Image Denoising Method Based on 3D Block Matching with Harmonic Filtering in Transform Domain

59 | International JournalofofInformatics Informatics Information System Computer Engineering (2026) 59-69 International Journal Information System andand Computer Engineering 7(1) 7(1) (2026) 59-69 International Journal of Informatics, Information System and Computer Engineering Image Denoising Method Based on 3D Block Matching with Harmonic Filtering in Transform Domain Mizanur Rashid*, Abdullah Ibne Sayed**, Md Masud Rana** * School of Electronics and Information Engineering, Nanjing University of Information Science and Technology, Nanjing, China ** Huazhong University of Science and Technology, Wuhan, China *Corresponding Email: ABSTRACTS Today, I will explain an image denoising method based on 3D block matching with harmonic filtering in the transform domain. This topic is important because digital images are susceptible to noise during acquisition, storage, and transmission. Image denoising is crucial in pre-processing and is a key research area in digital image processing and computer vision. Traditional denoising techniques face limitations such as high computational complexity, so combining multiple methods is more effective. The integration of wave-domain harmonic filtering and 3D block matching (BM3D) introduces a new and efficient denoising algorithm. The Euclidean distance approach is used to group similar 2D image blocks into a 3D array. The inverse transformation reconstructs the image, followed by wavelet decomposition to filter highfrequency noise. To prevent edge blurring, the Laplacian-Gaussian algorithm is applied to refine the diffusion model. Finally, wavelet reconstruction is performed to approximate the original image. Experimental results demonstrate that this approach improves information protection and processing speed, making it highly effective in practice. DOI: https://doi.org/10.34010/injiiscom.v7i1.15615 p-ISSN 2810-0670 e-ISSN 2775-5584 ARTICLE INFO Article History: Received 20 Feb 2025 Revised 01 Mar 2025 Accepted 19 Mar 2025 Available online 15 Apr 2025 Publication date 01 Jun 2026 Aug 2018 __________________ Keywords: Image denoising, Diffusion model, BM3D, Laplacian-Gaussian algorithm Mizanur et al. Image Denoising Method Based on 3D Block Matching with...| 60 1. INTRODUCTION As a common information carrier, digital images are widely used in many social fields such as cultural media, modern industry, military, medicine, agriculture and so on. However, digital images are susceptible to noise in the process of acquisition, storage and transmission. Therefore, image denoising has become an important method in the image pre-processing stage, and is also a recent research hotspot in the field of digital image processing and computer vision (Li & Zhao, 2013). Various researchers proposed a number of approach to deal with this issue before, here I go through some of the approaches starting with (Buades et al., 2005), he propose the idea of a nonlocal mean filter using Gaussian white noise in 2005, which is a denoising method to estimate the true image by weighted averaging of similar blocks between neighbourhoods. Later in (Dabov et al., 2007) combined the principles and advantages of NLM algorithm, wavelet transform and Wiener filtering, and proposed a threedimensional block matching image denoising algorithm (BM3D), At present, which is one of the most obvious algorithms, The high-frequency components obtained from the decomposing of the noise image in proposed by the authors are denoised by using the BM3D algorithm, and finally the wavelet reconstruction is performed, which greatly reduces the computational complexity. Prior to that in 2006, Hinton published a paper in Science, which showed the team’s research on deep learning (Hinton & Salakhutdinov, 2006), and then deep learning began to develop rapidly. In fact, deep learning was first DOI: https://doi.org/10.34010/injiiscom.v7i1.15615 p-ISSN 2810-0670 e-ISSN 2775-5584 tried in the field of image processing. A neural network model containing a convolutional layer, Convolutional Neural Network (CNN), was proposed by (LeCun, 1989) but this model did not greatly promote this field in image recognition when it was first born. Until 2012, Professor Hinton introduced the weight decay algorithm to optimize this algorithm. During the training process of the neural network, the weight range was better controlled to avoid over-fitting problems in the network. Deepen the network depth of the convolutional neural network (Krizhevsky et al., 2012), so, the convolutional neural network can be better applied to the field of image recognition. In 2015, Zhou et al. introduced a wave-domain harmonic denoising model for the edge information processing has given very good results (Xian-Xhun et al., 2015). The algorithms proposed by the above scholars all improve to some extent in the peak signal-to-noise ratio test, but they lack a balance in the running speed. Hence, a new method based on block matching collaborative filtering was proposed to estimate the noisy image processing, you can get the basic image estimates (Hwang & Haddad, 1995). Since the noise and the edge details of the image are mainly concentrated in the high frequency part of the image, the high frequency part of the pre-estimation image can be extracted by the wavelet decomposition, the edge blurring is caused by the transformation of the wave field, and the postreconstruction distortion of the image occurs, Laplacian algorithm (Elmoataz et al., 2012) is used to construct a new operator to bring into the diffusion model for image filtering, and then the final approximation of the image is obtained by wavelet reconstruction. 61 | International Journal of Informatics Information System and Computer Engineering 7(1) (2026) 59-69 2. IMAGE DENOISING BY MIXING 3D BLOCK MATCHING WITH HARMONIC FILTERING 2.1. BM3D algorithm This is an ideal denoising approach, that brings together the wavelet transform and local methods. Classed up into two: the initial denoising and final denoising (Elad et al., 2023; Fan et al., 2019). The initial de-noising uses orthogonally transformed windows of different sizes, and the hard threshold of the spectrum in these transforms means that in the approximate class Adaptive decline, and model order depends on the data. The most efficient adaptive sequence estimation is Discrete Cosine Transform (DCT) (Foi et al., 2007). The local estimate becomes nonlocal, when the Euclidean distance is used as a metric to find similar blocks of a reference block. The similar two-dimensional image blocks are combined into a threedimensional array matrix for joint filtering, then the three-dimensional array is inverse transformed and weighted averagely to eliminate overlapping parts of the image blocks to obtain the pre-estimation of the noisy image (Elmoataz et al., 2012). The final denoising step is to denoise twice based on the initial denoising. Image blocks are grouped again according to the similarities using (...truncated)