MATLAB Implementation of Contourlet Transform with Image Denoising Algorithm

Below is a MATLAB code example demonstrating the Contourlet transform implementation with an integrated image denoising algorithm. This algorithm effectively removes noise from images while enhancing overall image quality through a systematic three-stage approach. The implementation begins by applying the Contourlet transform to the input image, decomposing it into multiple directional subbands at different scales. This multi-scale geometric decomposition captures image edges and contours more efficiently than traditional wavelet transforms. In the thresholding phase, the algorithm processes each subband using a predetermined threshold value. Coefficients below this threshold (typically representing noise components) are set to zero, while significant coefficients representing actual image features are preserved. This selective thresholding can be implemented using either hard or soft thresholding functions, with the threshold value often determined by noise variance estimation. The final reconstruction stage applies the inverse Contourlet transform to the thresholded subbands, synthesizing the denoised image. The algorithm utilizes the Contourlet toolbox's critical functions including: - pdfbdec() for forward transform decomposition - Threshoding functions for coefficient processing - pdfbrec() for inverse transform reconstruction This implementation demonstrates how Contourlet's directional sensitivity combined with appropriate thresholding strategies can produce clearer, more accurate images with preserved edge information. The code structure follows MATLAB's matrix operations efficiently, handling image data through proper normalization and boundary processing.