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Image denoising is a fundamental challenge in image processing, where the objective is to remove noise while preserving critical image features. Traditional denoising methods, such as Wavelet, Total Variation (TV) minimization, and Non-Local Means (NLM), often struggle to maintain the topological integrity of image features, leading to the loss of essential structures. This study proposes a Cubical Persistent Homology-Based Technique (CPHBT) that leverages persistence barcodes to identify significant topological features and reduce noise. The method selects filtration levels that preserve important features like loops and connected components. Applied to digit images, our method demonstrates superior performance, achieving a Peak Signal-to-Noise Ratio (PSNR) of 46.88 and a Structural Similarity Index Measure (SSIM) of 0.99, outperforming TV (PSNR: 21.52, SSIM: 0.9812) and NLM (PSNR: 22.09, SSIM: 0.9822). These results confirm that cubical persistent homology offers an effective solution for image denoising by balancing noise reduction and preserving critical topological features, thus enhancing overall image quality.

Main Objective: This research targets AP sizing entrenched on image structure to raise denoising performance using an improved method for classifying image pixels. Background problem: Digital images may be blended by noise while the addition or communication process, affecting the authentic image signal. Image noise can cause problems at several stages of image processing equally image distribution. Accordingly, image denoising is a significant activity to recover the initial clean image signal from the detected noise signal. Novelty: The proposed WAV method has been refined and improved regarding the classification scheme, and the APS, and the classification results can be used as a mask on the noise image to fix identical patches. Research Method: This study proposes a WAV reprojection algorithm, with the PS being set dynamically entrenched on the image structure. Image structures are consistently taken with an upgraded and enhanced analysis method entrenched in the structure tensor matrix. Analysis results are also used to develop the analysis of comparable patches in images. Finding/Result: Empirical outcomes present that the noise cancellation work of the suggested method is better than the authentic WAVRA, along with several other modifications of the NLMA. Conclusion: In intensity profiles, the proposed method mostly has fewer changes to the original image values than other methods, thus, this method can be continued again to color images, and can also be applied to various types of data such as medical images.   Keywords: Weighted Average (WAV), Noise Cancellation Image, Non-Local Means (NLM), Adaptive Patch