Image Denoising Using Wavelet and Fractal Methods with Comparative Analysis

In this paper, we implemented image denoising using both wavelet and fractal methods, followed by a detailed comparative analysis of the results. For wavelet-based denoising, we typically employ discrete wavelet transform (DWT) decomposition using functions like wavedec2() in MATLAB, applying thresholding techniques (soft/hard thresholding) to wavelet coefficients at different decomposition levels to remove noise while preserving important image features. The fractal approach involves techniques like fractal coding and fractal dimension analysis, where we implement iterative algorithms to identify and enhance image patterns while suppressing random noise components. Our comparative results demonstrate that wavelet methods excel in overall noise reduction performance, particularly effective in handling Gaussian and additive noise through multi-resolution analysis. However, fractal methods show superior capability in preserving fine image details and texture characteristics, making them advantageous for images requiring high detail retention. The choice between these methods should be determined by specific image requirements: wavelet denoising is preferable for strong noise suppression, while fractal denoising is more suitable for detail-critical applications. Implementation considerations include computational complexity - wavelet methods generally offer faster processing, while fractal methods may require more iterative computations but provide better structural preservation.