Implementation of Contourlet Transform with Enhanced Laplacian Pyramid Decomposition

When performing Laplacian pyramid decomposition in contourlet transform, the resulting bandpass images generate oscillations near singularity points, adversely affecting image denoising performance. To solve this problem, we propose an improved Laplacian pyramid decomposition method that eliminates oscillations near edges and optimizes the image denoising process. The enhanced approach utilizes more precise Laplacian pyramid decomposition techniques to achieve more accurate contourlet transform, while incorporating adaptive denoising algorithms. Key implementation aspects include: modifying the pyramid decomposition filters to reduce Gibbs phenomena, implementing directional filter banks with improved frequency partitioning, and developing thresholding schemes that adapt to contourlet coefficient statistics. Through experimental analysis, we demonstrate that this algorithm achieves significant improvement in peak signal-to-noise ratio (PSNR) compared to traditional contourlet transform adaptive denoising methods, along with substantial enhancement in visual quality.