A New SURE Approach to Image Denoising: Interscale Orthonormal Wavelet Thresholding

This paper introduces a new approach to orthonormal wavelet image denoising. Instead of postulating a statistical model for the wavelet coefficients, we directly parametrize the denoising process as a sum of elementary nonlinear processes with unknown weights. We then minimize an estimate of the mean square error between the clean image and the denoised one. The key point is that we have at our disposal a very accurate, statistically unbiased, MSE estimate--Stein's unbiased risk estimate--that depends on the noisy image alone, not on the clean one. Like the MSE, this estimate is quadratic in the unknown weights, and its minimization amounts to solving a linear system of equations. The existence of this a…

• NS
  National Science Foundation

  Award: 200020
• ÉP
  École Polytechnique Fédérale de Lausanne
• SN
  Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung

  Awards: 109415, 200020
• CD
  Centre d'Imagerie BioMédicale