Image Anal., vol. 26, no. 2, pp. 285–293, Apr. 2016, doi: 10.1134/S1054661816020231.
4. K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image Denoising by Sparse 3-D Transform-Domain Collaborative Filtering,” IEEE Trans. Image Process., vol. 16, no. 8, pp. 2080-2095, 2007.
5. A. Buades, B. Coll, and J.-M. Morel, “A Non-Local Algorithm for Image Denoising,” in 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR’05), San Diego, CA, USA: IEEE, 2005, pp. 60–65. doi: 10.1109/CVPR.2005.38.
6. F. Marasli and S. Ozturk, “Inverse Gaussian Harmonic Filter (IGHF): Spatial Filter with Contrast Stretching Priority,” Int. J. Pattern Recognit. Artif. Intell., vol. 39, no. 12, p. 2534001, Sep. 2025, doi: 10.1142/S0218001425340018.
7. K. Zhang, W. Zuo, Y. Chen, D. Meng, and L. Zhang, “Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising,” IEEE Trans. Image Process., vol. 26, no. 7, pp. 3142-3155, 2017.
8. K. Zhang, W. Zuo, and L. Zhang, “FFDNet: Toward a Fast and Flexible Solution for CNN-Based Image Denoising,” IEEE Trans. Image Process., vol. 27, no. 9, pp. 4608–4622, Sep. 2018, doi: 10.1109/TIP.2018.2839891.

9. H. Fırat and H. Üzen, “Detection of Pneumonia Using A Hybrid Approach Consisting of MobileNetV2 and Squeeze-and-Excitation Network,” Türk Doğa Ve Fen Derg., vol. 13, no. 1, pp. 54–61, Mar. 2024, doi: 10.46810/tdfd.1363218.
10. Y. Tai, J. Yang, X. Liu, and C. Xu, “MemNet: A Persistent Memory Network for Image Restoration,” in 2017 IEEE International Conference on Computer Vision (ICCV), Venice: IEEE, Oct. 2017, pp. 4549–4557. doi: 10.1109/ICCV.2017.486.
11. S. Guo, Z. Yan, K. Zhang, W. Zuo, and L. Zhang, “Toward Convolutional Blind Denoising of Real Photographs,” in 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), Long Beach, CA, USA: IEEE, Jun. 2019, pp. 1712–1722. doi: 10.1109/CVPR.2019.00181.
12. H. Guo et al., “MambaIRv2: Attentive State Space Restoration,” in 2025 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), Nashville, TN, USA: IEEE, Jun. 2025, pp. 28124–28133. doi: 10.1109/CVPR52734.2025.02619.
13. J. Zhang, Y. Zhang, J. Gu, J. Dong, L. Kong, and X. Yang, “Xformer: Hybrid X-Shaped Transformer for Image Denoising,” presented at the The Twelfth International Conference on Learning Representations, ICLR, Feb. 2024. Accessed: Jan. 09, 2026. [Online]. Available: https://openreview.net/forum?id=vXrIQLzIKY
14. S. W. Zamir, A. Arora, S. Khan, M. Hayat, F. S. Khan, and M.-H. Yang, “Restormer: Efficient Transformer for High-Resolution Image Restoration,” in 2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), New Orleans, LA, USA: IEEE, Jun. 2022, pp. 5718–5729. doi: 10.1109/CVPR52688.2022.00564.
15. L. Sun et al., “The Tenth NTIRE 2025 Image Denoising Challenge Report,” in 2025 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW), Nashville, TN, USA: IEEE, Jun. 2025, pp. 1333–1360. doi: 10.1109/CVPRW67362.2025.00125.
16. R. Flepp, A. Ignatov, R. Timofte, and L. Van Gool, “Real-World Mobile Image Denoising Dataset with Efficient Baselines,” in 2024 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), Seattle, WA, USA: IEEE, Jun. 2024, pp. 22368–22377. doi: 10.1109/CVPR52733.2024.02111.
17. C. Yang, C. Wang, L. Liang, and Z. Su, “Real-world image denoising via efficient diffusion model with controllable noise generation,” J. Electron. Imaging, vol. 33, no. 04, Jul. 2024, doi: 10.1117/1.JEI.33.4.043003.
18. Y. Zou, C. Yan, and Y. Fu, “Iterative Denoiser and Noise Estimator for Self-Supervised Image Denoising,” in 2023 IEEE/CVF International Conference on Computer Vision (ICCV), Paris, France: IEEE, Oct. 2023, pp. 13219–13228. doi: 10.1109/ICCV51070.2023.01220.
19. Y. Zhu and Y. Chen, “A new diffusion method for blind image denoising,” Pattern Anal. Appl., vol. 27, no. 4, p. 124, Dec. 2024, doi: 10.1007/s10044-024-01346-0.
20. T. Li, H. Feng, L. Wang, L. Zhu, Z. Xiong, and H. Huang, “Stimulating Diffusion Model for Image Denoising via Adaptive Embedding and Ensembling,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 46, no. 12, pp. 8240–8257, Dec. 2024, doi: 10.1109/TPAMI.2024.3432812.
21. B. Li, H. Zhao, W. Wang, P. Hu, Y. Gou, and X. Peng, “MaIR: A Locality-and Continuity-Preserving Mamba for Image Restoration,” in 2025 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), Nashville, TN, USA: IEEE, Jun. 2025, pp. 7491–7501. doi: 10.1109/CVPR52734.2025.00702.
22. S. Wang, C. Zhao, Q. Wang, M. Liu, C. Mou, and F. Xu, “Zero-shot image denoising with hollow pair sampling and noise-aware attention,” Pattern Recognit., vol. 167, p. 111779, Nov. 2025, doi: 10.1016/j.patcog.2025.111779.
23. J. Hu, L. Shen, and G. Sun, “Squeeze-and-Excitation Networks,” in 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition, Salt Lake City, UT: IEEE, Jun. 2018, pp. 7132–7141. doi: 10.1109/CVPR.2018.00745.
24. I. Sobel and G. Feldman, “A 3x3 Isotropic gradient operator for image processing,” Pattern Classif. Scene Anal., pp. 271–272, 1973.
25. K. He, X. Zhang, S. Ren, and J. Sun, “Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification,” in 2015 IEEE International Conference on Computer Vision (ICCV), Santiago, Chile: IEEE, Dec. 2015, pp. 1026–1034. doi: 10.1109/ICCV.2015.123.