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This article focuses on comparing the discriminating power of the various multi-resolution based thresholding techniques - wavelet, curvelet, and contourlet for image denoising. Using multiresolution techniques, mammogram images are decomposed into different resolution levels, which are sensitive to different frequency bands. We implement the proposed algorithm on the mammogram images embedded in Random, Salt and Pepper, Poisson, Speckle and Gaussian noises. Curvelet transform employed in the proposed scheme provides sparse decomposition as compared to the wavelet and contourlet transform methods. The curvelet transform has a strong directional character which combines multiscale analysis and ideas of geometry to achieve the optimal rate of convergence by simple thresholding. The proposed algorithm succeeded in providing improved denoising performance to recover the shape of edges and important detailed components. Empirical results proved that the curvelet-based thresholding can obtain a better image estimate than the wavelet- based and contourlet-based restoration methods.